Module poly 

Utilities for distributed key generation: uni- and bivariate polynomials and commitments.

If G is a group of prime order r (written additively), and g is a generator, then multiplication by integers factors through r, so the map x -> x * g (the sum of x copies of g) is a homomorphism from the field Fr of integers modulo r to G. If the discrete logarithm is hard, i.e. it is infeasible to reverse this map, then x * g can be considered a commitment to x: By publishing it, you can guarantee to others that you won’t change your mind about the value x, without revealing it.

This concept extends to polynomials: If you have a polynomial f over Fr, defined as a * X * X + b * X + c, you can publish a * g, b * g and c * g. Then others will be able to verify any single value f(x) of the polynomial without learning the original polynomial, because f(x) * g == x * x * (a * g) + x * (b * g) + (c * g). Only after learning three (in general degree + 1) values, they can interpolate f itself.

This module defines univariate polynomials (in one variable) and symmetric bivariate polynomials (in two variables) over a field Fr, as well as their commitments in G.

Structs

BivarCommitment

A commitment to a symmetric bivariate polynomial.

BivarPoly

A symmetric bivariate polynomial in the prime field.

Commitment

A commitment to a univariate polynomial.

Poly

A univariate polynomial in the prime field.