Cheater identification on a secret sharing scheme using GCD
Hiroshi Kai, Shigenobu Inoue · ACM communications in computer algebra · 2011
A method to identify cheaters on the Shamir's ( k, n ) threshold secret sharing scheme is proposed using rational interpolation. When a rational interpolant is computed for l shares Di, i = 1, ... , l, where l = k + 2s, then s unattainable points of the rational interpolant may identify s cheaters. The cheaters can be computed by GCD of the numerator polynomial and the denominator polynomial.