Cheating Immune Secret Sharing

Paolo D’Arco, Wataru Kishimoto, Douglas R. Stinson

Sabyasachi Dutta, Reihaneh Safavi–Naini

わかは 尾形, Wakaha Ogata, 俊則 荒木 +1 more

Josef Pieprzyk, Xian-Mo Zhang

The paper addresses the cheating prevention in secret sharing. We consider secret sharing with binary shares. The secret also is binary. This model allows us to use results and constructions from the well developed theory of cryptographically strong boolean functions. In particular, we prove that for given secret sharing, the average cheating probability over all cheating vectors and all original vectors, i.e., 1/n 2^n ∑ _c=1...n ∑ _α ∈V n ρ _c,α , denoted by øverlineρ , satisfies øverlineρ ≥ \frac12 , and the equality holds if and only if ρ _c,α satisfies ρ _c,α = \frac12 for every cheating vector δ _c and every original vector α . In this case the secret sharing is said to be cheating immune. We further establish a relationship between cheating-immune secret sharing and cryptographic criteria of boolean functions.This enables us to construct cheating-immune secret sharing.

Prabhanjan Ananth, Vipul Goyal, Jiahui Liu +1 more

Jie Zhang

Cheating immune secret sharing in the unconditionally secure case was investigated. Secret sharing is a k-cheating immune if any k cheaters are not better off than a participant which follows the protocol honestly. k-cheating immune secret sharing scheme under the unconditionally secure would be given. The obtained function of the secret sharing scheme is k-resilient and satisfies k-strengthened propagation criterion. Furthermore, its degree is high. So it has better cryptographic properties than that of the known results.