Research On Cheating Immune Secret Sharing Boolean Functions

Secret sharing is the basic cryptographic tool .A (t,n) threshold secret sharing scheme permits any group of t or more participants to access the secret. Any group of t-1 or less participants cannot recover the secret. The group operation is normally formed by a trusted combiner who collects shares from participants, computes the result and communicates it to the members of the active group. We showed that a dishonest participant can cheat by providing an invalid share to combiner. If the secret sharing in use is linear then the cheater is able to recover the valid secret from an invalid secret returned by the combiner.This paper discusses the basic of Boolean function. And using the properties of Boolean function to construct secret sharing. Cheating immune secret sharing in the unconditionally secure case was investigated. Secret sharing is a k-cheating immune secret sharing scheme under the unconditionally secure would be given. The obtained function of 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 know results.