Elliptic Curve Cryptography Applied for (k,n) Threshold Secret Sharing Scheme

Abstract

Invention of Secret Sharing Scheme by Adi Shamir, along with the prevalent advancements offers strong protection of the secret key in communication network. Shamir’s scheme, which is established using Lagrange Interpolation polynomial. The group manager or dealer of the group splits the secret S to be communicated into n pieces allots all the n pieces to n participants. A subgroup of t or more participants of the group come together to reconstruct the secret key. Later, the cryptanalysis of secret sharing scheme came into picture in the direction of cheater detection whose motivation is to fool the honest participants. The present paper goals to describe a modification to (k,n) threshold secret scheme using elliptic curve cryptography to avoid the dishonest shareholders and faked shares. In this scheme, the group manager or dealer distributes the shares among the participants as affine points on the elliptic curve so that the share modification by the participants or faked shares can be easily detected.