Efficient Ideal Threshold Secret Sharing Schemes Based on EXCLUSIVE-OR Operations

Abstract

Most of secret sharing schemes have to be computed in a Galois field, such as Shamir’s scheme, which have relatively heavy computational cost. Kurihara et al. [1] recently proposed a fast secret sharing scheme using only Exclusive-OR(XOR) operations to make shares and recover the secret. Their proposed scheme was shown to be hundreds of times faster than Shamir’s (in GF(q=264)) in terms of both distribution and recovery with a 4.5 MB secret when k=3 and n=11. However, some steps in their scheme still need to be improved. Their security proofs were too complex and difficult to be understood and verified intuitively. In this paper, we present a conciser, cleaner, faster scheme which is also based on XOR. Moreover, we give two geometric explanations of making shares in both our and Kurihara’s schemes respectively, which would help to easier and further understand how the shares are made in the two schemes.