New Constructions of (2,n)-Threshold Secret Sharing Schemes Using Exclusive-OR Operations

Fast (k, n)-threshold secret sharing schemes with exclusive-OR operations have proposed by Kurihara et al. and Fujii et al. independently. Their method are ideal that share size is equal to the size of the data to be distributed with the benefits that can be handled very fast for using only XOR operation at distribution and restoration processes. In these cases for the number of shares n, target data must be equally divided into individual n_p - 1 pieces where n_p is a prime of more than n. Contributions of this paper are the followings: (1) the number of divisions for the original data n_p - 1 is able to be less than n - 1, (2) the size of the share is able to be smaller than the size of target data, and (3) makes it possible to select the number of shares other than prime numbers. For (1) it is possible to configure as well as assumptions on the conventional method, on the other hand for (2) and (3), to construct shares by introducing a hash function, as well as a conventional XOR operation. In addition, this paper also proposes a simple and efficient method based on the idea of (2) and (3) by reconsidering a (3,2,4) ramp secret sharing scheme proposed by Matsumoto et al. announced in SCIS2012.