A ramp threshold secret sharing scheme against cheating by substitution attacks
Wataru Nakamura, H. Yamamoto, Terence Chan · International Symposium on Information Theory and its Applications · 2016
In this paper, we propose a (k, L, n)-threshold ramp secret sharing scheme (SSS) against substitution attacks. This scheme can be applied to a secret SL uniformly distributed over GF(pm)L, where p is a prime satisfying p ≥ L + 2. We extend Koga and Koyano's analysis based on mutual information of shares for (k, n)-threshold SSSs to (k,L,n) ramp SSSs. The proposed scheme can achieve the minimum sizes of shares and a random number used in encoding. In addition, the success probability of substitution attack for strong (k, L, n) ramp SSSs is less than nearly L times the lower bound if the number of forged shares a satisfies 1 ≤ a ≤ k − 1, and the same holds for weak (k, L,n) ramp SSSs if a satisfies L − a ≤ k − 1.