Secret sharing schemes and application to e-voting

Abstract

We present a way of sharing a secret S into n shares such that the collusion of any k shares results in the reconstruction of secret S and no k − 1 shares can do so. This way of sharing secret was first introduced by Shamir in 1979 and is named after him as Shamir’s secret sharing scheme. We then mention some of the useful properties of Shamir’s secret sharing schemes. Various approaches towards constructing a perfect secret sharing scheme are made, one of them has been constructed by Simmons using projective varieties. The theory of projective varieties helps us to construct different types of schemes according to their requirements. We show that these schemes are perfect. These enable us to secure the secret S and are reliable. They are used in many practical applications and one of them is e-voting using the internet. With the wide availability of the internet everywhere these days, there is a need for the development of an e-voting scheme. It is easy for a person to vote over the internet, hence e-voting schemes help in increasing the number of electors and thus participation in democracy. It is being used in a number of countries presently, for example Switzerland. In India, it was first introduced in Gujarat in 2011. We introduce the construction of an e- voting scheme using secret sharing schemes. Later we discuss the advantages and issues of e-voting scheme.