NewProof generates a Schnorr proof of knowledge of exponent for public, using the Fiat-Shamir transform.

NewRandomness creates a new a ∈ ℤₚ and the corresponding commitment C = a•G.

Commitment = randomness•G, where.

Randomness = a ← ℤₚ.

Response = randomness + H(..., commitment, public)•secret (mod p).