A Novel Threshold Secret Sharing Scheme Using FFT Algorithm
Abdulrakeeb M. Al-Ssulami · 2013
Abstract- Secret sharing schemes (SSS) are very important, because they are used in critical applications such as e-voting, cryptographic key distribution and sharing, secure online auctions, information hiding, and secure multiparty computation. We explained some popular algorithms of secret sharing such as threshold, graph, and visual schemes and their access structures. Besides, we discussed the limitations of those available schemes. Additionally, we proposed a novel threshold secret sharing scheme based on Fast Fourier Transform (FFT) algorithm, which is used for the first time in this paper in the field of secret sharing. That is, we exploited the robust characteristics of FFT such as linearity, reversibility, efficiency, that has time complexity of ( log)O n n, and it provided us with a wider field, complex numbers. The presented scheme is ideal; the share’s size is smaller than the secret and very secure because it depends on solving a linear system of equations generated by FFT. Thus, Our SSS combines the merits of Shamir and Blakley schemes. Keywords- Secret sharing; secret hiding; FFT algorithm; linear algebra. 1.