On cheating immune secret sharing

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)Sigma(c)(n)= 1Sigmaalphaepsilonnuetarhoc,alpha, denoted by p ($) over bar, satisfies p ($) over bar greater than or equal to1/ 2, and the equality holds if and only if rhoc,alpha satisfies rhoc,alphaa = 1/2 for every cheating vector delta(c) and every original vector a. 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.