No abstract

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 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 ordinary discrete logarithm problem and the integer factorization problem, no subexponential-time algorithm is known for the elliptic curve discrete logarithm problem. For this reason, the strength-per-key-bit is substantially greater in an algorithm that uses elliptic curves. This paper describes the ANSI X9.62 ECDSA, and discusses related security, implementation, and interoperability issues.

No abstract

No abstract

Abstract. 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 than previous such methods. For this special class of curves, a speedup of up to 50% can be expected over the best general methods for point multiplication.