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Adding zero-knowledge #293

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Adding zero-knowledge #293

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Al-Kindi-0
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@Al-Kindi-0 Al-Kindi-0 commented Jul 23, 2024

Addresses #9 .

Based on the recent work. The most noticeable features are:

  1. We take into account the degree of the extension field when randomizing.
  2. We add randomization of the quotient segment polynomials.
  3. We add a random code-word to the DEEP composition polynomial as done in the Aurora paper.
  4. In addition to salting the vector commitment, we also salt the Fiat-Shamir as is done in the specification of the BCS transform.

This is ready for full review but I am putting in draft mode as the current solution for generating randomness for zero-knowledge is not clean. More specifically:

  1. For salted Merkle trees, should we also use a PRNG?
  2. For the PRNG used in the prover, I am not happy with the way it is currently implemented, I am thinking that it should be sort of optional to have it but I couldn't come up with a good way to do that.

There are also some unnecessary allocations but I can remove those once we agree on the general structure.

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