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| Adlai | is it OK to think of digital signatures as a trivial ZKP? I prove that I know the secret referred to by this pubkey, without revealing anything about the secret itself? | 07:07 |
|---|---|---|
| fluffypony | Adlai: I think so - in the sense that you have "zero knowledge" of the private key? | 07:09 |
| Adlai | the prover has knowledge, but transfers none of it to the verifier (in the case of bitcoin, anybody verifying the blockchain) | 07:10 |
| fluffypony | yes makes sense, although I'm unsure if there is a formal definition of the term | 07:11 |
| Adlai | ZKP is a newer concept than public key crypto, so I imagine the conventional formal definitions don't explain an older concept in terms of a newer one... this is my mental exercise to wrap my head around ZKP | 07:17 |
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| sipa | Adlai: i think a signature is a specific form of zkp yes | 07:22 |
| sipa | a very non-general one | 07:22 |
| sipa | not sure about the formal definition, though | 07:22 |
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| hearn | Adlai: technically i think a signature scheme can be called a non-interactive proof of knowledge | 07:45 |
| hearn | http://en.wikipedia.org/wiki/Proof_of_knowledge | 07:45 |
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| * Adlai adds this to the ever-growing reading list | 08:02 | |
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| andytoshi | Adlai: yes, a public key digital signature is a form of a nizk (noninteractive proof of knowledge) | 08:42 |
| andytoshi | Adlai: a term used to emphasize this is "signature of knowledge" | 08:42 |
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| andytoshi | actually i don't think it's true in general that an existentially unforgeable sig is a nizk. but this is true that schnorr signatures are nizk (and possibly ecdsa too) | 08:50 |
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| sipa | andytoshi: is it still a nizk if it has a requirement such as 'never use related nonces for the same message/key' ? | 09:00 |
| MRL-Relay | [surae] sipa probably not.. ZK protocols are built to avoid edge cases like using related nonces | 09:01 |
| MRL-Relay | [surae] in principal, a NIZK proof should be a general algorithm that proves knowledge without revealing any secret information, regardless of choices of input to the message like nonces... whereas a previously agreed-upon parameters (like the elliptic curve choice in ecdsa) could possibly ruin an NIZK scheme. but andytoshi will almost certainly correct | 09:03 |
| MRL-Relay | me on this | 09:03 |
| andytoshi | surae: the security property of nizk is roughly (a) soundness, ie it is "hard" to make a proof without a witness, (b) zero-knowledge, ie there exists a simulator which can produce a proof of any statement in the language which is statistically indistinguishable from an honest proof | 09:07 |
| andytoshi | here "simulator" is a term of art meaning an entity that can control the CRS, control the random oracle, in an interactive protocol can go back in time, etc | 09:07 |
| andytoshi | sipa: yeah, the trick is that against an adversary who controls the RO you -can't- have such a requirement, because you have to commit to the nonce before you know the hash challenge | 09:08 |
| sipa | the RO? | 09:08 |
| andytoshi | random oracle | 09:09 |
| sipa | ah random oracle | 09:09 |
| andytoshi | there are unique signature schemes which have this "no nonce reuse" condition baked into them, i expect there aren't any such schemes that are also nizks | 09:09 |
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| andytoshi | ah, this is deterministic but uses a RO ... and it is zero knowledge https://en.wikipedia.org/wiki/Boneh-Lynn-Shacham | 09:12 |
| andytoshi | (because you can set H(m) = g^y for uniformly random y, then H(m)^x is easy to compute as (g^x)^y, but H(m) will still appear to be uniformly random) | 09:13 |
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| andytoshi | here is one that is non-deterministic, but has no RO, so a simulator has no extra powers. so not a nizk: https://crypto.stanford.edu/~dabo/pubs/papers/bbsigs.pdf (page 8 is the actual scheme) | 09:16 |
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| petertodd | http://www.metzdowd.com/pipermail/cryptography/2014-December/024105.html <- "zero knowledge proofs in C++" interesting DSL for ZK proofs | 19:22 |
| zooko | petertodd: thanks! | 19:23 |
| petertodd | zooko: heh, I was thinking the exact same thing | 19:24 |
| petertodd | zooko: looks like you could implement zerocash on that library for sure | 19:25 |
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| petertodd | (er, well, to be clear, modulo alpha/productionizing issues) | 19:27 |
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| gmaxwell | oh hey, proofs for hashes. | 19:33 |
| petertodd | pity there isn't a clear license on the code :( | 19:34 |
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| gmaxwell | petertodd: you succesfully compiled it? it's a spew of template errors for me. | 19:51 |
| petertodd | gmaxwell: nah, gotta get thsi micropayment channel demo done this morning first | 19:55 |
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