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The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of the Digital Signature Algorithm (DSA). It was accepted in 1999 as an ANSI standard, and was accepted in 2000 as IEEE and NIST standards. It was also accepted in 1998 as an ISO standard, and is under consideration for inclusion in some other ISO standards. Unlike the(More)
Previously, no general-purpose algorithm was known for the elliptic curve logarithm problem that ran in better than exponential time. In this paper we demonstrate the reduction of the elliptic curve logarithm problem to the logarithm problem in the multiplicative group of an extension of the underlying hit e field. For the class of supersingu-lar elliptic(More)
Since the introduction of public-key cryptography by Diffie and Hellman in 1976, the potential for the use of the discrete logarithm problem in public-key cryptosystems has been recognized. Although the discrete logarithm problem as first employed by Diffie and Hellman was defined explicitly as the problem of finding logarithms with respect to a generator(More)
The fundamental operation in elliptic curve cryptographic schemes is the multiplication of an elliptic curve point by an integer. This paper describes a new method for accelerating this operation on classes of elliptic curves that have efficiently-computable endomorphisms. One advantage of the new method is that it is applicable to a larger class of curves(More)
A normal basis in GF(qm) is a basis of the form {a p9jugate elements in the field. In GF(2' ") squaring with respect to a normal basis representation becomes simply a cyclic shift of the vector. For hardware design this is one of the very attractive features of these bases. Multiplication with respect to a normal basis can be defined in terms of a certain(More)