Secure and Efficient Secret Sharing Scheme with General Access Structures Based on Elliptic Curve and Pairing

Abstract

Secret sharing techniques allow a secret to be shared among n participants in such a way that a specified subset of participant can reconstruct the secret by combining their shares. Secret sharing techniques are now the building blocks of several security protocols. Shamir's (t, n) threshold secret sharing scheme is one in which t or more participant can join together to retrieve the secret from the set of n participants. Traditional single secret sharing schemes are modified and generalized to share multiple secrets. Use of Elliptic Curve and Pairing in secret sharing is gaining more importance. The use of Elliptic Curve helps to improve the security and also the computational complexity is reduced. In this paper we propose a secret sharing scheme with a monotone generalized access structure. The scheme makes use of Shamir's scheme and Elliptic Curve pairing. The shares are chosen by the participant itself. So the consistency of the shares are ensured in this scheme. The participant shares remain secret during the reconstruction phase and this provides multi use facility where the same share can be used for the reconstruction of multiple secret. The shared secret, access structure or the participant set can be modified without updating the secret shadow of the participant. This provides dynamism and adds more flexibility to the scheme. The combiner can also verify the shares submitted by the participants during the reconstruction phase in order to identify the cheaters. The cheating detection and cheater identification is done by using bilinear pairing. This proposed scheme is simple and easy to implement compared with other generalized multi secret sharing scheme with extended capabilities using pairing.