A Novel (t, n) Threshold Secret Sharing Using Dot Product of Linearly Independent Vectors

Abstract: Threshold schemes are ideally suited to situations where a group of mutually suspicious individuals with conflicting interests must cooperate. The schemes allow a user to divide portions of a secret among a participants group. Any t or more participants from a participants group of n members can cooperate to regain the original secret while (t-1) or fewer participants cannot reveal anything about the original secret. In this paper we proposed a (t, n) threshold secret sharing scheme using dot product of linearly independent vectors and Vandermonde matrix. The proposed scheme is ideal as share size is same as secret, perfect as (t-1) participants cannot retrieve any information about the secret and secure as based on dot product of problem. Also the proposed scheme can be extended for additional capabilities of secret sharing using properties of dot product of vectors.

Keywords: Secret Sharing, Network Security, Information Security, Cryptography