New Cryptosystem Using Multiple Cryptographic Assumptions (Report‪)‬

INTRODUCTION Many designated cryptosystems (Diffie and Hellman, 1976) in the literature were developed based on a single cryptographic assumption like algebraic geometric code (Pramod and Manju, 2010), discrete logarithms (DL) (ElGamal, 1985), factorization (FAC) (Rivest et al., 1978), quadratic residue (QR) (Rabin, 1979), elliptic curve discrete logarithm (ECDL) (Koblitz, 1987; Miller, 1986) problems. Some of them remain secure and are resistant to attacks. However, one day in the future, one could find a polynomial algorithm that can efficiently solve the underlying assumption hence break the corresponding cryptosystem easily. Many cryptographers realize it and start to develop a more secure cryptosystem. One of the methods to design such scheme is by using multiple cryptographic assumptions (Ismail et al., 2008a; Elkamchouchi et al., 2004; Harn, 1994; Baocang and Yupu, 2005; Ismail et al., 2008b; Ismail and Hijazi, 2011). The reason behind this is an adversary needs a longer period of time in order to break the multiple cryptographic assumptions-based cryptosystem since it is very unlikely for the adversary to obtain the solutions of these cryptographic assumptions simultaneously.