Scalar Multiplication for ECC Pedersen Commitments

[qubits4all]

Homomorphic Scalar Multiplication for ECC Pedersen Commitments

Add support to the pedersen ECC Pedersen Commitments module for homomorphic "scalar" multiplication of sealed & revealed Pedersen Commitments.

• This implements a multiply(multiplier: int) method and the associated __mul__(multiplier: int) "dunder" method on the SealedPedersenCommitment & RevealedPedersenCommitment classes, which returns another sealed (or revealed, resp.) Pedersen Commitment.
  • These methods' multiplier parameter accepts an integer in the range [0, q-1], where q := O(G): the order of the configured elliptic curve's sub-group <G> generated by the generator (base) point G.
• Therefore a multiplier of zero is valid, but this case must be handled specially to avoid producing the point-at-infinity as the homomorphic product (i.e., otherwise naive scalar multiplication produces 0 * C = O, where C is a Pedersen Commitment ECC point & O is the point-at-infinity unit element).
  • Handling a zero multiplier involves essentially reblinding, by producing a new Pedersen Commitment to the value 0, which thereby generates a new random blinding factor.

Note: This scalar homomorphic multiplication feature can also be implemented for Vector Pedersen Commitments, and that extension will be handled by another issue.