Secure Key Authentication Scheme Based on Discrete Logarithm and Factoring Problems

Abstract

Protecting public key from being forged or misused by enemies is very important in public key cryptosystems. Thus, key authentication process must be done to ensure that no intrusion occurred. Most researchers develop the key authentication scheme based on a single problem such as factoring, discrete logarithm, elliptic curve discrete logarithm or knapsack. Although some of these systems look secure, but due to technological advancement nowadays, it is possible that intruders can solve the single problem easily. Hence, in this paper we develop a key authentication scheme based on multiple problems; discrete logarithm and factoring problems. This research proposes a scheme with two phases; user registration phase and key authentication phase. The efficiency performance of this scheme requires \(1442T_{\text{mul}} + T_{h} + T_{\text{qrt}}\) for user registration phase and \(481T_{\text{mul}}\) for key authentication phase. Security of the scheme was proven mathematically in the security analysis and it is more secure compared to the scheme that is based on a single problem. This scheme is developed as an alternative to existing key authentication schemes and can contribute towards the development of the cryptography system based on multiple problems.