AN EFFICIENT THRESHOLD SECRET SHARING SCHEME USING FAST FOURIER TRANSFORM

Abstract

Secret Sharing is a robust key management method which is having applications in password management, secure multi party computation, e-voting etc. Threshold secret sharing is a method in which out of all the parties only predefined or certain number of parties can reconstruct the secret. In this paper we will describe the most popular Shamir’s secret sharing scheme along with its limitations. In Shamir’s scheme each shareholder receives one share per secret. We can use alternative way ramp (packed variant) scheme which overcomes this limitation and reduces load on each individual shareholder. But this impacts on efficiency as degree of polynomial is increased. Either we must adjust the privacy threshold or number of shares needed to reconstruct. There is need of advance technique. An efficient secret sharing needs faster polynomial evaluation and interpolation. Here is an efficient secret sharing scheme using Fast Fourier Transform (FFT). In this polynomial evaluation as well as interpolation both speeds up. It has time complexity O(n log n).