A Novel and Secure Multiparty Key Exchange Scheme Using Trilinear Pairing Map Based on Elliptic Curve Cryptography

Abstract

Elliptic curves have been broadly studied for more than hundred years. Recently they have become a tool in various important applied fields such as coding theory, pseudorandom bit generation, number theory algorithms, etc. Actually, elliptic curve cryptography (ECC) is an alternative technique for conventional asymmetric cryptography like RSA, DSA, and Diffie–Hellman key exchange scheme. Instead of larger key size, ECC uses smaller key size to provide the highest strength-per-bit of any cryptographic system known today. This results in faster computations, lower power consumption, and less memory allocations. Another benefit of using ECC is that authentication schemes based on ECC are much secure even if a small key size is used. ECC also provides a methodology to obtain high speed, efficient, and scalable implementations of protocols for authentication and key agreement. In the present paper, we have discussed a trilinear pairing map on finitely generated free R-modules with rank three, where R is a commutative ring with unity. A trilinear pairing on an elliptic curve is constructed and we used this pairing map to a multiparty key exchange scheme. Since the secret shared key generated among the members of the group is constructed by the contribution of each member of the group, it increases the security of the proposed scheme.