This new scheme is attractive to those applications where the clients need identity protection and lightweight computation. Based on the MECDHP, we propose an authenticated D-H key agreement scheme which greatly improves client computational efficiency and protects client’s anonymity from outsiders. This paper proposes a new problem: the modified elliptic curves computational Diffie-Hellman problem (MECDHP) and proves that the MECDHP is as hard as the conventional elliptic curves computational Diffie-Hellman problem (ECDHP). As client’s privacy is a big concern in several e-commerce applications, it is desirable to extend authenticated D-H key agreement to protect client’s identity privacy. Regarding the computations of authenticated D-H key agreement, the operation of modular exponentiation is the most expensive computation, which incurs a heavy loading on those clients where either their computational capacities or their batteries are limited and precious. Authenticated Diffie-Hellman key agreement (D-H key) is the de facto building block for establishing secure session keys in many security systems.
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