ECDSA bitFlyer USA

Rein - Decentralized Labor Market

Rein is an experiment in decentralized labor that combines Bitcoin multisig escrow, digital signatures, and an internet-like microhosting model to build an uncensorable labor market.
[link]

Technical: Confidential Transactions and Their Implementation Tradeoffs

As requested by estradata here: https://old.reddit.com/Bitcoin/comments/iylou9/what_are_some_of_the_latest_innovations_in_the/g6heez1/
It is a general issue that crops up at the extremes of cryptography, with quantum breaks being just one of the extremes of (classical) cryptography.

Computational vs Information-Theoretic

The dichotomy is between computationally infeasible vs informationally-theoretic infeasible. Basically:
Quantum breaks represent a possible reduction in computational infeasibility of certain things, but not information-theoretic infeasibility.
For example, suppose you want to know what 256-bit preimages map to 256-bit hashes. In theory, you just need to build a table with 2256 entries and start from 0x0000000000000000000000000000000000000000000000000000000000000000 and so on. This is computationally infeasible, but not information-theoretic infeasible.
However, suppose you want to know what preimages, of any size, map to 256-bit hashes. Since the preimages can be of any size, after finishing with 256-bit preimages, you have to proceed to 257-bit preimages. And so on. And there is no size limit, so you will literally never finish. Even if you lived forever, you would not complete it. This is information-theoretic infeasible.

Commitments

How does this relate to confidential transactions? Basically, every confidential transaction simply hides the value behind a homomorphic commitment. What is a homomorphic commitment? Okay, let's start with commitments. A commitment is something which lets you hide something, and later reveal what you hid. Until you reveal it, even if somebody has access to the commitment, they cannot reverse it to find out what you hid. This is called the "hiding property" of commitments. However, when you do reveal it (or "open the commitment"), then you cannot replace what you hid with some other thing. This is called the "binding property" of commitments.
For example, a hash of a preimage is a commitment. Suppose I want to commit to something. For example, I want to show that I can predict the future using the energy of a spare galaxy I have in my pocket. I can hide that something by hashing a description of the future. Then I can give the hash to you. You still cannot learn the future, because it's just a hash, and you can't reverse the hash ("hiding"). But suppose the future event occurs. I can reveal that I did, in fact, know the future. So I give you the description, and you hash it and compare it to the hash I gave earlier. Because of preimage resistance, I cannot retroactively change what I hid in the hash, so what I gave must have been known to me at the time that I gave you the commitment i..e. hash ("binding").

Homomorphic Commitments

A homomorphic commitment simply means that if I can do certain operations on preimages of the commitment scheme, there are certain operations on the commitments that would create similar ("homo") changes ("morphic") to the commitments. For example, suppose I have a magical function h() which is a homomorphic commitment scheme. It can hide very large (near 256-bit) numbers. Then if h() is homomorphic, there may be certain operations on numbers behind the h() that have homomorphisms after the h(). For example, I might have an operation <+> that is homomorphic in h() on +, or in other words, if I have two large numbers a and b, then h(a + b) = h(a) <+> h(b). + and <+> are different operations, but they are homomorphic to each other.
For example, elliptic curve scalars and points have homomorphic operations. Scalars (private keys) are "just" very large near-256-bit numbers, while points are a scalar times a standard generator point G. Elliptic curve operations exist where there is a <+> between points that is homomorphic on standard + on scalars, and a <*> between a scalar and a point that is homomorphic on standard * multiplication on scalars.
For example, suppose I have two large scalars a and b. I can use elliptic curve points as a commitment scheme: I can take a <*> G to generate a point A. It is hiding since nobody can learn what a is unless I reveal it (a and A can be used in standard ECDSA private-public key cryptography, with the scalar a as the private key and the point A as the public key, and the a cannot be derived even if somebody else knows A). Thus, it is hiding. At the same time, for a particular point A and standard generator point G, there is only one possible scalar a which when "multiplied" with G yields A. So scalars and elliptic curve points are a commitment scheme, with both hiding and binding properties.
Now, as mentioned there is a <+> operation on points that is homomorphic to the + operation on corresponding scalars. For example, suppose there are two scalars a and b. I can compute (a + b) <*> G to generate a particular point. But even if I don't know scalars a and b, but I do know points A = a <*> G and B = b <*> G, then I can use A <+> B to derive (a + b) <*> G (or equivalently, (a <*> G) <+> (b <*> G) == (a + b) <*> G). This makes points a homomorphic commitment scheme on scalars.

Confidential Transactions: A Sketch

This is useful since we can easily use the near-256-bit scalars in SECP256K1 elliptic curves to easily represent values in a monetary system, and hide those values by using a homomorphic commitment scheme. We can use the hiding property to prevent people from learning the values of the money we are sending and receiving.
Now, in a proper cryptocurrency, a normal, non-coinbase transaction does not create or destroy coins: the values of the input coins are equal to the value of the output coins. We can use a homomorphic commitment scheme. Suppose I have a transaction that consumes an input value a and creates two output values b and c. That is, a = b + c, i.e. the sum of all inputs a equals the sum of all outputs b and c. But remember, with a homomorphic commitment scheme like elliptic curve points, there exists a <+> operation on points that is homomorphic to the ordinary school-arithmetic + addition on large numbers. So, confidential transactions can use points a <*> G as input, and points b <*> G and c <*> G as output, and we can easily prove that a <*> G = (b <*> G) <+> (c <*> G) if a = b + c, without revealing a, b, or c to anyone.

Pedersen Commitments

Actually, we cannot just use a <*> G as a commitment scheme in practice. Remember, Bitcoin has a cap on the number of satoshis ever to be created, and it's less than 253 satoshis, which is fairly trivial. I can easily compute all values of a <*> G for all values of a from 0 to 253 and know which a <*> G corresponds to which actual amount a. So in confidential transactions, we cannot naively use a <*> G commitments, we need Pedersen commitments.
If you know what a "salt" is, then Pedersen commitments are fairly obvious. A "salt" is something you add to e.g. a password so that the hash of the password is much harder to attack. Humans are idiots and when asked to generate passwords, will output a password that takes less than 230 possibilities, which is fairly easy to grind. So what you do is that you "salt" a password by prepending a random string to it. You then hash the random string + password, and store the random string --- the salt --- together with the hash in your database. Then when somebody logs in, you take the password, prepend the salt, hash, and check if the hash matches with the in-database hash, and you let them log in. Now, with a hash, even if somebody copies your password database, the can't get the password. They're hashed. But with a salt, even techniques like rainbow tables make a hacker's life even harder. They can't hash a possible password and check every hash in your db for something that matches. Instead, if they get a possible password, they have to prepend each salt, hash, then compare. That greatly increases the computational needs of a hacker, which is why salts are good.
What a Pedersen commitment is, is a point a <*> H, where a is the actual value you commit to, plus <+> another point r <*> G. H here is a second standard generator point, different from G. The r is the salt in the Pedersen commitment. It makes it so that even if you show (a <*> H) <+> (r <*> G) to somebody, they can't grind all possible values of a and try to match it with your point --- they also have to grind r (just as with the password-salt example above). And r is much larger, it can be a true near-256-bit number that is the range of scalars in SECP256K1, whereas a is constrained to "reasonable" numbers of satoshi, which cannot exceed 21 million Bitcoins.
Now, in order to validate a transaction with input a and outputs b and c, you only have to prove a = b + c. Suppose we are hiding those amounts using Pedersen commitments. You have an input of amount a, and you know a and r. The blockchain has an amount (a <*> H) <+> (r <*> G). In order to create the two outputs b and c, you just have to create two new r scalars such that r = r[0] + r[1]. This is trivial, you just select a new random r[0] and then compute r[1] = r - r[0], it's just basic algebra.
Then you create a transaction consuming the input (a <*> H) <+> (r <*> G) and outputs (b <*> H) <+> (r[0] <*> G) and (c <*> H) <+> (r[1] <*> G). You know that a = b + c, and r = r[0] + r[1], while fullnodes around the world, who don't know any of the amounts or scalars involved, can just take the points (a <*> H) <+> (r <*> G) and see if it equals (b <*> H) <+> (r[0] <*> G) <+> (c <*> H) <+> (r[1] <*> G). That is all that fullnodes have to validate, they just need to perform <+> operations on points and comparison on points, and from there they validate transactions, all without knowing the actual values involved.

Computational Binding, Information-Theoretic Hiding

Like all commitments, Pedersen Commitments are binding and hiding.
However, there are really two kinds of commitments:
What does this mean? It's just a measure of how "impossible" binding vs hiding is. Pedersen commitments are computationally binding, meaning that in theory, a user of this commitment with arbitrary time and space and energy can, in theory, replace the amount with something else. However, it is information-theoretic hiding, meaning an attacker with arbitrary time and space and energy cannot figure out exactly what got hidden behind the commitment.
But why?
Now, we have been using a and a <*> G as private keys and public keys in ECDSA and Schnorr. There is an operation <*> on a scalar and a point that generates another point, but we cannot "revrese" this operation. For example, even if I know A, and know that A = a <*> G, but do not know a, I cannot derive a --- there is no operation between A G that lets me know a.
Actually there is: I "just" need to have so much time, space, and energy that I just start counting a from 0 to 2256 and find which a results in A = a <*> G. This is a computational limit: I don't have a spare universe in my back pocket I can use to do all those computations.
Now, replace a with h and A with H. Remember that Pedersen commitments use a "second" standard generator point. The generator points G and H are "not really special" --- they are just random points on the curve that we selected and standardized. There is no operation H G such that I can learn h where H = h <*> G, though if I happen to have a spare universe in my back pocket I can "just" brute force it.
Suppose I do have a spare universe in my back pocket, and learn h = H G such that H = h <*> G. What can I do in Pedersen commitments?
Well, I have an amount a that is committed to by (a <*> H) <+> (r <*> G). But I happen to know h! Suppose I want to double my money a without involving Elon Musk. Then:
That is what we mean by computationally binding: if I can compute h such that H = h <*> G, then I can find another number which opens the same commitment. And of course I'd make sure that number is much larger than what I originally had in that address!
Now, the reason why it is "only" computationally binding is that it is information-theoretically hiding. Suppose somebody knows h, but has no money in the cryptocurrency. All they see are points. They can try to find what the original amounts are, but because any amount can be mapped to "the same" point with knowledge of h (e.g. in the above, a and 2 * a got mapped to the same point by "just" replacing the salt r with r - a * h; this can be done for 3 * a, 4 * a etc.), they cannot learn historical amounts --- the a in historical amounts could be anything.
The drawback, though, is that --- as seen above --- arbitrary inflation is now introduced once somebody knows h. They can multiply their money by any arbitrary factor with knowledge of h.
It is impossible to have both perfect hiding (i.e. historical amounts remain hidden even after a computational break) and perfect binding (i.e. you can't later open the commitment to a different, much larger, amount).
Pedersen commitments just happen to have perfect hiding, but only computationally-infeasible binding. This means they allow hiding historical values, but in case of anything that allows better computational power --- including but not limited to quantum breaks --- they allow arbitrary inflation.

Changing The Tradeoffs with ElGamal Commitments

An ElGamal commitment is just a Pedersen commitment, but with the point r <*> G also stored in a separate section of the transaction.
This commits the r, and fixes it to a specific value. This prevents me from opening my (a <*> H) <+> (r <*> G) as ((2 * a) <*> H) <+> ((r - a * h) <*> G), because the (r - a * h) would not match the r <*> G sitting in a separate section of the transaction. This forces me to be bound to that specific value, and no amount of computation power will let me escape --- it is information-theoretically binding i.e. perfectly binding.
But that is now computationally hiding. An evil surveillor with arbitrary time and space can focus on the r <*> G sitting in a separate section of the transaction, and grind r from 0 to 2256 to determine what r matches that point. Then from there, they can negate r to get (-r) <*> G and add it to the (a <*> H) <+> (r <*> G) to get a <*> H, and then grind that to determine the value a. With massive increases in computational ability --- including but not limited to quantum breaks --- an evil surveillor can see all the historical amounts of confidential transactions.

Conclusion

This is the source of the tradeoff: either you design confidential transactions so in case of a quantum break, historical transactions continue to hide their amounts, but inflation of the money is now unavoidable, OR you make the money supply sacrosanct, but you potentially sacrifice amount hiding in case of some break, including but not limited to quantum breaks.
submitted by almkglor to Bitcoin [link] [comments]

Why is Bitcoin secure? Answer: it has very little to do with decentralization.

ECDSA can be broken, with enough computational power applied to the problem over time, for a single keypair.
If you use a new keypair for each transaction, it makes this attack exponentially hard for an attacker. Knowing the details of the RNG, makes it even easier.
In reality, there is no such thing as a true random number generator. That is the main flaw in elliptic curve cryptography. You can make it really hard, but you can never make it computationally impossible.
The security mechanism of bitcoin, is that it constantly moves, taking the goalpoasts with it. So all the work you might have done to break a single kepair, is immediately invalidated, by the utxo model, when those coins now are controlled by a new keypair. The attacker has to start over, from the beginning.
Velocity is important, in this security model. Which is why those who think an account based model on this system are ultimately doomed.
Cryptographic functions create a difficult, but not impossible problem.
Constant creation of new problems makes this a hard problem for attackers.
Store of value bullshit. Where you store bitcoin for years, and consolidate all your bitcoin into a single UTXO. If you are not using your bitcoin, you are opening yourself up to attack.
submitted by m_murfy to bitcoincashSV [link] [comments]

Thanks to all who submitted questions for Shiv Malik in the GAINS AMA yesterday, it was great to see so much interest in Data Unions! You can read the full transcript here:

Thanks to all who submitted questions for Shiv Malik in the GAINS AMA yesterday, it was great to see so much interest in Data Unions! You can read the full transcript here:

Gains x Streamr AMA Recap

https://preview.redd.it/o74jlxia8im51.png?width=1236&format=png&auto=webp&s=93eb37a3c9ed31dc3bf31c91295c6ee32e1582be
Thanks to everyone in our community who attended the GAINS AMA yesterday with, Shiv Malik. We were excited to see that so many people attended and gladly overwhelmed by the amount of questions we got from you on Twitter and Telegram. We decided to do a little recap of the session for anyone who missed it, and to archive some points we haven’t previously discussed with our community. Happy reading and thanks to Alexandre and Henry for having us on their channel!
What is the project about in a few simple sentences?
At Streamr we are building a real-time network for tomorrow’s data economy. It’s a decentralized, peer-to-peer network which we are hoping will one day replace centralized message brokers like Amazon’s AWS services. On top of that one of the things I’m most excited about are Data Unions. With Data Unions anyone can join the data economy and start monetizing the data they already produce. Streamr’s Data Union framework provides a really easy way for devs to start building their own data unions and can also be easily integrated into any existing apps.
Okay, sounds interesting. Do you have a concrete example you could give us to make it easier to understand?
The best example of a Data Union is the first one that has been built out of our stack. It's called Swash and it's a browser plugin.
You can download it here: http://swashapp.io/
And basically it helps you monetize the data you already generate (day in day out) as you browse the web. It's the sort of data that Google already knows about you. But this way, with Swash, you can actually monetize it yourself. The more people that join the union, the more powerful it becomes and the greater the rewards are for everyone as the data product sells to potential buyers.
Very interesting. What stage is the project/product at? It's live, right?
Yes. It's live. And the Data Union framework is in public beta. The Network is on course to be fully decentralized at some point next year.
How much can a regular person browsing the Internet expect to make for example?
So that's a great question. The answer is no one quite knows yet. We do know that this sort of data (consumer insights) is worth hundreds of millions and really isn't available in high quality. So With a union of a few million people, everyone could be getting 20-50 dollars a year. But it'll take a few years at least to realise that growth. Of course Swash is just one data union amongst many possible others (which are now starting to get built out on our platform!)
With Swash, I believe they now have 3,000 members. They need to get to 50,000 before they become really viable but they are yet to do any marketing. So all that is organic growth.
I assume the data is anonymized btw?
Yes. And there in fact a few privacy protecting tools Swash supplys to its users.
How does Swash compare to Brave?
So Brave really is about consent for people's attention and getting paid for that. They don't sell your data as such.
Swash can of course be a plugin with Brave and therefore you can make passive income browsing the internet. Whilst also then consenting to advertising if you so want to earn BAT.
Of course it's Streamr that is powering Swash. And we're looking at powering other DUs - say for example mobile applications.
The holy grail might be having already existing apps and platforms out there, integrating DU tech into their apps so people can consent (or not) to having their data sold - and then getting a cut of that revenue when it does sell.
The other thing to recognise is that the big tech companies monopolise data on a vast scale - data that we of course produce for them. That is stifling innovation.
Take for example a competitor map app. To effectively compete with Google maps or Waze, they need millions of users feeding real time data into it.
Without that - it's like Google maps used to be - static and a bit useless.
Right, so how do you convince these big tech companies that are producing these big apps to integrate with Streamr? Does it mean they wouldn't be able to monetize data as well on their end if it becomes more available through an aggregation of individuals?
If a map application does manage to scale to that level then inevitably Google buys them out - that's what happened with Waze.
But if you have a data union which bundles together the raw location data of millions of people then any application builder can come along and license that data for their app. This encourages all sorts of innovation and breaks the monopoly.
We're currently having conversations with Mobile Network operators to see if they want to pilot this new approach to data monetization. And that's what even more exciting. Just be explicit with users - do you want to sell your data? Okay, if yes, then which data point do you want to sell.
Then the mobile network operator (like T-mobile for example) then organises the sale of the data of those who consent and everyone gets a cut.
Streamr - in this example provides the backend to port and bundle the data, and also the token and payment rail for the payments.
So for big companies (mobile operators in this case), it's less logistics, handing over the implementation to you, and simply taking a cut?
It's a vision that we'll be able to talk more about more concretely in a few weeks time 😁
Compared to having to make sense of that data themselves (in the past) and selling it themselves
Sort of.
We provide the backened to port the data and the template smart contracts to distribute the payments.
They get to focus on finding buyers for the data and ensuring that the data that is being collected from the app is the kind of data that is valuable and useful to the world.
(Through our sister company TX, we also help build out the applications for them and ensure a smooth integration).
The other thing to add is that the reason why this vision is working, is that the current data economy is under attack. Not just from privacy laws such as GDPR, but also from Google shutting down cookies, bidstream data being investigated by the FTC (for example) and Apple making changes to IoS14 to make third party data sharing more explicit for users.
All this means that the only real places for thousands of multinationals to buy the sort of consumer insights they need to ensure good business decisions will be owned by Google/FB etc, or from SDKs or through this method - from overt, rich, consent from the consumer in return for a cut of the earnings.
A couple of questions to get a better feel about Streamr as a whole now and where it came from. How many people are in the team? For how long have you been working on Streamr?
We are around 35 people with one office in Zug, Switzerland and another one in Helsinki. But there are team members all over the globe, we’ve people in the US, Spain, the UK, Germany, Poland, Australia and Singapore. I joined Streamr back in 2017 during the ICO craze (but not for that reason!)
And did you raise funds so far? If so, how did you handle them? Are you planning to do any future raises?
We did an ICO back in Sept/Oct 2017 in which we raised around 30 Millions CHF. The funds give us enough runway for around five/six years to finalize our roadmap. We’ve also simultaneously opened up a sister company consultancy business, TX which helps enterprise clients implementing the Streamr stack. We've got no more plans to raise more!
What is the token use case? How did you make sure it captures the value of the ecosystem you're building
The token is used for payments on the Marketplace (such as for Data Union products for example) also for the broker nodes in the Network. ( we haven't talked much about the P2P network but it's our project's secret sauce).
The broker nodes will be paid in DATAcoin for providing bandwidth. We are currently working together with Blockscience on our tokeneconomics. We’ve just started the second phase in their consultancy process and will be soon able to share more on the Streamr Network’s tokeneconoimcs.
But if you want to summate the Network in a sentence or two - imagine the Bittorrent network being run by nodes who get paid to do so. Except that instead of passing around static files, it's realtime data streams.
That of course means it's really well suited for the IoT economy.
Well, let's continue with questions from Twitter and this one comes at the perfect time. Can Streamr Network be used to transfer data from IOT devices? Is the network bandwidth sufficient? How is it possible to monetize the received data from a huge number of IOT devices? From u/ EgorCypto
Yes, IoT devices are a perfect use case for the Network. When it comes to the network’s bandwidth and speed - the Streamr team just recently did extensive research to find out how well the network scales.
The result was that it is on par with centralized solutions. We ran experiments with network sizes between 32 to 2048 nodes and in the largest network of 2048 nodes, 99% of deliveries happened within 362 ms globally.
To put these results in context, PubNub, a centralized message brokering service, promises to deliver messages within 250 ms — and that’s a centralized service! So we're super happy with those results.
Here's a link to the paper:
https://medium.com/streamrblog/streamr-network-performance-and-scalability-whitepaper-adb461edd002
While we're on the technical side, second question from Twitter: Can you be sure that valuable data is safe and not shared with service providers? Are you using any encryption methods? From u/ CryptoMatvey
Yes, the messages in the Network are encrypted. Currently all nodes are still run by the Streamr team. This will change in the Brubeck release - our last milestone on the roadmap - when end-to-end encryption is added. This release adds end-to-end encryption and automatic key exchange mechanisms, ensuring that node operators can not access any confidential data.
If BTW - you want to get very technical the encryption algorithms we are using are: AES (AES-256-CTR) for encryption of data payloads, RSA (PKCS #1) for securely exchanging the AES keys and ECDSA (secp256k1) for data signing (same as Bitcoin and Ethereum).
Last question from Twitter, less technical now :) In their AMA ad, they say that Streamr has three unions, Swash, Tracey and MyDiem. Why does Tracey help fisherfolk in the Philippines monetize their catch data? Do they only work with this country or do they plan to expand? From u/ alej_pacedo
So yes, Tracey is one of the first Data Unions on top of the Streamr stack. Currently we are working together with the WWF-Philippines and the UnionBank of the Philippines on doing a first pilot with local fishing communities in the Philippines.
WWF is interested in the catch data to protect wildlife and make sure that no overfishing happens. And at the same time the fisherfolk are incentivized to record their catch data by being able to access micro loans from banks, which in turn helps them make their business more profitable.
So far, we have lots of interest from other places in South East Asia which would like to use Tracey, too. In fact TX have already had explicit interest in building out the use cases in other countries and not just for sea-food tracking, but also for many other agricultural products.
(I think they had a call this week about a use case involving cows 😂)
I recall late last year, that the Streamr Data Union framework was launched into private beta, now public beta was recently released. What are the differences? Any added new features? By u/ Idee02
The main difference will be that the DU 2.0 release will be more reliable and also more transparent since the sidechain we are using for micropayments is also now based on blockchain consensus (PoA).
Are there plans in the pipeline for Streamr to focus on the consumer-facing products themselves or will the emphasis be on the further development of the underlying engine?by u/ Andromedamin
We're all about what's under the hood. We want third party devs to take on the challenge of building the consumer facing apps. We know it would be foolish to try and do it all!
As a project how do you consider the progress of the project to fully developed (in % of progress plz) by u/ Hash2T
We're about 60% through I reckon!
What tools does Streamr offer developers so that they can create their own DApps and monetize data?What is Streamr Architecture? How do the Ethereum blockchain and the Streamr network and Streamr Core applications interact? By u/ CryptoDurden
We'll be releasing the Data UNion framework in a few weeks from now and I think DApp builders will be impressed with what they find.
We all know that Blockchain has many disadvantages as well,
So why did Streamr choose blockchain as a combination for its technology?
What's your plan to merge Blockchain with your technologies to make it safer and more convenient for your users? By u/ noonecanstopme
So we're not a blockchain ourselves - that's important to note. The P2P network only uses BC tech for the payments. Why on earth for example would you want to store every single piece of info on a blockchain. You should only store what you want to store. And that should probably happen off chain.
So we think we got the mix right there.
What were the requirements needed for node setup ? by u/ John097
Good q - we're still working on that but those specs will be out in the next release.
How does the STREAMR team ensure good data is entered into the blockchain by participants? By u/ kartika84
Another great Q there! From the product buying end, this will be done by reputation. But ensuring the quality of the data as it passes through the network - if that is what you also mean - is all about getting the architecture right. In a decentralised network, that's not easy as data points in streams have to arrive in the right order. It's one of the biggest challenges but we think we're solving it in a really decentralised way.
What are the requirements for integrating applications with Data Union? What role does the DATA token play in this case? By u/ JP_Morgan_Chase
There are no specific requirements as such, just that your application needs to generate some kind of real-time data. Data Union members and administrators are both paid in DATA by data buyers coming from the Streamr marketplace.
Regarding security and legality, how does STREAMR guarantee that the data uploaded by a given user belongs to him and he can monetize and capitalize on it? By u/ kherrera22
So that's a sort of million dollar question for anyone involved in a digital industry. Within our system there are ways of ensuring that but in the end the negotiation of data licensing will still, in many ways be done human to human and via legal licenses rather than smart contracts. at least when it comes to sizeable data products. There are more answers to this but it's a long one!
Okay thank you all for all of those!
The AMA took place in the GAINS Telegram group 10/09/20. Answers by Shiv Malik.
submitted by thamilton5 to streamr [link] [comments]

ECDSA In Bitcoin

Digital signatures are considered the foundation of online sovereignty. The advent of public-key cryptography in 1976 paved the way for the creation of a global communications tool – the Internet, and a completely new form of money – Bitcoin. Although the fundamental properties of public-key cryptography have not changed much since then, dozens of different open-source digital signature schemes are now available to cryptographers.

How ECDSA was incorporated into Bitcoin

When Satoshi Nakamoto, a mystical founder of the first crypto, started working on Bitcoin, one of the key points was to select the signature schemes for an open and public financial system. The requirements were clear. An algorithm should have been widely used, understandable, safe enough, easy, and, what is more important, open-sourced.
Of all the options available at that time, he chose the one that met these criteria: Elliptic Curve Digital Signature Algorithm, or ECDSA.
At that time, native support for ECDSA was provided in OpenSSL, an open set of encryption tools developed by experienced cipher banks in order to increase the confidentiality of online communications. Compared to other popular schemes, ECDSA had such advantages as:
These are extremely useful features for digital money. At the same time, it provides a proportional level of security: for example, a 256-bit ECDSA key has the same level of security as a 3072-bit RSA key (Rivest, Shamir и Adleman) with a significantly smaller key size.

Basic principles of ECDSA

ECDSA is a process that uses elliptic curves and finite fields to “sign” data in such a way that third parties can easily verify the authenticity of the signature, but the signer himself reserves the exclusive opportunity to create signatures. In the case of Bitcoin, the “data” that is signed is a transaction that transfers ownership of bitcoins.
ECDSA has two separate procedures for signing and verifying. Each procedure is an algorithm consisting of several arithmetic operations. The signature algorithm uses the private key, and the verification algorithm uses only the public key.
To use ECDSA, such protocol as Bitcoin must fix a set of parameters for the elliptic curve and its finite field, so that all users of the protocol know and apply these parameters. Otherwise, everyone will solve their own equations, which will not converge with each other, and they will never agree on anything.
For all these parameters, Bitcoin uses very, very large (well, awesomely incredibly huge) numbers. It is important. In fact, all practical applications of ECDSA use huge numbers. After all, the security of this algorithm relies on the fact that these values are too large to pick up a key with a simple brute force. The 384-bit ECDSA key is considered safe enough for the NSA's most secretive government service (USA).

Replacement of ECDSA

Thanks to the hard work done by Peter Wuille (a famous cryptography specialist) and his colleagues on an improved elliptical curve called secp256k1, Bitcoin's ECDSA has become even faster and more efficient. However, ECDSA still has some shortcomings, which can serve as a sufficient basis for its complete replacement. After several years of research and experimentation, a new signature scheme was established to increase the confidentiality and efficiency of Bitcoin transactions: Schnorr's digital signature scheme.
Schnorr's signature takes the process of using “keys” to a new level. It takes only 64 bytes when it gets into the block, which reduces the space occupied by transactions by 4%. Since transactions with the Schnorr signature are the same size, this makes it possible to pre-calculate the total size of the part of the block that contains such signatures. A preliminary calculation of the block size is the key to its safe increase in the future.
Keep up with the news of the crypto world at CoinJoy.io Follow us on Twitter and Medium. Subscribe to our YouTube channel. Join our Telegram channel. For any inquiries mail us at [[email protected]](mailto:[email protected]).
submitted by CoinjoyAssistant to btc [link] [comments]

tBTC an erc20 wrapped version of BTC, like erc20 wBTC; but is trustless and does not require a centralised party to mint wrapped btc like wBTC

I found this article on /Ethereum though it didnt go into the specs of how this works:
https://np.reddit.com/ethereum/comments/ftqdna/bitcoin_to_ethereum_bridge_raises_77_million_in/
https://decrypt.co/24336/bitcoin-to-ethereum-bridge-raises-7-7-million-in-token-sale?utm_source=reddit&utm_medium=social&utm_campaign=sm
as the article says wrapped bitcoin has been done before e.g. wBTC but wBTC requires a centralised party to mint wBTC from BTC held by this party; making it out of the question as its centralised.
did some digging there is a whitepaper , but i wanted more details on the tBTC implementation.
I went on their github and looked at the readme on some projects; found a few interesting things, though not an entire explanation.
https://github.com/keep-network/tbtc
tBTC is a trustlessly Bitcoin-backed ERC-20 token.
The goal of the project is to provide a stronger 2-way peg than federated sidechains like Liquid, expanding use cases possible via today’s Bitcoin network, while bringing superior money to other chains.
This repo contains the Solidity smart contracts and specification.
https://github.com/keep-network/tbtc
tbtc.js provides JS bindings to the tBTC system. The tBTC system is a bonded, multi-federated peg made up of many deposits backed by single-use BTC wallets to enable their value’s corresponding usage on the Ethereum chain, primarily through the minting of a TBTC ERC20 token whose supply is guaranteed to be backed by at least 1 BTC per TBTC in circulation.
finally this is the best:
https://tbtc.network/developers/tbtc-technical-system-overview
here is the first few pargarphs
2020-04-01 tBTC incorporates novel design features that carry important implications for users. This piece explains four of these: TDT receipts, multiple lot sizes, Keep's random beacon, and threshold signatures.
TBTC Deposit Token (TDT) The TBTC Deposit Token (TDT) is a non-fungible token that is minted when a user requests a deposit. A TDT is a non-fungible ERC-721 token that serves as a counterpart to TBTC. It represents a claim to a deposit's underlying UTXO on the Bitcoin blockchain.
TBTC deposits can be locked or unlocked. A locked deposit can only be redeemed by the deposit owner with the corresponding TDT. Each TDT is unique to the deposit that mints it and carries the exclusive right for up to a 6 month term to redeem the deposit.
also this paragraph addresses creating wallets with the created tokens
Random Beacon for Signer Selection
The Keep network requires a trusted source of randomness to select tBTC signers. This takes the form of a BLS Threshold Relay.
When a request comes in to create a signing group, the tBTC system uses a random seed from a secure decentralized random beacon to randomly select signing group members from the eligible pool of signers. These signers coordinate a distributed key generation protocol that results in a public ECDSA key for the group, which is used to produce a wallet address that is then published to the host chain. This completes the signer selection phase.
my take away from this is that by using side chains that a trustless, not fedeared like liquid bitcoin sidechains sold by blockstream. it uses NFT erc-721 tokens as representation of the bitccoin UTXO from the bitcoin blockchain, store it in a wallet and mint it into tBTC. given this is all smart contracts generating wallets and minting the tBTC, it does away with the need of a centralised party to provide the funds of BTC to create a wrapped erc20 version on ethereum and so should be trustles.
perhaps erc20 token trading is the way to go forward. just requires wrapping of exisitng tokens. this looks promising for DeXs and DeFi if it happens.
also opens the possibiliy of multicollateral Dai (MCD) using tBTC in addition to eth and BAT. though personally i think btc should not be used in MCD.
any thoughts on this? or if my understanding is off.
thanks
edit: got some more info from px403
I talked to James a bit about tBTC in Osaka, so I have a vague idea of how it works, so I might be able to explain it in a somewhat coherent way.
Basically, the magic here is they reimplemented Bitcoin's SPV as an Ethereum smart contract, effectively letting them query the current state of the Bitcoin network, including validity of payments, directly in contract. Using this, they built an auction system where people can at any time claim ETH by paying BTC, or claim BTC by paying ETH. By design the spread is wide, so this isn't actually intended to be a high volume exchange, but what you do get is a pretty good price oracle.
From the price oracle, I think there were doing some Maker style CDPs or something, where people could lock up their BTC on the Bitcoin network to redeem tBTC, and any of the locked BTC could be reclaimed by burning tBTC or something.
Sorry it's not a complete picture of what's going on, but I think that's the general gist of what they're doing.
submitted by Neophyte- to CryptoTechnology [link] [comments]

k value in ECDSA

Hello,

In ECDSA, I always understood the `k` value to be used to ensure non-deterministic signature.
(am I correct in this understanding?)
What I learned today surprised me. Apparently `k` must be kept completely secret, as important as the private key!

If `k` is leaked, one can determine the private key in ECDSA, am I interpreting this correctly? I always thought nonces were ok to disclose.

I know in Bitcoin usage, signatures are deterministic as `k` is calculated from the message and private key, however, what if one is signing the same message payload with the same private key, surely this occurs and would also leak the private key?

Does EdDSA suffer the same? It doesn't seem to have a `k` value?
submitted by anonXMR to crypto [link] [comments]

ECDSA In Bitcoin

Digital signatures are considered the foundation of online sovereignty. The advent of public-key cryptography in 1976 paved the way for the creation of a global communications tool – the Internet, and a completely new form of money – Bitcoin. Although the fundamental properties of public-key cryptography have not changed much since then, dozens of different open-source digital signature schemes are now available to cryptographers.

How ECDSA was incorporated into Bitcoin

When Satoshi Nakamoto, a mystical founder of the first crypto, started working on Bitcoin, one of the key points was to select the signature schemes for an open and public financial system. The requirements were clear. An algorithm should have been widely used, understandable, safe enough, easy, and, what is more important, open-sourced.
Of all the options available at that time, he chose the one that met these criteria: Elliptic Curve Digital Signature Algorithm, or ECDSA.
At that time, native support for ECDSA was provided in OpenSSL, an open set of encryption tools developed by experienced cipher banks in order to increase the confidentiality of online communications. Compared to other popular schemes, ECDSA had such advantages as:
These are extremely useful features for digital money. At the same time, it provides a proportional level of security: for example, a 256-bit ECDSA key has the same level of security as a 3072-bit RSA key (Rivest, Shamir и Adleman) with a significantly smaller key size.

Basic principles of ECDSA

ECDSA is a process that uses elliptic curves and finite fields to “sign” data in such a way that third parties can easily verify the authenticity of the signature, but the signer himself reserves the exclusive opportunity to create signatures. In the case of Bitcoin, the “data” that is signed is a transaction that transfers ownership of bitcoins.
ECDSA has two separate procedures for signing and verifying. Each procedure is an algorithm consisting of several arithmetic operations. The signature algorithm uses the private key, and the verification algorithm uses only the public key.
To use ECDSA, such protocol as Bitcoin must fix a set of parameters for the elliptic curve and its finite field, so that all users of the protocol know and apply these parameters. Otherwise, everyone will solve their own equations, which will not converge with each other, and they will never agree on anything.
For all these parameters, Bitcoin uses very, very large (well, awesomely incredibly huge) numbers. It is important. In fact, all practical applications of ECDSA use huge numbers. After all, the security of this algorithm relies on the fact that these values are too large to pick up a key with a simple brute force. The 384-bit ECDSA key is considered safe enough for the NSA's most secretive government service (USA).

Replacement of ECDSA

Thanks to the hard work done by Peter Wuille (a famous cryptography specialist) and his colleagues on an improved elliptical curve called secp256k1, Bitcoin's ECDSA has become even faster and more efficient. However, ECDSA still has some shortcomings, which can serve as a sufficient basis for its complete replacement. After several years of research and experimentation, a new signature scheme was established to increase the confidentiality and efficiency of Bitcoin transactions: Schnorr's digital signature scheme.
Schnorr's signature takes the process of using “keys” to a new level. It takes only 64 bytes when it gets into the block, which reduces the space occupied by transactions by 4%. Since transactions with the Schnorr signature are the same size, this makes it possible to pre-calculate the total size of the part of the block that contains such signatures. A preliminary calculation of the block size is the key to its safe increase in the future.
Keep up with the news of the crypto world at CoinJoy.io Follow us on Twitter and Medium. Subscribe to our YouTube channel. Join our Telegram channel. For any inquiries mail us at [[email protected]](mailto:[email protected]).
submitted by CoinjoyAssistant to Bitcoin [link] [comments]

Bitcoin (BTC)A Peer-to-Peer Electronic Cash System.

Bitcoin (BTC)A Peer-to-Peer Electronic Cash System.
  • Bitcoin (BTC) is a peer-to-peer cryptocurrency that aims to function as a means of exchange that is independent of any central authority. BTC can be transferred electronically in a secure, verifiable, and immutable way.
  • Launched in 2009, BTC is the first virtual currency to solve the double-spending issue by timestamping transactions before broadcasting them to all of the nodes in the Bitcoin network. The Bitcoin Protocol offered a solution to the Byzantine Generals’ Problem with a blockchain network structure, a notion first created by Stuart Haber and W. Scott Stornetta in 1991.
  • Bitcoin’s whitepaper was published pseudonymously in 2008 by an individual, or a group, with the pseudonym “Satoshi Nakamoto”, whose underlying identity has still not been verified.
  • The Bitcoin protocol uses an SHA-256d-based Proof-of-Work (PoW) algorithm to reach network consensus. Its network has a target block time of 10 minutes and a maximum supply of 21 million tokens, with a decaying token emission rate. To prevent fluctuation of the block time, the network’s block difficulty is re-adjusted through an algorithm based on the past 2016 block times.
  • With a block size limit capped at 1 megabyte, the Bitcoin Protocol has supported both the Lightning Network, a second-layer infrastructure for payment channels, and Segregated Witness, a soft-fork to increase the number of transactions on a block, as solutions to network scalability.

https://preview.redd.it/s2gmpmeze3151.png?width=256&format=png&auto=webp&s=9759910dd3c4a15b83f55b827d1899fb2fdd3de1

1. What is Bitcoin (BTC)?

  • Bitcoin is a peer-to-peer cryptocurrency that aims to function as a means of exchange and is independent of any central authority. Bitcoins are transferred electronically in a secure, verifiable, and immutable way.
  • Network validators, whom are often referred to as miners, participate in the SHA-256d-based Proof-of-Work consensus mechanism to determine the next global state of the blockchain.
  • The Bitcoin protocol has a target block time of 10 minutes, and a maximum supply of 21 million tokens. The only way new bitcoins can be produced is when a block producer generates a new valid block.
  • The protocol has a token emission rate that halves every 210,000 blocks, or approximately every 4 years.
  • Unlike public blockchain infrastructures supporting the development of decentralized applications (Ethereum), the Bitcoin protocol is primarily used only for payments, and has only very limited support for smart contract-like functionalities (Bitcoin “Script” is mostly used to create certain conditions before bitcoins are used to be spent).

2. Bitcoin’s core features

For a more beginner’s introduction to Bitcoin, please visit Binance Academy’s guide to Bitcoin.

Unspent Transaction Output (UTXO) model

A UTXO transaction works like cash payment between two parties: Alice gives money to Bob and receives change (i.e., unspent amount). In comparison, blockchains like Ethereum rely on the account model.
https://preview.redd.it/t1j6anf8f3151.png?width=1601&format=png&auto=webp&s=33bd141d8f2136a6f32739c8cdc7aae2e04cbc47

Nakamoto consensus

In the Bitcoin network, anyone can join the network and become a bookkeeping service provider i.e., a validator. All validators are allowed in the race to become the block producer for the next block, yet only the first to complete a computationally heavy task will win. This feature is called Proof of Work (PoW).
The probability of any single validator to finish the task first is equal to the percentage of the total network computation power, or hash power, the validator has. For instance, a validator with 5% of the total network computation power will have a 5% chance of completing the task first, and therefore becoming the next block producer.
Since anyone can join the race, competition is prone to increase. In the early days, Bitcoin mining was mostly done by personal computer CPUs.
As of today, Bitcoin validators, or miners, have opted for dedicated and more powerful devices such as machines based on Application-Specific Integrated Circuit (“ASIC”).
Proof of Work secures the network as block producers must have spent resources external to the network (i.e., money to pay electricity), and can provide proof to other participants that they did so.
With various miners competing for block rewards, it becomes difficult for one single malicious party to gain network majority (defined as more than 51% of the network’s hash power in the Nakamoto consensus mechanism). The ability to rearrange transactions via 51% attacks indicates another feature of the Nakamoto consensus: the finality of transactions is only probabilistic.
Once a block is produced, it is then propagated by the block producer to all other validators to check on the validity of all transactions in that block. The block producer will receive rewards in the network’s native currency (i.e., bitcoin) as all validators approve the block and update their ledgers.

The blockchain

Block production

The Bitcoin protocol utilizes the Merkle tree data structure in order to organize hashes of numerous individual transactions into each block. This concept is named after Ralph Merkle, who patented it in 1979.
With the use of a Merkle tree, though each block might contain thousands of transactions, it will have the ability to combine all of their hashes and condense them into one, allowing efficient and secure verification of this group of transactions. This single hash called is a Merkle root, which is stored in the Block Header of a block. The Block Header also stores other meta information of a block, such as a hash of the previous Block Header, which enables blocks to be associated in a chain-like structure (hence the name “blockchain”).
An illustration of block production in the Bitcoin Protocol is demonstrated below.

https://preview.redd.it/m6texxicf3151.png?width=1591&format=png&auto=webp&s=f4253304912ed8370948b9c524e08fef28f1c78d

Block time and mining difficulty

Block time is the period required to create the next block in a network. As mentioned above, the node who solves the computationally intensive task will be allowed to produce the next block. Therefore, block time is directly correlated to the amount of time it takes for a node to find a solution to the task. The Bitcoin protocol sets a target block time of 10 minutes, and attempts to achieve this by introducing a variable named mining difficulty.
Mining difficulty refers to how difficult it is for the node to solve the computationally intensive task. If the network sets a high difficulty for the task, while miners have low computational power, which is often referred to as “hashrate”, it would statistically take longer for the nodes to get an answer for the task. If the difficulty is low, but miners have rather strong computational power, statistically, some nodes will be able to solve the task quickly.
Therefore, the 10 minute target block time is achieved by constantly and automatically adjusting the mining difficulty according to how much computational power there is amongst the nodes. The average block time of the network is evaluated after a certain number of blocks, and if it is greater than the expected block time, the difficulty level will decrease; if it is less than the expected block time, the difficulty level will increase.

What are orphan blocks?

In a PoW blockchain network, if the block time is too low, it would increase the likelihood of nodes producingorphan blocks, for which they would receive no reward. Orphan blocks are produced by nodes who solved the task but did not broadcast their results to the whole network the quickest due to network latency.
It takes time for a message to travel through a network, and it is entirely possible for 2 nodes to complete the task and start to broadcast their results to the network at roughly the same time, while one’s messages are received by all other nodes earlier as the node has low latency.
Imagine there is a network latency of 1 minute and a target block time of 2 minutes. A node could solve the task in around 1 minute but his message would take 1 minute to reach the rest of the nodes that are still working on the solution. While his message travels through the network, all the work done by all other nodes during that 1 minute, even if these nodes also complete the task, would go to waste. In this case, 50% of the computational power contributed to the network is wasted.
The percentage of wasted computational power would proportionally decrease if the mining difficulty were higher, as it would statistically take longer for miners to complete the task. In other words, if the mining difficulty, and therefore targeted block time is low, miners with powerful and often centralized mining facilities would get a higher chance of becoming the block producer, while the participation of weaker miners would become in vain. This introduces possible centralization and weakens the overall security of the network.
However, given a limited amount of transactions that can be stored in a block, making the block time too longwould decrease the number of transactions the network can process per second, negatively affecting network scalability.

3. Bitcoin’s additional features

Segregated Witness (SegWit)

Segregated Witness, often abbreviated as SegWit, is a protocol upgrade proposal that went live in August 2017.
SegWit separates witness signatures from transaction-related data. Witness signatures in legacy Bitcoin blocks often take more than 50% of the block size. By removing witness signatures from the transaction block, this protocol upgrade effectively increases the number of transactions that can be stored in a single block, enabling the network to handle more transactions per second. As a result, SegWit increases the scalability of Nakamoto consensus-based blockchain networks like Bitcoin and Litecoin.
SegWit also makes transactions cheaper. Since transaction fees are derived from how much data is being processed by the block producer, the more transactions that can be stored in a 1MB block, the cheaper individual transactions become.
https://preview.redd.it/depya70mf3151.png?width=1601&format=png&auto=webp&s=a6499aa2131fbf347f8ffd812930b2f7d66be48e
The legacy Bitcoin block has a block size limit of 1 megabyte, and any change on the block size would require a network hard-fork. On August 1st 2017, the first hard-fork occurred, leading to the creation of Bitcoin Cash (“BCH”), which introduced an 8 megabyte block size limit.
Conversely, Segregated Witness was a soft-fork: it never changed the transaction block size limit of the network. Instead, it added an extended block with an upper limit of 3 megabytes, which contains solely witness signatures, to the 1 megabyte block that contains only transaction data. This new block type can be processed even by nodes that have not completed the SegWit protocol upgrade.
Furthermore, the separation of witness signatures from transaction data solves the malleability issue with the original Bitcoin protocol. Without Segregated Witness, these signatures could be altered before the block is validated by miners. Indeed, alterations can be done in such a way that if the system does a mathematical check, the signature would still be valid. However, since the values in the signature are changed, the two signatures would create vastly different hash values.
For instance, if a witness signature states “6,” it has a mathematical value of 6, and would create a hash value of 12345. However, if the witness signature were changed to “06”, it would maintain a mathematical value of 6 while creating a (faulty) hash value of 67890.
Since the mathematical values are the same, the altered signature remains a valid signature. This would create a bookkeeping issue, as transactions in Nakamoto consensus-based blockchain networks are documented with these hash values, or transaction IDs. Effectively, one can alter a transaction ID to a new one, and the new ID can still be valid.
This can create many issues, as illustrated in the below example:
  1. Alice sends Bob 1 BTC, and Bob sends Merchant Carol this 1 BTC for some goods.
  2. Bob sends Carols this 1 BTC, while the transaction from Alice to Bob is not yet validated. Carol sees this incoming transaction of 1 BTC to him, and immediately ships goods to B.
  3. At the moment, the transaction from Alice to Bob is still not confirmed by the network, and Bob can change the witness signature, therefore changing this transaction ID from 12345 to 67890.
  4. Now Carol will not receive his 1 BTC, as the network looks for transaction 12345 to ensure that Bob’s wallet balance is valid.
  5. As this particular transaction ID changed from 12345 to 67890, the transaction from Bob to Carol will fail, and Bob will get his goods while still holding his BTC.
With the Segregated Witness upgrade, such instances can not happen again. This is because the witness signatures are moved outside of the transaction block into an extended block, and altering the witness signature won’t affect the transaction ID.
Since the transaction malleability issue is fixed, Segregated Witness also enables the proper functioning of second-layer scalability solutions on the Bitcoin protocol, such as the Lightning Network.

Lightning Network

Lightning Network is a second-layer micropayment solution for scalability.
Specifically, Lightning Network aims to enable near-instant and low-cost payments between merchants and customers that wish to use bitcoins.
Lightning Network was conceptualized in a whitepaper by Joseph Poon and Thaddeus Dryja in 2015. Since then, it has been implemented by multiple companies. The most prominent of them include Blockstream, Lightning Labs, and ACINQ.
A list of curated resources relevant to Lightning Network can be found here.
In the Lightning Network, if a customer wishes to transact with a merchant, both of them need to open a payment channel, which operates off the Bitcoin blockchain (i.e., off-chain vs. on-chain). None of the transaction details from this payment channel are recorded on the blockchain, and only when the channel is closed will the end result of both party’s wallet balances be updated to the blockchain. The blockchain only serves as a settlement layer for Lightning transactions.
Since all transactions done via the payment channel are conducted independently of the Nakamoto consensus, both parties involved in transactions do not need to wait for network confirmation on transactions. Instead, transacting parties would pay transaction fees to Bitcoin miners only when they decide to close the channel.
https://preview.redd.it/cy56icarf3151.png?width=1601&format=png&auto=webp&s=b239a63c6a87ec6cc1b18ce2cbd0355f8831c3a8
One limitation to the Lightning Network is that it requires a person to be online to receive transactions attributing towards him. Another limitation in user experience could be that one needs to lock up some funds every time he wishes to open a payment channel, and is only able to use that fund within the channel.
However, this does not mean he needs to create new channels every time he wishes to transact with a different person on the Lightning Network. If Alice wants to send money to Carol, but they do not have a payment channel open, they can ask Bob, who has payment channels open to both Alice and Carol, to help make that transaction. Alice will be able to send funds to Bob, and Bob to Carol. Hence, the number of “payment hubs” (i.e., Bob in the previous example) correlates with both the convenience and the usability of the Lightning Network for real-world applications.

Schnorr Signature upgrade proposal

Elliptic Curve Digital Signature Algorithm (“ECDSA”) signatures are used to sign transactions on the Bitcoin blockchain.
https://preview.redd.it/hjeqe4l7g3151.png?width=1601&format=png&auto=webp&s=8014fb08fe62ac4d91645499bc0c7e1c04c5d7c4
However, many developers now advocate for replacing ECDSA with Schnorr Signature. Once Schnorr Signatures are implemented, multiple parties can collaborate in producing a signature that is valid for the sum of their public keys.
This would primarily be beneficial for network scalability. When multiple addresses were to conduct transactions to a single address, each transaction would require their own signature. With Schnorr Signature, all these signatures would be combined into one. As a result, the network would be able to store more transactions in a single block.
https://preview.redd.it/axg3wayag3151.png?width=1601&format=png&auto=webp&s=93d958fa6b0e623caa82ca71fe457b4daa88c71e
The reduced size in signatures implies a reduced cost on transaction fees. The group of senders can split the transaction fees for that one group signature, instead of paying for one personal signature individually.
Schnorr Signature also improves network privacy and token fungibility. A third-party observer will not be able to detect if a user is sending a multi-signature transaction, since the signature will be in the same format as a single-signature transaction.

4. Economics and supply distribution

The Bitcoin protocol utilizes the Nakamoto consensus, and nodes validate blocks via Proof-of-Work mining. The bitcoin token was not pre-mined, and has a maximum supply of 21 million. The initial reward for a block was 50 BTC per block. Block mining rewards halve every 210,000 blocks. Since the average time for block production on the blockchain is 10 minutes, it implies that the block reward halving events will approximately take place every 4 years.
As of May 12th 2020, the block mining rewards are 6.25 BTC per block. Transaction fees also represent a minor revenue stream for miners.
submitted by D-platform to u/D-platform [link] [comments]

Google and NASA have reached quantum supremacy in a year collaboration. What does it mean for future blockchain security?

As can be read in this article. Although quantum supremacy simply means that at least 1 specific problem has been proven to be solved by a quantum computer that can't be solved (in a realistic timeframe) by any existing classical computer, it is a very important milestone. Many have been skeptical on crossing this milestone at all.
Supremacy does not mean that current cryptography is at risk tomorrow. It does however prove quantum computing is real, and has advantage over classical computers in certain tasks as has always been thought. For blockchain this means that in the future, Shor's algorithm could be used to break ECDSA, the signature scheme that is used in most blockchain. This signature scheme can be upgraded to a quantum resistant signature scheme. It does come with specific challenges though. As opposed to banks, websites, government systems, email services etc, blockchain is decentralized. That makes the following challenges exclusive blockchain challenges:
Consider the full analysis on this subject here
Blockchains that implement quantum resistance from the very beginning, from genesis block, will not face these challenges. See for example QRL which has launched over a year ago.
submitted by QRCollector to CryptoCurrency [link] [comments]

Best General RenVM Questions of February 2020

Best General RenVM Questions of January 2020

\These questions are sourced directly from Telegram*
Q: Are all the projects listed in the Ren Alliance, the final set of members?
A: No, please do keep in mind this just our first round of partners, some larger orgs require a bit more DD (i.e our audit). We’ll release the final set of members when Mainnet goes live.

Q: How do projects join the Ren Alliance?
A: It’s simple, just fill out this application. It takes about five minutes, and all you need is your company’s logo files and your preferred area(s) of involvement. Joining the Alliance requires no binding commitments, only a desire to help bring cross-chain assets to DeFi.

Q: For example let's say there is a crypto index which contains 1 BTC and 1 ZEC. I have 1 BTC and 1 ZEC and I would like to “mint” this index token with RenVM. Will something like this possible in the future?
A: This is already possible today. RenVM allows you to mint renBTC and renZEC (and renBCH) on Ethereum. This result is an ERC20 like any other with the addition that when you burn it, you get real BTC and ZEC back.
Another nice feature is that you can directly call smart contracts when minting. This is not possible in any other system, and results in a very clean and simple user experience. People can make a BTC transaction followed by a ZEC transaction and with no other blockchain actions end up with their BTC and ZEC in your example system (your example system would have functions for accepting BTC and ZEC and when receiving both, it would output some kind of index token; exactly how it functions is up to how you want to implement your contract!)

Q: What blockchains does RenVM support?
A: RenVM can support any ECDSA based blockchain but we'll be starting with BTC, ZEC, and BCH. More info here: https://github.com/renproject/ren/wiki/Supported-Blockchains

Q: Another concern is chain rollback. In the case of MakerDAO getting hacked (unlikely, but not impossible), the Ethereum network could rollback just like with the DAO. (Unlikely, but not impossible). But what if the attacker already has deposited the hacked funds into RenVM and gotten a private coin?
A: A roll-back would still revert that state. Privacy on-chain != no state tracking something (just in a way that doesn’t reveal information). So reverts don’t really matter in that sense. They do matter in a broader sense: you have renBTC and you burn it for BTC, then Ethereum rolls back to when you had renBTC still. This is something the Ethereum community has to consider very carefully these days if they were to ever do such a revert. This is an ultimately unavoidable truth RE interoperability; you are compounding risks of the chains you are using. In general, this is why it’s always safer to keep your BTC on Bitcoin unless there is a specific reason you need it on Ethereum at any given point in time.

Q: If BTC can be transferred with zero confirmation how many transactions RenVM can handle?
A: RenVMs throughput isn’t affected by conf-less transactions. This is a service provided by L2 technology (like the 0Conf team, who are building exactly this!). This doesn’t affect RenVM directly, but it does have the pleasant impact that users won’t notice network congestion if it happens.

Q: Can you explain the over-collateralization security dynamic between tBTC and RenVM? Does this play into Maker using RenVM vs. tBTC to collaetize their CDP’s
A1: It’s not the over collateralization that’s the problem. It’s that to get $X BTC they need 1.5x $X ETH locked up in their protocol. What about other places that give better ETH returns? What about the fact that ETH doesn’t go up in price just because tBTC is used?
With REN, we are actually over collateralized (so they’re wrong that they are more secure in this regard). The big difference: BTC flowing through REN increases the value of the REN collateral, increasing the security, increasing the capacity of BTC that can flow through the system. It’s a positive feedback loop for capacity and security that simply doesn’t exist if you don’t use an isolated token.
A2: Maker wants to use BTC to collateralise Dai, because it diversifies risk and expands the possible Dai supply (by expanding possible collateral). If you use tBTC, then tBTC is collateralised by ETH so you actually become less efficient at minting Dai, and you don’t diversify risk because tBTC gets liquidated by ETH price movements.
You don’t want your network secured by collateral that has speculative value that is not correlated with the usage of the network. That makes things unstable.
If RenVM is being used, the value of REN increases, and the more RenVM can be used (and Darknodes get the positive upside of their bond increasing in value). This means by pumping lots of BTC into RenVM, you gain more capacity to pump more BTC into RenVM. This creates a positive feedback loop for the returns earned by Darknodes, the value of their bond, and overall/capacity security of the network.
Compare to tBTC: you are waiting for ETH to go up in value. It’s value, which does not correlate with the amount of BTC in the system, limits the AUM that the system can hold. You’re hoping it will go up independently of the usage of your network and if it doesn’t you’re out of luck. Network growth does not drive the ability for the network to grow. Your are also competing with the returns on ETH that other ecosystems allow you to get (why bond ETH in tBTC if you can get better returns on that ETH in other places; lending it or staking it in Eth2.0). (Btw: we’re doing research to get our collateralisation of REN to 150%. It’s already possible, and could be done today, but we are just seeing if we can make it safelivelier than the current best-in-class algorithms.)

Q: How do we define the value of L and R if we don't use oracle price feed?
A: It will be decided by the Darknodes. The best mechanism of doing this is still being decided upon. However, it won’t simply be taken from the current market price / third-party oracles as those are vulnerable to manipulation. Ultimately, the only valuation that matters is the Darknodes (because they’re the ones being potentially bribed).

Q: In my opinion, RenVM (and tBTC adoption bottleneck: 300% collateral ratio» this ratio is important for security and decentralization» to sustain this ratio we need significant fees to be imposed on Renbtc holders» example: if there was 100m$ Renbtc total supply then we need 300m$ ren locked in darknodes» if 3-5% fees paid for those 300m$ then we need to extract 9-15 million fees from the 100m renbtc» that equal 9-15% annual fees» of course it will be lower with the minting and burning fees but I don't think it will cover half of the total needed fees» the result with the current design there are still too much economic friction IMO.
A: The key thing to keep in mind is velocity. Not just TVL. Let’s take Kyber as an example: they have $4.9M AUM. But, they did $3.7M in trades in the last 24 hours. Over the year, that’s 275x their AUM.
So, if RenVM is holding $100M AUM, and achieves a volume multiplier of 200x then it gets $1M p/a in holding fees but $40M in minting/burning fees. This is all assuming the minimum fee as well (it rises as TVL approaches the limit). So RenVM would need a $300M market cap on $41M in revenue. That’s 13% p/a, assuming we don’t make the move to only 150% collateral. If we do move to that, then it’s almost 33% p/a.
RenVM is by far and away the best UX for instantly swapping BTC on DEXs (with no gas, and no confirmations). All of the interfaces we’re building and the tools we’re providing give people that native experience. This is precisely because high TVL is not what yields good returns and increases cap for the protocol.
Even systems like MakerDAO/Compound have people moving BTC in/out. Their AUM is by no means static. People are constantly opening/closing/liquidating positions and all of this is would create velocity through RenVM.

Q: How was ETHDenver?
A: ETHDenver was great, and very productive, confirmed a lot of our thoughts on what needs to be done but also gave us a good amount of exposure, so overall it was a positive for the team and RenVM.
submitted by RENProtocol to RenProject [link] [comments]

Best General RenVM Questions of January 2020

Best General RenVM Questions of January 2020

‌*These questions are sourced directly from Telegram
Q: When you say RenVM is Trustless, Permissionless, and Decentralized, what does that actually mean?
A: Trustless = RenVM is a virtual machine (a network of nodes, that do computations), this means if you ask RenVM to trade an asset via smart contract logic, it will. No trusted intermediary that holds assets or that you need to rely on. Because RenVM is a decentralized network and computes verified information in a secure environment, no single party can prevent users from sending funds in, withdrawing deposited funds, or computing information needed for updating outside ledgers. RenVM is an agnostic and autonomous virtual broker that holds your digital assets as they move between blockchains.
Permissionless = RenVM is an open protocol; meaning anyone can use RenVM and any project can build with RenVM. You don't need anyone's permission, just plug RenVM into your dApp and you have interoperability.
Decentralized = The nodes that power RenVM ( Darknodes) are scattered throughout the world. RenVM has a peak capacity of up to 10,000 Darknodes (due to REN’s token economics). Realistically, there will probably be 100 - 500 Darknodes run in the initial Mainnet phases, ample decentralized nonetheless.

Q: Okay, so how can you prove this?
A: The publication of our audit results will help prove the trustlessness piece; permissionless and decentralized can be proven today.
Permissionless = https://github.com/renproject/ren-js
Decentralized = https://chaosnet.renproject.io/

Q: How does Ren sMPC work? Sharmir's secret sharing? TSS?
A: There is some confusion here that keeps arising so I will do my best to clarify.TL;DR: *SSS is just data. It’s what you do with the data that matters. RenVM uses sMPC on SSS to create TSS for ECDSA keys.*SSS and TSS aren’t fundamental different things. It’s kind of like asking: do you use numbers, or equations? Equations often (but not always) use numbers or at some point involve numbers.
SSS by itself is just a way of representing secret data (like numbers). sMPC is how to generate and work with that data (like equations). One of the things you can do with that work is produce a form of TSS (this is what RenVM does).
However, TSS is slightly different because it can also be done *without* SSS and sMPC. For example, BLS signatures don’t use SSS or sMPC but they are still a form of TSS.
So, we say that RenVM uses SSS+sMPC because this is more specific than just saying TSS (and you can also do more with SSS+sMPC than just TSS). Specifically, all viable forms of turning ECDSA (a scheme that isn’t naturally threshold based) into a TSS needs SSS+sMPC.
People often get confused about RenVM and claim “SSS can’t be used to sign transactions without making the private key whole again”. That’s a strange statement and shows a fundamental misunderstanding about what SSS is.
To come back to our analogy, it’s like saying “numbers can’t be used to write a book”. That’s kind of true in a direct sense, but there are plenty of ways to encode a book as numbers and then it’s up to how you interpret (how you *use*) those numbers. This is exactly how this text I’m writing is appearing on your screen right now.
SSS is just secret data. It doesn’t make sense to say that SSS *functions*. RenVM is what does the functioning. RenVM *uses* the SSSs to represent private keys. But these are generated and used and destroyed as part of sMPC. The keys are never whole at any point.

Q: Thanks for the explanation. Based on my understanding of SSS, a trusted dealer does need to briefly put the key together. Is this not the case?
A: Remember, SSS is just the representation of a secret. How you get from the secret to its representation is something else. There are many ways to do it. The simplest way is to have a “dealer” that knows the secret and gives out the shares. But, there are other ways. For example: we all act as dealers, and all give each other shares of our individual secret. If there are N of us, we now each have N shares (one from every person). Then we all individually add up the shares that we have. We now each have a share of a “global” secret that no one actually knows. We know this global secret is the sum of everyone’s individual secrets, but unless you know every individual’s secret you cannot know the global secret (even though you have all just collectively generates shares for it). This is an example of an sMPC generation of a random number with collusion resistance against all-but-one adversaries.

Q: If you borrow Ren, you can profit from the opposite Ren gain. That means you could profit from breaking the network and from falling Ren price (because breaking the network, would cause Ren price to drop) (lower amount to be repaid, when the bond gets slashed)
A: Yes, this is why it’s important there has a large number of Darknodes before moving to full decentralisation (large borrowing becomes harder). We’re exploring a few other options too, that should help prevent these kinds of issues.

Q: What are RenVM’s Security and Liveliness parameters?
A: These are discussed in detail in our Wiki, please check it out here: https://github.com/renproject/ren/wiki/Safety-and-Liveliness#analysis

Q: What are the next blockchain under consideration for RenVM?
A: These can be found here: https://github.com/renproject/ren/wiki/Supported-Blockchains

Q: I've just read that Aztec is going to be live this month and currently tests txs with third parties. Are you going to participate in early access or you just more focused on bringing Ren to Subzero stage?
A: At this stage, our entire focus is on Mainnet SubZero. But, we will definitely be following up on integrating with AZTEC once everything is out and stable.

Q: So how does RenVM compare to tBTC, Thorchain, WBTC, etc..?
A: An easy way to think about it is..RenVM’s functionality is a combination of tBTC (+ WBTC by extension), and Thorchain’s (proposed) capabilities... All wrapped into one. Just depends on what the end-user application wants to do with it.

Q1: What are the core technical/security differences between RenVM and tBTC?A1: The algorithm used by tBTC faults if even one node goes offline at the wrong moment (and the whole “keep” of nodes can be penalised for this). RenVM can survive 1/3rd going offline at any point at any time. Advantage for tBTC is that collusion is harder, disadvantage is obviously availability and permissionlessness is lower.
tBTC an only mint/burn lots of 1 BTC and requires an on-Ethereum SPV relay for Bitcoin headers (and for any other chain it adds). No real advantage trade-off IMO.
tBTC has a liquidation mechanism that means nodes can have their bond liquidated because of ETH/BTC price ratio. Advantage means users can get 1 BTC worth of ETH. Disadvantage is it means tBTC is kind of a synthetic: needs a price feed, needs liquid markets for liquidation, users must accept exposure to ETH even if they only hold tBTC, nodes must stay collateralized or lose lots of ETH. RenVM doesn’t have this, and instead uses fees to prevent becoming under-collateralized. This requires a mature market, and assumed Darknodes will value their REN bonds fairly (based on revenue, not necessarily what they can sell it for at current —potentially manipulated—market value). That can be an advantage or disadvantage depending on how you feel.
tBTC focuses more on the idea of a tokenized version of BTC that feels like an ERC20 to the user (and is). RenVM focuses more on letting the user interact with DeFi and use real BTC and real Bitcoin transactions to do so (still an ERC20 under the hood, but the UX is more fluid and integrated). Advantage of tBTC is that it’s probably easier to understand and that might mean better overall experience, disadvantage really comes back to that 1 BTC limit and the need for a more clunky minting/burning experience that might mean worse overall experience. Too early to tell, different projects taking different bets.
tBTC supports BTC (I think they have ZEC these days too). RenVM supports BTC, BCH, and ZEC (docs discuss Matic, XRP, and LTC).
Q2: This are my assumed differences between tBTC and RenVM, are they correct? Some key comparisons:
-Both are vulnerable to oracle attacks
-REN federation failure results in loss or theft of all funds
-tBTC failures tend to result in frothy markets, but holders of tBTC are made whole
-REN quorum rotation is new crypto, and relies on honest deletion of old key shares
-tBTC rotates micro-quorums regularly without relying on honest deletion
-tBTC relies on an SPV relay
-REN relies on federation honesty to fill the relay's purpose
-Both are brittle to deep reorgs, so expanding to weaker chains like ZEC is not clearly a good idea
-REN may see total system failure as the result of a deep reorg, as it changes federation incentives significantly
-tBTC may accidentally punish some honest micro-federations as the result of a deep reorg
-REN generally has much more interaction between incentive models, as everything is mixed into the same pot.
-tBTC is a large collection of small incentive models, while REN is a single complex incentive model
A2: To correct some points:
The oracle situation is different with RenVM, because the fee model is what determines the value of REN with respect to the cross-chain asset. This is the asset is what is used to pay the fee, so no external pricing is needed for it (because you only care about the ratio between REN and the cross-chain asset).
RenVM does rotate quorums regularly, in fact more regularly than in tBTC (although there are micro-quorums, each deposit doesn’t get rotated as far as I know and sticks around for up to 6 months). This rotation involves rotations of the keys too, so it does not rely on honest deletion of key shares.
Federated views of blockchains are easier to expand to support deep re-orgs (just get the nodes to wait for more blocks for that chain). SPV requires longer proofs which begins to scale more poorly.
Not sure what you mean by “one big pot”, but there are multiple quorums so the failure of one is isolated from the failures of others. For example, if there are 10 shards supporting BTC and one of them fails, then this is equivalent to a sudden 10% fee being applied. Harsh, yes, but not total failure of the whole system (and doesn’t affect other assets).
Would be interesting what RenVM would look like with lots more shards that are smaller. Failure becomes much more isolated and affects the overall network less.
Further, the amount of tBTC you can mint is dependent on people who are long ETH and prefer locking it up in Keep for earning a smallish fee instead of putting it in Compound or leveraging with dydx. tBTC is competing for liquidity while RenVM isn't.

Q: I understand correctly RenVM (sMPC) can get up to a 50% security threshold, can you tell me more?
A: The best you can theoretically do with sMPC is 50-67% of the total value of REN used to bond Darknodes (RenVM will eventually work up to 50% and won’t go for 67% because we care about liveliness just as much as safety). As an example, if there’s $1M of REN currently locked up in bonded Darknodes you could have up to $500K of tokens shifted through RenVM at any one specific moment. You could do more than that in daily volume, but at any one moment this is the limit.Beyond this limit, you can still remain secure but you cannot assume that players are going to be acting to maximize their profit. Under this limit, a colluding group of adversaries has no incentive to subvert safety/liveliness properties because the cost to attack roughly outweighs the gain. Beyond this limit, you need to assume that players are behaving out of commitment to the network (not necessarily a bad assumption, but definitely weaker than the maximizing profits assumption).

Q: Why is using ETH as collateral for RenVM a bad idea?
A: Using ETH as collateral in this kind of system (like having to deposit say 20 ETH for a bond) would not make any sense because the collateral value would then fluctuate independently of what kind of value RenVM is providing. The REN token on the other hand directly correlates with the usage of RenVM which makes bonding with REN much more appropriate. DAI as a bond would not work as well because then you can't limit attackers with enough funds to launch as many darknodes as they want until they can attack the network. REN is limited in supply and therefore makes it harder to get enough of it without the price shooting up (making it much more expensive to attack as they would lose their bonds as well).
A major advantage of Ren's specific usage of sMPC is that security can be regulated economically. All value (that's being interopped at least) passing through RenVM has explicit value. The network can self-regulate to ensure an attack is never worth it.

Q: Given the fee model proposal/ceiling, might be a liquidity issue with renBTC. More demand than possible supply?A: I don’t think so. As renBTC is minted, the fees being earned by Darknodes go up, and therefore the value of REN goes up. Imagine that the demand is so great that the amount of renBTC is pushing close to 100% of the limit. This is a very loud and clear message to the Darknodes that they’re going to be earning good fees and that demand is high. Almost by definition, this means REN is worth more.
Profits of the Darknodes, and therefore security of the network, is based solely on the use of the network (this is what you want because your network does not make or break on things outside the systems control). In a system like tBTC there are liquidity issues because you need to convince ETH holders to bond ETH and this is an external problem. Maybe ETH is pumping irrespective of tBTC use and people begin leaving tBTC to sell their ETH. Or, that ETH is dumping, and so tBTC nodes are either liquidated or all their profits are eaten by the fact that they have to be long on ETH (and tBTC holders cannot get their BTC back in this case). Feels real bad man.

Q: I’m still wondering which asset people will choose: tbtc or renBTC? I’m assuming the fact that all tbtc is backed by eth + btc might make some people more comfortable with it.
A: Maybe :) personally I’d rather know that my renBTC can always be turned back into BTC, and that my transactions will always go through. I also think there are many BTC holders that would rather not have to “believe in ETH” as an externality just to maximize use of their BTC.

Q: How does the liquidation mechanism work? Can any party, including non-nodes act as liquidators? There needs to be a price feed for liquidation and to determine the minting fee - where does this price feed come from?
A: RenVM does not have a liquidation mechanism.
Q: I don’t understand how the price feeds for minting fees make sense. You are saying that the inputs for the fee curve depend on the amount of fees derived by the system. This is circular in a sense?
A: By evaluating the REN based on the income you can get from bonding it and working. The only thing that drives REN value is the fact that REN can be bonded to allow work to be done to earn revenue. So any price feed (however you define it) is eventually rooted in the fees earned.

Q: Who’s doing RenVM’s Security Audit?
A: ChainSecurity | https://chainsecurity.com/

Q: Can you explain RenVM’s proposed fee model?
A: The proposed fee model can be found here: https://github.com/renproject/ren/wiki/Safety-and-Liveliness#fees

Q: Can you explain in more detail the difference between "execution" and "powering P2P Network". I think that these functions are somehow overlapping? Can you define in more detail what is "execution" and "powering P2P Network"? You also said that at later stages semi-core might still exist "as a secondary signature on everything (this can mathematically only increase security, because the fully decentralised signature is still needed)". What power will this secondary signature have?
A: By execution we specifically mean signing things with the secret ECDSA keys. The P2P network is how every node communicates with every other node. The semi-core doesn’t have any “special powers”. If it stays, it would literally just be a second signature required (as opposed to the one signature required right now).
This cannot affect safety, because the first signature is still required. Any attack you wanted to do would still have to succeed against the “normal” part of the network. This can affect liveliness, because the semi-core could decide not to sign. However, the semi-core follows the same rules as normal shards. The signature is tolerant to 1/3rd for both safety/liveliness. So, 1/3rd+ would have to decide to not sign.
Members of the semi-core would be there under governance from the rest of our ecosystem. The idea is that members would be chosen for their external value. We’ve discussed in-depth the idea of L<3. But, if RenVM is used in MakerDAO, Compound, dYdX, Kyber, etc. it would be desirable to capture the value of these ecosystems too, not just the value of REN bonded. The semi-core as a second signature is a way to do this.
Imagine if the members for those projects, because those projects want to help secure renBTC, because it’s used in their ecosystems. There is a very strong incentive for them to behave honestly. To attack RenVM you first have to attack the Darknodes “as per usual” (the current design), and then somehow convince 1/3rd of these projects to act dishonestly and collapse their own ecosystems and their own reputations. This is a very difficult thing to do.
Worth reminding: the draft for this proposal isn’t finished. It would be great for everyone to give us their thoughts on GitHub when it is proposed, so we can keep a persistent record.

Q: Which method or equation is used to calculate REN value based on fees? I'm interested in how REN value is calculated as well, to maintain the L < 3 ratio?
A: We haven’t finalized this yet. But, at this stage, the plan is to have a smart contract that is controlled by the Darknodes. We want to wait to see how SubZero and Zero go before committing to a specific formulation, as this will give us a chance to bootstrap the network and field inputs from the Darknodes owners after the earnings they can make have become more apparent.
submitted by RENProtocol to RenProject [link] [comments]

Question about ECDSA private key recovery from known k parameter

I'm trying to solve a challenge about finding ECDSA private key from known k, and I encountered a problem that I can't google, so I hope someone will help me here.

I have a signature, a Bitcoin address, a message and the k parameter used to create the signature. I wrote a solution that works with my own test cases, but it fails with the challenge in the following way: the public key that gets derived from found private key is not the same as as the public key that corresponds to the Bitcoin address. However, signing the same message with the same k produces the same signature as the challenge signature (aside from special byte appended by Bitcoin). I suspected that the problem might be with the R, but R, and tried a few different values, even though it's already supplied by Bitcoin signature format, but still failed to produce the same public key.
Update: found the R value that leads to the same public key that I can derive from my found private key. Seems like this was a part of the challenge. Still, want to know the answer to my last question, as I don't know much theory about Ecdsa.
Update 2: after getting a hint, I found the private key by using -s instead of s to calculate the private key. But I don't fully understand how it worked, I see it has something to do with ECDSA malleability, so my second question is - how it all worked?
So, my question is - what I could be doing wrong? Can different private keys produce the same signature when k and message are the same?
submitted by Satoshi_Hodler to crypto [link] [comments]

A brief history of the Monero development (Part I)

or a struggle for anonymity and confidentiality of blockchain transaction.
The issues of privacy of electronic currency faced researchers and developers for a long time, long before Bitcoin. In 1991, Tatsuaki Okamoto and Kazuo Ohta from the NTT research laboratory (Japan's largest telecommunications company) introduced 6 criteria for an ideal e-currency, including privacy: "relationship between the user and his purchases must be untraceable by anyone". Nicholas van Saberhagen, an anonymous author behind the work on the CryptoNote protocol, which formed the basis of Monero, in December 2012 summarized these 6 criteria to two specific properties:
Untraceability: for every incoming transaction, all possible senders are equally likely.Unlinkability: for any two outgoing transactions, it is impossible to prove that they were sent to the same person.
None of the other properties are characteristic of Bitcoin, since all transactions are broadcasted publicly. Of course, by the time this work was written, various tumblers made it possible to combine outputs of several transactions and send them through some intermediate address. Also, by that time, some protocols based on the zero-knowledge proof were known, but at that time such evidence was large enough to make them impractical to use.
What was proposed to tackle the issues: firstly, each transaction was signed on behalf of the group, not the individual, as in BTC. To do this, we used the option of an electronic digital signature called "Ring Signature" (further development of the so-called "Group Signature"). However, when implementing a completely anonymous ring signature, a (very high) probability of double spending of coins arose, and therefore the so-called linkable anonymity primitive was taken, which was implemented through a one-time-key mechanism (i.e., when creating each new transaction, the group key changes).
Essentially, although it's certainly worth noting that the CryptoNote implementation used a different scheme of elliptical curves (EdDSA instead of ECDSA, as a result, an elliptic curve with a different equation was used, etc.).
Anonymity achieved, but what about privacy? RingCT to the rescue
You know how it happens: everything seems to be there, but something is missing. The problem with the original CryptoNote protocol was that the user balances were not hidden, and thus, it was possible to analyze the blockchain and deanonymize the members of the group who signed the transaction. An additional problem with hiding balances is that with simple encryption of balances, it is not possible to reach a consensus on whether coins were produced from the thin air or not.
To solve this problem, the developer Shen Noether from Monero Research Lab proposed the use of the Pederson Commitment, which allows the prover to calculate the obligation for the amount without disclosing it and being unable to change it.
Short explanation from Monero Wiki:
As long as the encrypted output amounts created, which include an output for the recipient and a change output back to the sender, and the unencrypted transaction fee is equal to the sum of the inputs that are being spent, it is a legitimate transaction and can be confirmed to not be creating Monero out of thin air.
Thus, it is possible to obtain a ring confidential transaction (hence the name). And, the inquisitive reader will ask, what is wrong this time?
The problem is one, but twofold. On the one hand, the size of the transaction increases with RingCT, which does not have the best effect on scalability and transaction fees. Besides, again, due to the large size of the signature, the number of possible subscribers n is limited. So, the n value in the official software of Monero wallet is from 5 to 20 by default. As a result, the sender anonymity for RingCT1.0 is at most 1 out of 20.
To be continued...
submitted by CUTcoin to cutc0in [link] [comments]

Bottos 2020 Research and Development Scheme

Bottos 2020 Research and Development Scheme

https://preview.redd.it/umh8ivbsua841.png?width=554&format=png&auto=webp&s=5c16d9d9e61503e4c9d44212eecd176eda11550a
As 2020 is now here, Bottos has solemnly released its “2020 Research and development scheme”. On one hand, we adhere to the principle of transparency so that the whole community can comprehend our next step as a whole, but more importantly, it also helps our whole team to think deeply about the future and reach consensus. It is strongly believed that following these consistent follow-ups will help us to in order to achieve the best results.
Based on the efficient development of Bottos, the team’s technical achievements in consensus algorithms and smart contracts are used to deeply implement and optimize the existing technical architecture. At the same time using the community’s technical capabilities, horizontal development, expanding new functional modules and technical directions it stays closely integrated with the whole community.
In the future, we will keep on striving to achieve in-depth thinking, comprehensive planning, and flexible adjustment.


Overview of Technical Routes

https://preview.redd.it/rk9tpg2uua841.png?width=554&format=png&auto=webp&s=77e607b81f31c0d20feaa90eca81f09a23addca4
User feedback within the community is the driving force behind Bottos progress. In the development route of the community and industry we have formulated a roadmap for technical development, pointing out the right path for the team towards the right direction among the massive routes of modern technology.
As part of our 2020 research and development objective we have the following arrangements:
1. Intensifying enormous number of smart contracts and related infrastructures
After many years of development, smart contracts have gradually become the core and standard function in blockchain projects. The strength of smart contracts, ease of use, and stability represent the key capabilities of a blockchain project. As a good start, Bottos has already made great progress in the field of smart contracts. In smart contracts we still need to increase development efforts, making the ease of use and stability of smart contracts the top priority of our future development.
Reducing the barriers for developers and ordinary users to use, shortening the contract development cycle and saving users time is another important task for the team to accomplish. To this end, we have planned an efficient and easy-to-use one-stop contract development, debugging, and deployment tool that will provide multiple access methods and interfaces to the test network to support rapid deployment and rapid debugging.
2. Establishing an excellent client and user portal
The main goal here is to add an entrance point to the creation and deployment of smart contracts in the wallet client. To this end, the wallet needs to be transformed, a local compiler for smart contracts must be added, and an easy-to-use UI interface can be provided for the purpose of creating, deploying, and managing contracts to meet the needs of users with a single mouse click only.
3. Expanding distributed storage
Distributed storage is another focus of our development in the upcoming year. Only by using a distributed architecture can completely solve the issue of performance and scalability of stand-alone storage. Distributed storage suitable for blockchain needs to provide no less than single machine performance, extremely high availability, no single point of failure, easy expansion, and strong consistent transactions. These are the main key points and difficulties of Bottos in field of distributed storage in the upcoming days.
4. Reinforcing multi party secured computing
Privacy in computing is also a very important branch to deal with. In this research direction, Bottos has invested a lot of time and produced many research results on multi-party secured computing, such as technical articles and test cases. In the future, we will continue to give efforts in the direction of multi-party secured computing and apply mature technology achievements into the functions of the chain.

2020 Bottos — Product Development

Support for smart contract deployment in wallets
The built-in smart contract compiler inside the wallet supports compilation of the smart contracts in all languages provided by Bottos and integrates with the functions in the wallet. It also supports one-click deployment of the compiled contract source code in the wallet.
When compiling a contract, one can choose whether to pre-execute the contract code. If pre-execution is selected, it will connect to the remote contract pre-execution service and return the execution result to the wallet.
When deploying a contract, one can choose to deploy to the test network or main network and the corresponding account and private key of the test network or main network should be provided.

2020 Bottos-Technical Research

https://preview.redd.it/x2k65j7xua841.png?width=553&format=png&auto=webp&s=a40eae3c56b664c031b3db96f608923e670ff331
1. Intelligent smart contract development platform (BISDP)
The smart contract development platform BISDP is mainly composed of user-oriented interfaces, as well as back-end compilation and deployment tools, debugging tools, and pre-execution frameworks.
The user-oriented interface provides access methods based on WEB, PC, and mobile apps, allowing developers to quickly and easily compile and deploy contracts and provide contract template management functions. It can also manage the contract remotely by viewing the contract execution status, the consumed resources and other information.
In the compilation and deployment tool a set of smart contract source code editing, running, debugging, and deployment solutions as well as smart contract templates for common tasks are provided, which greatly reduces the threshold for developers to learn and use smart contracts. At the same time, developers and ordinary users are provided with a smart contract pre-execution framework, which can check the logical defects and security risks in smart contracts before actual deployment and promptly remind users a series of problems even before the smart contracts are actually run.
In the debugging tool, there are built-in local debugging and remote debugging tools. Multiple breakpoints can be set in the debugging tool. When the code reaches the breakpoint, one can view the variables and their contents in the current execution stack. One can also make conditional breakpoints based on the value of the variable. The code will not execute until the value reaches a preset value in memory.
In the pre-execution framework, developers can choose to pre-execute contract code in a virtual environment or a test net, checking out problems in some code that cannot be detected during compilation time and perform deeper code inspection. The pre-execution framework can also prompt the user in advance about the time and space resources required for execution.
2. Supporting Python and PHP in BVM virtual machine for writing smart contracts
We have added smart contract writing tools based on Python and PHP languages. These languages can be compiled into the corresponding BVM instruction set for implementation. These two reasons are used as the programming language for smart contracts.
For the Python language, the basic language elements supported by the first phase are:
- Logic control: If, Else, Eli, While, Break, method calls, for x in y
- Arithmetic and relational operators: ADD, SUB, MUL, DIV, ABS, LSHIFT, RSHIFT, AND, OR, XOR, MODULE, INVERT, GT, GTE, LT, LTE, EQ, NOTEQ
-
Data structure:
- Supports creation, addition, deletion, replacement, and calculation of length of list data structure
- Supports creation, append, delete, replace, and calculation of length of dict data structure
Function: Supports function definition and function calls
For the PHP language, the basic language elements supported by the first phase are :
- Logic control: If, Else, Eli, While, Break, method calls
- Arithmetic and relational operators: ADD, SUB, MUL, DIV, ABS, LSHIFT, RSHIFT, AND, OR, XOR, MODULE, INVERT, GT, GTE, LT, LTE, EQ, NOTEQ
Data structure:
- Support for creating, appending, deleting, replacing, and calculating length of associative arrays
Function: Supports the definition and calling of functions
For these two above mentioned languages, the syntax highlighting and code hinting functions are also provided in BISDP, which is very convenient for developers to debug any errors.
3. Continuous exploration of distributed storage solutions
Distributed storage in blockchain technology actually refers to a distributed database. Compared with the traditional DMBS, in addition to the ACID characteristics of the traditional DBMS, the distributed database also provides the high availability and horizontal expansion of the distributed system. The CAP principle of distributed system reveals that for a common distributed system there is an impossible triangle, only two of them can be selected among its three directions, consistency, availability, and partition fault tolerance. Distributed databases in China must require strong consistency. This is due to the characteristics of the blockchain system itself, because it needs to provide reliable distributed transaction capabilities. For these technical issues, before ensuring that the distributed storage solution reaches 100% availability, we will continue to invest more time and technical strength, do more functional and performance testing, and conduct targeted tests for distributed storage systems.
4. Boosting secured multi-party computing research and development
Secured multi-party Computing (MPC) is a cryptographic mechanism that enables multiple entities to share data while protecting the confidentiality of the data without exposing the secret encryption key. Its performance indicators, such as security and reliability are important for the realization of the blockchain. The transparent sharing of the data privacy on the distributed ledger and the privacy protection of the client wallet’s private key are truly essential.
At present, the research and development status of the platform provided by Bottos in terms of privacy-enhanced secured multi-party computing is based on the BIP32 / 44 standard in Bitcoin wallets to implement distributed management of client wallet keys and privacy protection.
Considering the higher level of data security and the distributed blockchain account as the public data of each node, further research and development are being planned on:
(1) Based on RSA, Pailliar, ECDSA and other public key cryptosystems with homomorphic attributes, as well as the GC protocol, OT protocol, and ZKP protocol to generate and verify transaction signatures between two parties;
(2) Introduce the international mainstream public key system with higher security and performance, national secret public key encryption system, and fewer or non-interactive ZKP protocols to achieve secured multi-party computing with more than two parties, allowing more nodes to participate Privacy protection of ledger data.

Summary

After years of exploration, we are now full of confidence in our current research and development direction. We are totally determined to move forward by continuous hard work. In the end, all members of Bottos also want to thank all the friends in the community for their continuous support and outstanding contributions. Your certainty is our greatest comfort and strongest motivation.

Be smart. Be data-driven. Be Bottos.
If you aren’t already in our group, please join now! https://t.me/bottosofficial
Join Our Community and Stay Updated!
Bottos Website | Twitter |Facebook | Telegram | Reddit
submitted by BOTTOS_AI to Bottos [link] [comments]

After 6 years of community pressure, RedHat legal approves Elliptical Curve algorithms to be enabled in distributed packages. This makes compiling Bitcoin related software much easier!

submitted by AgentZeroM to Bitcoin [link] [comments]

Best General RenVM Questions | August 2019

Best General RenVM Questions of August 2019

These questions are sourced directly from Telegram, other monthly FAQ can be found here: https://docs.renproject.io/darknodes/community/monthly-community-faq
Q: So RenVM is essentially a BFT protocol (with 1/3 malicious nodes) that does ECDSA threshold key generation and signing? Is that right?
A: Yes, that's exactly what we have! We are exploring getting this to 1/2 and are confident it is possible, but the current implementation on Testnet is 1/3. Just today we also pushed an update that doubled the speed (and halved the bandwidth) of the sMPC signing algorithm.

Q: Have any tests been done on the speed of Interoperability?
A: The Testnet demo is live and open to the public, have a play with it and let us know about your experience (including speed). We have done some preliminary profiling; numbers look good so far. Fast enough for a single shard to keep up with Bitcoin.
The next version of RZL sMPC is under development and will introduce pre-computations that significantly increase the peak performance of RenVM from 10 TPS to over 100 TPS (these numbers are based on our initial conservative estimates).

Q: Currently, we see a quick performance of the swaps. When migrating to the mainnet (considering there will be real mainnet of say 250 Darknodes and real BTC, ETH, etc.) will it affect the speed?
A: Speed is a complex issue when it comes to RenVM. I'll try and break it down:
The biggest concern for speed is that RenVM needs to wait for a transaction to be confirmed on one chain before shifting the tokens to another chain. When working with Bitcoin this can take hours. -So latency is unavoidable (think of latency as how long a tunnel is) -So what about throughput (how wide the tunnel is)?
First, how to solve the latency problem. Well, we cannot actually solve it because we cannot change Bitcoin. But we can work around it by using "Universal Interoperability." In this model, a third party takes on the confirmation risk. While RenVM waits for the confirmation of a transaction on Bitcoin, the third party steps in and fulfills the Ethereum side of the transaction with BTC that has already been shifted previously. When the Bitcoin transaction is finally confirmed, the third party is refunded using the newly shifted BTC. This means the third party is taking on risk (the Bitcoin transaction may be shuffled away), so they charge a fee to cover this + their services. This means that the shift can be almost instant, and the only thing we need to worry about is throughput.
We believe we can get 10 TPS throughput, which is more than Bitcoin, so throughput isn't a problem (we only need to be as fast as Bitcoin). For other chains that are faster, we can introduce multiple shards. If one shard can do 10 TPS, then 10 shards can do 100 TPS.
I've described this process with Bitcoin, but it works for any pair of chains. Also, the third party cannot be guaranteed to step in (maybe they don't want to take the risk today) but if they do not, then the transaction will still go through but just at the slower speed. If the third party does step in, they're guaranteed to be refunded. So the introduction of "Universal Interoperability" does not introduce any central trust into the system.

Q: So Universal Interoperability is a partially centralized thing?
A: No because any third party can step in and provide the service. Further, the processes involved are all handled by smart contracts.

Q: Has there been a discussion of security in terms of sharding? Getting 1/3 stake and compromising a shard is obviously much easier than compromising the network, what's everyone's thoughts on that?
A: Yes there has; once you move to a sharding model, the risk of an attacker gaining control of a shard becomes a probabilistic problem rather than an absolute one (for example if you're sampling with replacement, in theory, a single attacker can corrupt the whole network).
Let's say an attacker owns enough of the network to have a 2^-1 chance of corrupting a shard (expected time to attack = ~2 days). If you are using a 20/20 multi-sig, where each shard controls one signature, then the chance of corrupting enough shards becomes 2^-20 (expected time to attack = ~2800 years).
In line with this example, the shard could be around N=24 (which would have a corruption chance of ~0.56) so each shard can be very fast (and shards would be running in parallel). Obviously we want to avoid multisigs (they're expensive and not all blockchains can support them) but this is mostly an example of the larger concept: requiring multiple shards to work together.

Q: Just got curious if the bug-fixing and developing has been overwhelming since the release of testnet? How do you feel it's been so far?
A: I wouldn't say overwhelming. It's definitely keeping us busy. Finding bugs and fixing them is actually very satisfying work; it reduces stress by increasing confidence, and this helps improve motivation and productivity.
It's also good to be able to revisit parts of the system and go about perfecting them. Often in software development, there is the adage "never optimize early". Well, the time has finally come to optimize (not just performance, but design, safety, etc.). Everyone wants the thing they build to be perfect, and being able to make that the focus is an awesome feeling.

Q: Is there a reason for having private repos?
A: It's important for the success of the network to maintain a competitive advantage, and important to avoid "day zero" bugs from people that find them but don't report (in the hopes to take advantage). We'll be getting the code (and our maths) reviewed and audited, and probably show it to first adopting groups so they can verify it themselves, and as Mainnet grows we will open-source everything, along with a Transperency Plan that outlines when and how repos will be open-sourced.

Q: My Darknodes still show the old command center. How do I view them on the new one?
A: The new Command Center is for RenVM specifically (and it's only viewable on RenVM Testnet); once we switch Darknodes over to the RenVM network, they will utilize the new Command Center.
To play around with it, put your MetaMask on Kovan Test Network. A video that a community member created can be found here: https://twitter.com/RenIsLyfe/status/1166091169853579265?s=20

Q: Digital Ocean (DO) sent me a message saying my VPS would be down for maintenance, is this an issue?
A: Nope, this is just part and parcel of using a VPS. From time to time, they need to do maintenance. They will inform you if you need to take action.
This is a real-world example of why it's crazy to expect a decentralized network to have all participants online all the time, and why you cannot "incentivize" being online by punishing being offline. It's unavoidable even when there are entire expert teams with years of experience on the job. The more nodes you have, the more likely any one of them is to experience an issue like this at any one time.
Your REN is not at risk if your Darknode does go offline. It is also unlikely that a Darknode that is offline due to these kinds of circumstances will remain offline long enough to be forced out of the network.

Q: Will the community darknodes be partaking in the RenVM Testnet, or are you using your own nodes to test it out, or is it a gradual deploy?
A: The team has about 24 Testnet Darknodes that power it. We may open these Testnet nodes up to a few groups in the Working Group, but no public participation of Testnet Darknodes will be pursued at this time.

Q: A couple of questions for the team: 1) Bonded REN value informs how much value can be securely shifted through RenVM at any given time. If bonded value drops below the threshold, are there any risks beyond incentive to collude which arise? is there any liquidation risk ala TBTCsigners? 2) Does RenVM enforce any time floors/ceilings on shifting/locking tokens? I assume anything like that would be enforced by a third party like Compound?
A: 1. There are collusion risks but we plan to mitigate this by having Darknodes able to "tell on each other" so if you are colluding with someone that you don't trust 100% you risk losing your bond so attacks only really make sense if you own all the colluding Darknodes (which, by definition, isn't really collusion it's buying up a bunch of REN). There is no liquidation risk. This is one key reason why we bond using REN, not another token; the "value of REN" is tied only to the use of RenVM. The safety of RenVM is predicated on the use of RenVM. RenVM is used = RenVM is safe
  1. No time ceilings. We've been having discussions about how to keep Darknode well incentivized to maintain long-term deposits, but (a) most of RenVM's UX is built around handling the native token, not a wrapped version of it (how is a BTC maxi going to get a hold of ETH to use their ERC20 BTC?), and (b) payments will be paid out over time to RenVM not instantly so this creates a more stable income for the Darknodes instead of large but infrequent lumps of pay, (c) we got another trick up our sleeve that I'll be adding to the GitHub any day now, (d) if you have ideas about how to incentive Darknodes to maintain BTC that is being deposited long-term, please feel free to let us know!

Q: Has there been a pattern established where third-parties could pay the gas for the eth transactions needed during shifting? For instance, would it be straightforward for an app dev to pay the gas for the user but add a small additional fee onto the RenVM transaction? They would pay the gas in ETH for the user in exchange for that value collected in BTC or zBTC?
A: This is going to be very straightforward for devs. We are designing examples as we speak to set the standard for doing this and therefore make integration as easy as possible.

Q: Can a RenVM gateway addresses be reused? As in if a user creates a gateway address for 0.1 BTC, can they send exactly 0.1 BTC that address, mint zBTC, and then repeat that process again without creating a new gateway?
A: Currently no, a gateway can only be used once; but we are in the process of creating that feature and it should be ready within the next month or so.

Q: What’s the best way to set up a Darknode if I only have Microsoft?
A: We do not formally support a Windows CLI as of right now, but we are adding Windows CLI support prior to Mainnet, so please do stay tuned.
submitted by RENProtocol to RenProject [link] [comments]

Technical: Pay-to-contract and Sign-to-contract

What's this? I don't make a Technical post for a month and now BitPay is censoring the Hong Kong Free Press? Shit I'm sorry, it's all my fault for not posting a Technical post regularly!! Now posting one so that we have a censorship-free Bitcoin universe!
Pay-to-contract and sign-to-contract are actually cryptographic techniques to allow you to embed a commitment in a public key (pay-to-contract) or signature (sign-to-contract). This commitment can be revealed independently of the public key / signature without leaking your private key, and the existence of the commitment does not prevent you from using the public key / signature as a normal pubkey/signature for a normal digital signing algorithm.
Both techniques utilize elliptic curve homomorphism. Let's digress into that a little first.

Elliptic Curve Homomorphism

Let's get an oversimplified view of the maths involved first.
First, we have two "kinds" of things we can compute on.
  1. One kind is "scalars". These are just very large single numbers. Traditionally represented by small letters.
  2. The other kind is "points". These are just pairs of large numbers. Traditionally represented by large letters.
Now, an "Elliptic Curve" is just a special kind of curve with particular mathematical properties. I won't go into those properties, for the very reasonable reason that I don't actually understand them (I'm not a cryptographer, I only play one on reddit!).
If you have an Elliptic Curve, and require that all points you work with are on some Elliptic Curve, then you can do these operations.
  1. Add, subtract, multiply, and divide scalars. Remember, scalars are just very big numbers. So those basic mathematical operations still work on big numbers, they're just big numbers.
  2. "Multiply" a scalar by a point, resulting in a point. This is written as a * B, where a is the scalar and B is a point. This is not just multiplying the scalar to the point coordinates, this is some special Elliptic Curve thing that I don't understand either.
  3. "Add" two points together. This is written as A + B. Again, this is some special Elliptic Curve thing.
The important part is that if you have:
A = a * G B = b * G Q = A + B 
Then:
q = a + b Q = q * G 
That is, if you add together two points that were each derived from multiplying an arbitarry scalar with the same point (G in the above), you get the same result as adding the scalars together first, then multiplying their sum with the same point will yield the same number. Or:
a * G + b * G = (a + b) * G 
And because multiplication is just repeated addition, the same concept applies when multiplying:
a * (b * G) = (a * b) * G = (b * a) * G = b * (a * G) 
Something to note in particular is that there are few operations on points. One operation that's missing is "dividing" a point by a point to yield a scalar. That is, if you have:
A = a * G 
Then, if you know A but don't know the scalar a, you can't do the below:
a = A / G 
You can't get a even if you know both the points A and G.
In Elliptic Curve Cryptography, scalars are used as private keys, while points are used as public keys. This is particularly useful since if you have a private key (scalar), you can derive a public key (point) from it (by multiplying the scalar with a certain standard point, which we call the "generator point", traditionally G). But there is no reverse operation to get the private key from the public key.

Commitments

Let's have another mild digression.
Sometimes, you want to "commit' to something that you want to keep hidden for now. This is actually important in some games and so on. For example, if you are paying a game of Twenty Questions, one player must first write the object they are thinking of, then fold or hide it in such a way that what they wrote is not visible. Then, after the guessing player has asked twenty questions to narrow down what the object is and has revealed what he or she thinks the object being guessed was, the guessee reveals the object by unfodling and showing the paper.
The act of writing down commits you to the specific thing you wrote down. Folding the paper and/or hiding it, err, hides what you wrote down. Later, when you unfold the paper, you reveal your commitment.
The above is the analogy to the development of cryptographic commitments.
  1. First you select some thing --- it could be anything, a song, a random number, a promise to deliver products and services, the real identity of Satoshi Nakamoto.
  2. You commit to it by giving it as input to a one-way function. A one-way function is a function which allows you to get an output from an input, but after you perform that there is no way to reverse it and determine the original input knowing only the final output. Hash functions like SHA are traditionally used as one-way functions. As a one-way function, this hides your original input.
  3. You give the commitment (the output of the one-way function given your original input) to whoever wants you to commit.
  4. Later, when somebody demands to show what you committed to (for example after playing Twenty Questions), you reveal the commitment by giving the original input to the one-way function (i.e. the thing you selected in the first step, which was the thing you wanted to commit to).
  5. Whoever challenged you can verify your commitment by feeding your supposed original input to the same one-way function. If you honestly gave the correct input, then the challenger will get the output that you published above in step 3.

Salting

Now, sometimes there are only a few possible things you can select from. For example, instead of Twenty Questions you might be playing a Coin Toss Guess game.
What we'd do would be that, for example, I am the guesser and you the guessee. You select either "heads" or "tails" and put it in a commitment which you hand over to me. Then, I say "heads" or "tails" and have you reveal your commitment. If I guessed correctly I win, if not you win.
Unfortunately, if we were to just use a one-way function like an SHA hash function, it would be very trivial for me to win. All I would need to do would be to try passing "heads" and "tails" to the one-way function and see which one matches the commitment you gave me. Then I can very easily find out what your committed value was, winning the game consistently. In hacking, this can be made easier by making Rainbow Tables, and is precisely the technique used to derive passwords from password databases containing hashes of the passwords.
The way to solve this is to add a salt. This is basically just a large random number that we prepend (or append, order doesn't matter) to the actual value you want to commit to. This means that not only do I have to feed "heads" or "tails", I also have to guess the large random number (the salt). If the possible space of large random numbers is large enough, this prevents me from being able to peek at your committed data. The salt is sometimes called a blinding factor.

Pay-to-contract

Hiding commitments in pubkeys!
Pay-to-contract allows you to publish a public key, whose private key you can derive, while also being a cryptographic commitment. In particular, your private key is also used to derive a salt.
The key insight here is to realize that "one-way function" is not restricted to hash functions like SHA. The operation below is an example of a one-way function too:
h(a) = a * G 
This results in a point, but once the point (the output) is known, it is not possible to derive the input (the scalar a above). This is of course restricted to having the input be a scalar only, instead of an arbitrary-length message, but you can add a hash function (which can accept an arbitrary-length input) and then make its output (a fixed-length scalar) as the scalar to use.
First, pay-to-contract requires you to have a public and private keypair.
; p is private key P = p * G ; P is now public key 
Then, you have to select a contract. This is just any arbitrary message containing any arbitrary thing (it could be an object for Twenty Questions, or "heads" or "tails" for Coin Toss Guessing). Traditionally, this is symbolized as the small letter s.
In order to have a pay-to-contract public key, you need to compute the below from your public key P (called the internal public key; by analogy the private key p is the internal private key):
Q = P + h(P | s) * G 
"h()" is any convenient hash function, which takes anything of arbitrary length, and outputs a scalar, which you can multiply by G. The syntax "P | s" simply means that you are prepending the point P to the contract s.
The cute thing is that P serves as your salt. Any private key is just an arbitrary random scalar. Multiplying the private key by the generator results in an arbitrary-seeming point. That random point is now your salt, which makes this into a genuine bonafide hiding cryptographic commitment!
Now Q is a point, i.e. a public key. You might be interested in knowing its private key, a scalar. Suppose you postulate the existence of a scalar q such that:
 Q = q * G 
Then you can do the below:
 Q = P + h(P | s) * G Q = p * G + h(P | s) * G Q = (p + h(P | s)) * G 
Then we can conclude that:
 q = p + h(P | s) 
Of note is that somebody else cannot learn the private key q unless they already know the private key p. Knowing the internal public key P is not enough to learn the private key q. Thus, as long as you are the only one who knows the internal private key p, and you keep it secret, then only you can learn the private key q that can be used to sign with the public key Q (that is also a pay-to-contract commitment).
Now Q is supposed to be a commitment, and once somebody else knows Q, they can challenge you to reveal your committed value, the contract s. Revealing the pay-to-contract commitment is done by simply giving the internal public key P (which doubles as the salt) and the committed value contract s.
The challenger then simply computes:
P + h(P | s) * G 
And verifies that it matches the Q you gave before.
Some very important properties are:
  1. If you reveal first, then you still remain in sole control of the private key. This is because revelation only shows the internal public key and the contract, neither of which can be used to learn the internal private key. So you can reveal and sign in any order you want, without precluding the possibility of performing the other operation in the future.
  2. If you sign with the public key Q first, then you do not need to reveal the internal public key P or the contract s. You can compute q simply from the internal private key p and the contract s. You don't even need to pass those in to your signing algorithm, it could just be given the computed q and the message you want to sign!
  3. Anyone verifying your signature using the public key Q is unaware that it is also used as a cryptographic commitment.
Another property is going to blow your mind:
  1. You don't have to know the internal private key p in order to create a commitment pay-to-contract public key Q that commits to a contract s you select.
Remember:
Q = P + h(P | s) * G 
The above equation for Q does not require that you know the internal private key p. All you need to know is the internal public key P. Since public keys are often revealed publicly, you can use somebody else's public key as the internal public key in a pay-to-contract construction.
Of course, you can't sign for Q (you need to know p to compute the private key q) but this is sometimes an interesting use.
The original proposal for pay-to-contract was that a merchant would publish their public key, then a customer would "order" by writing the contract s with what they wanted to buy. Then, the customer would generate the public key Q (committing to s) using the merchant's public key as the internal public key P, then use that in a P2PKH or P2WPKH. Then the customer would reveal the contract s to the merchant, placing their order, and the merchant would now be able to claim the money.
Another general use for pay-to-contract include publishing a commitment on the blockchain without using an OP_RETURN output. Instead, you just move some of your funds to yourself, using your own public key as the internal public key, then selecting a contract s that commits or indicates what you want to anchor onchain. This should be the preferred technique rather than OP_RETURN. For example, colored coin implementations over Bitcoin usually used OP_RETURN, but the new RGB colored coin technique uses pay-to-contract instead, reducing onchain bloat.

Taproot

Pay-to-contract is also used in the nice new Taproot concept.
Briefly, taproot anchors a Merkle tree of scripts. The root of this tree is the contract s committed to. Then, you pay to a SegWit v1 public key, where the public key is the Q pay-to-contract commitment.
When spending a coin paying to a SegWit v1 output with a Taprooted commitment to a set of scripts s, you can do one of two things:
  1. Sign directly with the key. If you used Taproot, use the commitment private key q.
  2. Reveal the commitment, then select the script you want to execute in the Merkle tree of scripts (prove the Markle tree path to the script). Then satisfy the conditions of the script.
Taproot utilizes the characteristics of pay-to-contract:
  1. If you reveal first, then you still remain in sole control of the private key.
    • This is important if you take the Taproot path and reveal the commitment to the set of scripts s. If your transaction gets stalled on the mempool, others can know your commitment details. However, revealing the commitment will not reveal the internal private key p (which is needed to derive the commitment private key q), so nobody can RBF out your transaction by using the sign-directly path.
  2. If you sign with the public key Q first, then you do not need to reveal the internal public key P or the contract s.
    • This is important for privacy. If you are able to sign with the commitment public key, then that automatically hides the fact that you could have used an alternate script s instead of the key Q.
  3. Anyone verifying your signature using the public key Q is unaware that it is also used as a cryptographic commitment.
    • Again, privacy. Fullnodes will not know that you had the ability to use an alternate script path.
Taproot is intended to be deployed with the switch to Schnorr-based signatures in SegWit v1. In particular, Schnorr-based signatures have the following ability that ECDSA cannot do except with much more difficulty:
As public keys can, with Schnorr-based signatures, easily represent an n-of-n signing set, the internal public key P can also actually be a MuSig n-of-n signing set. This allows for a number of interesting protocols, which have a "good path" that will be private if that is taken, but still have fallbacks to ensure proper execution of the protocol and prevent attempts at subverting the protocol.

Escrow Under Taproot

Traditionally, escrow is done with a 2-of-3 multisignature script.
However, by use of Taproot and pay-to-contract, it's possible to get more privacy than traditional escrow services.
Suppose we have a buyer, a seller, and an escrow service. They have keypairs B = b * G, S = s * G, and E = e * G.
The buyer and seller then generate a Taproot output (which the buyer will pay to before the seller sends the product).
The Taproot itself uses an internal public key that is the 2-of-2 MuSig of B and S, i.e. MuSig(B, S). Then it commits to a pair of possible scripts:
  1. Release to a 2-of-2 MuSig of seller and escrow. This path is the "escrow sides with seller" path.
  2. Release to a 2-of-2 MuSig of buyer and escrow. This path is the "escrow sides with buyer" path.
Now of course, the escrow also needs to learn what the transaction was supposed to be about. So what we do is that the escrow key is actually used as the internal public key of another pay-to-contract, this time with the script s containing the details of the transaction. For example, if the buyer wants to buy some USD, the contract could be "Purchase of 50 pieces of United States Federal Reserve Green Historical Commemoration papers for 0.357 satoshis".
This takes advantage of the fact that the committer need not know the private key behind the public key being used in a pay-to-contract commitment. The actual transaction it is being used for is committed to onchain, because the public key published on the blockchain ultimately commits (via a taproot to a merkle tree to a script containing a MuSig of a public key modified with the committed contract) to the contract between the buyer and seller.
Thus, the cases are:
  1. Buyer and seller are satisfied, and cooperatively create a signature that spends the output to the seller.
    • The escrow service never learns it could have been an escrow. The details of their transaction remain hidden and private, so the buyer is never embarrassed over being so tacky as to waste their hard money buying USD.
  2. The buyer and seller disagree (the buyer denies having received the goods in proper quality).
    • They contact the escrow, and reveal the existence of the onchain contract, and provide the data needed to validate just what, exactly, the transaction was supposed to be about. This includes revealing the "Purchase of 50 pieces of United States Federal Reserve Green Historical Commemoration papers for 0.357 satoshis", as well as all the data needed to validate up to that level. The escrow then investigates the situation and then decides in favor of one or the other. It signs whatever transaction it decides (either giving it to the seller or buyer), and possibly also extracts an escrow fee.

Smart Contracts Unchained

Developed by ZmnSCPxj here: https://zmnscpxj.github.io/bitcoin/unchained.html
A logical extension of the above escrow case is to realize that the "contract" being given to the escrow service is simply some text that is interpreted by the escrow, and which is then executed by the escrow to determine where the funds should go.
Now, the language given in the previous escrow example is English. But nothing prevents the contract from being written in another language, including a machine-interpretable one.
Smart Contracts Unchained simply makes the escrow service an interpreter for some Smart Contract scripting language.
The cute thing is that there still remains an "everything good" path where the participants in the smart contract all agree on what the result is. In that case, with Taproot, there is no need to publish the smart contract --- only the participants know, and nobody else has to. This is an improvement in not only privacy, but also blockchain size --- the smart contract itself never has to be published onchain, only the commitment to it is (and that is embedded in a public key, which is necessary for basic security on the blockchain anyway!).

Sign-to-contract

Hiding commitments in signatures!
Sign-to-contract is something like the dual or inverse of pay-to-contract. Instead of hiding a commitment in the public key, it is hidden in the signature.
Sign-to-contract utilizes the fact that signatures need to have a random scalar r which is then published as the point R = r * G.
Similarly to pay-to-contract, we can have an internal random scalar p and internal point P that is used to compute R:
R = P + h(P | s) * G 
The corresponding random scalar r is:
r = p + h(P | s) 
The signing algorithm then uses the modified scalar r.
This is in fact just the same method of commitment as in pay-to-contract. The operations of committing and revealing are the same. The only difference is where the commitment is stored.
Importantly, however, is that you cannot take somebody else's signature and then create an alternate signature that commits to some s you select. This is in contrast with pay-to-contract, where you can take somebody else's public key and then create an alternate public key that commits to some s you select.
Sign-to-contract is somewhat newer as a concept than pay-to-contract. It seems there are not as many applications of pay-to-contract yet.

Uses

Sign-to-contract can be used, like pay-to-contract, to publish commitments onchain.
The difference is below:
  1. Signatures are attached to transaction inputs.
  2. Public keys are attached to transaction outputs.
One possible use is in a competitor to Open Timestamps. Open Timestamps currently uses OP_RETURN to commit to a Merkle Tree root of commitments aggregated by an Open Timestamps server.
Instead of using such an OP_RETURN, individual wallets can publish a timestamped commitment by making a self-paying transaction, embedding the commitment inside the signature for that transaction. Such a feature can be added to any individual wallet software. https://blog.eternitywall.com/2018/04/13/sign-to-contract/
This does not require any additional infrastructure (i.e. no aggregating servers like in Open Timestamps).

R Reuse Concerns

ECDSA and Schnorr-based signature schemes are vulnerable to something called "R reuse".
Basically, if the same R is used for different messages (transactions) with the same public key, a third party with both signatures can compute the private key.
This is concerning especially if the signing algorithm is executed in an environment with insufficient entropy. By complete accident, the environment might yield the same random scalar r in two different runs. Combined with address reuse (which implies public key reuse) this can leak the private key inadvertently.
For example, most hardware wallets will not have any kind of entropy at all.
The usual solution to this is, instead of selecting an arbitrary random r (which might be impossible in limited environments with no available entropy), is to hash the message and use the hash as the r.
This ensures that if the same public key is used again for a different message, then the random r is also different, preventing reuse at all.
Of course, if you are using sign-to-contract, then you can't use the above "best practice".
It seems to me plausible that computing the internal random scalar p using the hash of the message (transaction) should work, then add the commitment on top of that. However, I'm not an actual cryptographer, I just play one on Reddit. Maybe apoelstra or pwuille can explain in more detail.
Copyright 2019 Alan Manuel K. Gloria. Released under CC-BY.
submitted by almkglor to Bitcoin [link] [comments]

Getting the ECDSA Z Value from a Single Input Multi Signature Transaction Konec leta 2021 bo cena Bitcoina 337.080,00 USD. Tukaj je razlog zakaj? Digital Currency Has Real Value — Here’s Why  CNBC Bitcoin Millionaire Mindset & Investing Advice 5 minut za Bitcoin: Do katere cene bo padel Bitcoin?

ECDSA and Bitcoin. For Bitcoin, we have the following parameters: Prime modulo: 2²⁵⁶ - 2³² - 2⁹ - 2⁸ - 2⁷ - 2⁶ - 2⁴ - 1 → this is a really really big number approximately equal ... This has nothing to do with RFC6979, but with ECDSA signing and public key recovery. The (r, s) is the normal output of an ECDSA signature, where r is computed as the X coordinate of a point R, modulo the curve order n. In Bitcoin, for message signatures, we use a trick called public key recovery. ECDSA. ECDSA stands for Elliptic Curve Digital Signature Algorithm. This is a Digital Signature Algorithm (DSA) that uses an elliptic curve cipher. The Bitcoin network utilizes this to ensure that only authorized parties can spend their bitcoins. Descrtiption [] Key and signature-size comparison to DSA []. As with elliptic-curve cryptography in general, the bit size of the public key believed to be needed for ECDSA is about twice the size of the security level, in bits. For example, at a security level of 80 bits (meaning an attacker requires a maximum of about 2 80 operations to find the private key) the size of an ECDSA public key ... More specifically, the Bitcoin core client software will only accept “low s-value” ECDSA signatures where a signature has a low s-value if is less or equal to half the curve order [3]. The secp256k1 curve library used by the client will always generate signatures in low s-value form and the verifier expects provided signatures to also be in ...

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Getting the ECDSA Z Value from a Single Input Multi Signature Transaction

Bitcoin price, charts, market cap, and other metrics CoinMarketCap - Get Bitcoin price, charts, and other cryptocurrency info. ... pripada par javnega in zasebnega ključa ECDSA iz domene ... A speculative store of value can be a great wealth creator assuming it becomes a store of value in the future. Bitcoin is a wealth creator in a very high-risk environment. ... the ECDSA algorithm ... Bitcoin price, charts, market cap, and other metrics CoinMarketCap - Get Bitcoin price, charts, and other cryptocurrency info. ... pripada par javnega in zasebnega ključa ECDSA iz domene ... Bitcoin price, charts, market cap, and other metrics CoinMarketCap - Get Bitcoin price, charts, and other cryptocurrency info. ... pripada par javnega in zasebnega ključa ECDSA iz domene ... Getting the ECDSA Z Value from a Bitcoin Single Input Transaction - Duration: 6:43. seanwasere ytbe 6,214 views. 6:43. 2018-01-07; Electrum PGP signature verification instructions - Duration: 20:15.

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