test(VDF): bench rsa vs class

[0xmountaintop]

as discussed in #27

[0xmountaintop]

@omershlo I have refactored the H_g() for RSA,

and setup() for class.

However I am not quite happy about the codes, because now I need to pass x into setup?

[0xmountaintop]

and setup() for class.

tested via cargo test --lib vdf -- --test-threads=1

[0xmountaintop]

@omershlo I've also refactored RSA one now. The PR is ready, you can take a look again.

[0xmountaintop]

BTW, I've got a few questions:

1. where does prng-style h_g come from? I couldn't find it in
   • https://eprint.iacr.org/2018/712.pdf
   • https://eprint.iacr.org/2018/623.pdf
   • https://eprint.iacr.org/2018/601.pdf
2. why in https://github.com/poanetwork/vdf/blob/master/vdf/src/proof_pietrzak.rs#L45-L58, they assert iteration as an even number >=66? I couldn't find evidence for it either.
   • https://eprint.iacr.org/2018/627.pdf
   • https://eprint.iacr.org/2018/712.pdf

[omershlo]

Hi,

I see you made a bunch of commits, does it mean the PR is ready for another review ?
about your questions:

1. h_g is not specified in the papers, It is one of those things that authors love to keep abstract - they just assume that there exist a hash function mapping strings to group elements. Our implementation is something we came up with that we argue achieve the required functionality and security guarantees.

2. That's a good question - nothing come to mind immediately but I am not an expert on Pietrzak proof. I suggest opening an issue in that repo to ask, or ask in our telegram group- I would also be interested to learn.

[0xmountaintop]

Hi,

I see you made a bunch of commits, does it mean the PR is ready for another review ?
about your questions:

1. h_g is not specified in the papers, It is one of those things that authors love to keep abstract - they just assume that there exist a hash function mapping strings to group elements. Our implementation is something we came up with that we argue achieve the required functionality and security guarantees.
2. That's a good question - nothing come to mind immediately but I am not an expert on Pietrzak proof. I suggest opening an issue in that repo to ask, or ask in our telegram group- I would also be interested to learn.

yes it's ready again. @omershlo

[omershlo]

I see you use M13 prime for the modulus. In RSA the modulus should be a bi-prime ( N = p*q for p,q 1024 bit primes)

[0xmountaintop]

RSA the modulus should be a bi-prime

So a 2048 bi-prime for N?

What about using https://en.wikipedia.org/wiki/RSA_numbers#RSA-2048 here?

[omershlo]

Looks good.