Paper 2011/186

Some aspects of multi-variable secret sharing

Umadevi Ganugula and Prabal Paul

Abstract

In this paper we introduce a technique that reduces a multi-variable polynomial to a single variable polynomial in such a way that it is easy to evaluate the multi-variable polynomial. Moreover, this single variable polynomial is optimal in certain cases. Based on this lemma, we propose a new optimal multi-variable secret sharing scheme. We improve upon some existing schemes. We propose a secret sharing scheme to realize a compartmental access structure scheme. Using the lemma, we prove that multi-variable secret sharing schemes are just a generalization of Shamir secret sharing scheme, which is based on single variable polynomials.

Note: The paper is being withdrawn to incorporate accurate security proofs for the schemes proposed.