On Zero-Knowledge Proofs in Blockchains

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The buyer and seller do not need to trust each other or depend on bitcoin zero knowledge systems by a third party. This type of sale is inherently irreversible, potentially crosses multiple jurisdictions, and involves parties whose financial stability is uncertain—meaning that both parties either take a great deal of risk or have to make difficult arrangement.

Using a ZKCP avoids the significant transactional costs involved in a sale which can otherwise easily go wrong. I played my part in the transaction remotely from California. I first proposed the ZKCP protocol in in an article on the Bitcoin Wiki as an example of how tremendously powerful the existing primitives in Bitcoin Script already were.

My ZKCP protocol required as a building block a zero-knowledge proof for arbitrary programs. Many kind of specialized zero-knowledge proofs exist: A zero-knowledge proof for general computation is a bitcoin zero knowledge systems system which lets a person run an arbitrary program with a mixture of public and secret inputs and prove to bitcoin zero knowledge systems that this specific program accepted the inputs, without revealing anything more about its operation or the secret inputs.

As my initial write-up on ZKCP noted, no such system was readily available in but they were believed to be possible, especially under specific constraints that would have worked for ZKCP.

Since then, several bitcoin zero knowledge systems have continued to advance this work, creating compilers, performance improvements, and most critically, bitcoin zero knowledge systems tools like libsnark. Because of this work, ZKCP can now become a practical tool. Because these efficient ZKPs are cutting-edge technology which depend on new strong cryptographic assumptions, their security is not settled yet.

But in applications like ZKCP where our only alternatives are third-party trust, they can be used in ways which are a strict improvement over what we could do without them.

If you accept the existence of the zero-knowledge proof system as a black box, the rest of the ZKCP protocol is quite simple. The buyer first creates a program that can decide whether the input it is given is the data the buyer wants to buy. This program only verifies the information, it does not produce it—the buyer does not even have to have any idea how to produce it. Bitcoin zero knowledge systems example, it is easy to write a program to verify that a Sudoku solution is correct, but harder to write a Sudoku solver, Sudoku is NP-complete.

The buyer here only needs to write the solution verifier. The buyer performs the trusted setup for the proof system and sends the resulting setup information over to the seller. The seller sends Ex, Y, the proof, and his pubkey to the buyer. So the buyer initially wanted to buy an input for his program, but now he would be just as happy to buy the preimage of a hash.

As it turns out, Bitcoin already provides a way to sell hash preimages in a secure manner. The effect of this payment is that the seller can collect it if he provides the hash preimage of Y and a signature with his key. As a result, when the seller collects his payment he is forced to reveal the information that the buyer needs in order to decrypt the answer.

This Bitcoin zero knowledge systems is also the same as would be used for a cross-chain atomic swap or a lightning payment channel. Wallet support for these transactions has been implemented for Bitcoin Core in PR This wallet support is used by the sudoku ZKCP client and server available at https: There are two primary restrictions of this approach.

First, that it is interactive: And second, that the ZKP system, while fast enough to be practical, is still not very fast. For example, in our demo the ZKP system proves 5 executions of SHA and the Sudoku constraints, and takes about 20 seconds to execute on a laptop. The verification of the proof takes only a few milliseconds. In Paypub, instead of using a zero-knowledge proof the buyer is shown a random subset of the data they are attempting to buy, and the seller is forced to unlock the rest when they collect their payment.

Paypub avoids the complexity of dealing with a zero-knowledge proof— and also allowing the exchange of information that only humans can verify—, but at the cost of some vulnerability to cheating, and only being usable with a relatively large set of randomly verifiable information.

I look forward to the exciting applications people will find for them as the technology becomes increasingly practical. The first successful Zero-Knowledge Contingent Payment. The transfer involved two transactions: See the slides from the live demo.

Background I first proposed the ZKCP bitcoin zero knowledge systems in in an article on the Bitcoin Wiki as bitcoin zero knowledge systems example of bitcoin zero knowledge systems tremendously powerful bitcoin zero knowledge systems existing primitives in Bitcoin Script already were.

The seller picks a random encryption key and encrypts the information the buyer wishes to buy. Using the ZKP system, the seller proves a composite statement: Y is the sha hash of the decryption key for Ex. The buyer makes his payment to the following ScriptPubkey: Recommended View all posts Bitcoin Core 0.

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However, Z-Cash is a big deal, not primarily as a medium of exchange, but as the first practical, global deployment of a very advanced form of cryptography.

When we began socializing our cryptography research initiative among our client and partner base, we came up with a diagram illustrating the progress made by different classes of cryptographic technologies see below:. This started with keyless cryptography hashing , symmetric cryptography, public key cryptography, and highlights that the future will bring cryptography based on Zero-Knowledge-Proof and Fully Homomorphic Encryption.

Z-Cash is a cryptocurrency like Bitcoin. Its primary purpose is to allow markets to assign value to a token that is artificially scarce but easily transferrable. Unlike Bitcoin, whose design principles focused entirely on making it impossible to censor, but also made it public and allowed all parties, including law enforcement, to trace tokens as they move through the system, Z-Cash promises complete anonymity, while allowing everyone to have confidence in the resilience of the system.

How is that possible? Suffice to say, zk-SNARK makes it possible to prove to the entire world that you're entitled to make a payment and have then made it , without ever disclosing how you came into possession of the money in the first place, and with the recipient being the only one to know how much you're paying. This should make everyone's hair stand on end: When we presented our views to MEPs at a European Parliament roundtable earlier this year, we seconded an opinion that even relatively benign opposition to Bitcoin could spark a much more difficult opponent.

Z-Cash is that opponent. There is an old saying about the internet: While it can be disputed, the only effective regulation of the internet has to start with a comprehensive understanding of it. As part of our research initiative, we have shared the vision of the development of cryptographic technologies. We have been right with the timing so far:. With the successful completion of the Parameter Generation Ceremony earlier this week, and the subsequent launch of the Genesis Block of Z-Cash five hours ago, we're now witnessing the validation of the first thousand Z-Cash blocks.

We do not expect that everyone should, or even can, follow the details of the Multi-Party-Computation, or the mathematical incantations therein - in the same way that people can't be bothered to understand the intricacies of Border Gateway Protocol that ensure you can get your weekly Netflix fix. We are both glad and excited that Z-Cash has come to life as it will serve as a powerful demonstrator of this new generation of technologies.

We look forward to referring to it, and explaining how similar systems can be used, for example, to prove eligibility for insurance products without exposing personal information, or in healthcare, finance and voting. When we began socializing our cryptography research initiative among our client and partner base, we came up with a diagram illustrating the progress made by different classes of cryptographic technologies see below: