Proceedings of CRYPTO 84 on Advances in cryptology
Communications of the ACM
On the Information Rate of Secret Sharing Schemes (Extended Abstract)
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
A Fast (3,n)-Threshold Secret Sharing Scheme Using Exclusive-OR Operations
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Ideal secret sharing schemes with share selectability
ICICS'11 Proceedings of the 13th international conference on Information and communications security
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In Shamir's (k, n)-threshold secret sharing scheme (threshold scheme) [1], a heavy computational cost is required to make n shares and recover the secret from k shares. As a solution to this problem, several fast threshold schemes have been proposed. However, there is no fast ideal (k, n)-threshold scheme, where k and n are arbitrary. This paper proposes a new fast (k, n)-threshold scheme which uses just EXCLUSIVE-OR(XOR) operations to make n shares and recover the secret from k shares. We prove that every combination of k or more participants can recover the secret, but every group of less than k participants cannot obtain any information about the secret in the proposed scheme. Moreover, the proposed scheme is an ideal secret sharing scheme similar to Shamir's scheme, in which every bit-size of shares equals that of the secret. We also evaluate the efficiency of the scheme, and show that our scheme realizes operations that are much faster than Shamir's.