Updates Schnorr native and circuit verifier challenge with public key, removing salt

[howardwu]

Motivation

• Updates Schnorr native and circuit verifier challenge with public key, removing the salt.
• Updates Schnorr native and circuit randomization scheme.
• Adds CryptoRng to Signature scheme traits.

Approach

This implementation of Schnorr constructs a signature with a verifier_challenge defined as:

verifier_challenge := ToScalarField( H( prover_commitment || public_key || message_length || message ))

As part of this, the former salt has been removed. In addition, by introducing the public key to the hash, this requires rearchitecting signature randomization. Previously we employed randomization as follows:

[G] := {0, 1}*

private_key := {0, 1}*
[public_key] := private_key * [G]
message := "Hello World"
(prover_response, verifier_challenge) := Sign(private_key, message)

randomizer := {0, 1}*
[randomized_public_key] := randomizer * [public_key]
randomized_prover_response := prover_response - (verifier_challenge * randomizer)
randomized_verifier_challenge := verifier_challenge

However, with the public key in the preimage of the hash, we update the scheme to continue support for randomization as follows (credits to @Pratyush):

[G] := {0, 1}*

private_key := {0, 1}*
[public_key] := private_key * [G]
message := "Hello World"
(prover_response, verifier_challenge) := Sign(private_key, message)

randomizer := {0, 1}*
randomized_private_key := private_key * randomizer
[randomized_public_key] := randomized_private_key * [G] == randomizer * [public_key]
(randomized_prover_response, randomized_verifier_challenge) := Sign(randomized_private_key, message)

Test Plan

• Updates existing Schnorr tests to reflect the new convention.
• Adds a new check that randomized_private_key * [G] == randomizer * [public_key]

[howardwu]

I can confirm that the Schnorr native and circuit tests are passing on my local machine.

[howardwu]

As this is an extension of the feat/hash_to_parameters branch with is still in draft, I am merging this branch in to prevent drift as higher-level changes are made using hash_to_curve on DPC components.