Development of a New Elliptic Curve Cryptosystem with Factoring Problem

Problem statement: The security of elliptic curve cryptosystems are based on elliptic curve discrete logarithm problem (ECDLP). However, if an attacker finds a solution to ECDLP, the elliptic curve-based systems will no longer be secure. Approach: To improve this, we develop a new elliptic curve cryptosystem using one of the old/novel problem in computational number theory; factoring problem (FAC). Specifically, our encrypting and decrypting equations will heavily depends on two public keys and two secret keys respectively. Results: We show that, the newly designed cryptosystem is heuristically secure against various algebraic attacks. The complexity of the scheme shows that the time complexity for each encryption and decryption are given by 299T_mul and 270T_mul. Conclusion: The new system provides greater security than that system based on a single hard problem. The attacker has not enough resources to solve the two hard problems simultaneously in a polynomial time.