How to share a secret with cheaters
Journal of Cryptology
How to avoid the cheaters succeeding in the key sharing scheme
Designs, Codes and Cryptography
A perfect threshold secret sharing scheme to identify cheaters
Designs, Codes and Cryptography
On sharing secrets and Reed-Solomon codes
Communications of the ACM
Communications of the ACM
Detection and identification of cheaters in (t, n) secret sharing scheme
Designs, Codes and Cryptography
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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.