Efficient generation of elliptic curve cryptosystems
Security is one of the most important aspects in the design of system for electronic commerce, while public key cryptography is a major technique for implementing security mechanisms in the electronic world. This paper discusses the security of discrete logarithm-based public key cryptosystems and the efficiency of generating elliptic curve cryptosystems. The paper suggests a secure scheme for curve generation such that, without compromising security, the number of curves available for use by cryptosystems is substantially increased from existing techniques. In addition, the process of finding a suitable prime will be faster as the chance of finding a suitable value is higher. These features help to enhance the security of the cryptosystem in that, from a practical point of view, one can change the curve more frequently. Results from experimental analysis demonstrated the efficiency of the new curve generation scheme.
KeywordsCryptography Number theory Elliptic curve Experimental analysis
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- 1.G.B. Agnew, R.C. Mullin and S.A. Vanstone, An implementation of elliptic curve cryptosystems over F 2155', IEEE Journal on Selected Areas in Communications 11 (5) (1993) 804–813.Google Scholar
- 2.A. Menezes, T. Okamota and S.A. Vanstone, Reducing elliptic curve logarithms in a finite field, in: Proceedings 22nd Annu. ACM Symp. Theory Computing (1991) pp. 80–89.Google Scholar
- 3.A.O.L. Atkin and F. Morain, Elliptic curves and primality proving, Research Report 1256, INRIA, June 1990.Google Scholar
- 4.J. Chao, K. Tanada and S. Tsujii, Design of elliptic curves with controllable lower boundary of extension degree for reduction attacks, in: Advances in Cryptology, Proceedings of Crypto'94, Springer Verlag LNCS 837 (1994) 50–55.Google Scholar
- 5.N. Koblitz, Constructing elliptic curve cryptosystems in characteristic 2, in: Advances in Cryptology, Proceedings of Crypto'90, Springer Verlag LNCS 537 (1991) 156–167.Google Scholar
- 6.V. Miller, Uses of elliptic curves in Cryptography, in Advances in Cryptology, Proceedings of Crypto'85, Springer Verlag LNCS 218 (1986) 417–426.Google Scholar