We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure, because the analog of the discrete logarithm problem on elliptic curves is likely to be harder than the classical discrete logarithm problem, especially over GF(2"). We discuss the question of prim...

In this paper, we present algorithms for implementation of the GHS attack to Elliptic curve cryptosystems (ECC). In particular, we consider two large classes of elliptic curves over cubic extension fields of odd characteristics which have weak covering curves against GHS attack, whose existence have been shown recently [16][17][18]. We show an algorithm to find definition equation of the coveri...

Nowadays, elliptic curve cryptosystems receive attention and much effort is being dedicated to make it more and more practical. It is worthwhile to construct discrete logarithm based cryptosystems using more general algebraic curves, because it supplies more security sources for public key cryptosystems. The presented paper introduces Cab curves. Roughly speaking, a curve is Cab if it is non-si...

Cryptographic systems based on elliptic curves have been introduced as an alternative to conventional public key cryptosystems. The security of both kinds of cryptosystems relies on the hypothesis that the underlying mathematical problems are computationally intractable, in the sense that they cannot be solved in polynomial time. In this paper, we study the performance of artificial neural netw...

This paper provides an overview of elliptic curves and their use in cryptography. The focus of the paper is on the performance advantages obtained in the wireless environments by using elliptic curve cryptography instead of traditional cryptosystems such as RSA. Specific applications to secure messaging and identity-based encryption are also discussed. keywords: elliptic curves, wireless, Digit...

Because of their shorter key sizes, cryptosystems based on elliptic curves are being increasingly used in practical applications. A special class of elliptic curves, namely, Koblitz curves, offers an additional but crucial advantage of considerably reduced processing time. In this article, power analysis attacks are applied to cryptosystems that use scalar multiplication on Koblitz curves. Both...

The security of most elliptic curve cryptosystems is based on the intractability of the Elliptic Curve Discrete Logarithm Problem (ECDLP). Such a problem turns out to be computationally unfeasible when elliptic curves are suitably chosen. This paper provides an algorithm to obtain cryptographically good elliptic curves from a given one. The core of such a procedure lies on the usage of successi...

Elliptic curve cryptosystems are expected to be a next standard of public-key cryptosystems. A security level of elliptic curve cryptosystems depends on a difficulty of a discrete logarithm problem on elliptic curves. The security level of a elliptic curve cryptosystem which has a public-key of 160-bit is equivalent to that of a RSA system which has a public-key of 1024-bit. We propose an ellip...

The security of most elliptic curve cryptosystems is based on the intractability of the Elliptic Curve Discrete Logarithm Problem (ECDLP). Such a problem turns out to be computationally unfeasible when elliptic curves are suitably chosen. This paper provides an algorithm to obtain cryptographically good elliptic curves from a given one. The core of such a procedure lies on the usage of successi...