A Fast (3,n)-Threshold Secret Sharing Scheme Using Exclusive-OR Operations

Toshiaki TANAKA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A    No.1    pp.127-138
Publication Date: 2008/01/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.1.127
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Protocols
secret sharing schemes,  xor,  entropy,  random number,  ideal secret sharing schemes,  

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In Shamir's (k,n)-threshold secret sharing 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 ≥ 3 and n is arbitrary. This paper proposes a new fast (3,n)-threshold scheme by using just EXCLUSIVE-OR(XOR) operations to make shares and recover the secret, which is an ideal secret sharing scheme similar to Shamir's scheme. Furthermore, we evaluate the efficiency of the scheme, and show that it is more efficient than Shamir's in terms of computational cost. Moreover, we suggest a fast (k,n)-threshold scheme can be constructed in a similar way by increasing the sets of random numbers constructing pieces of shares.