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 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. Keywords: Signature schemes, elliptic curve cryptography, DSA, ECDSA.

Abstract. In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has been done and, more importantly, what remains to be done in the area. We hope to show that the study of algorithms not only increases our understanding of algebraic number fields but also stimulates our curiosity about them. The discussion is concentrated of three topics: the determination of Galois groups, the determination of the ring of integers of an algebraic number field, and the computation of the group of units and the class group of that ring of integers. 1.

this document, authentication will generally refer to the use of digital signatures, which play a function for digital documents similar to that played by handwritten signatures for printed documents: the signature is an unforgeable piece of data asserting that a named person wrote or otherwise agreed to the document to which the signature is attached. The recipient, as well as a third party, can verify both that the document did indeed originate from the person whose signature is attached and that the document has not been altered since it was signed. A secure digital signature system thus consists of two parts: a method of signing a document such that forgery is infeasible, and a method of verifying that a signature was actually generated by whomever it represents. Furthermore, secure digital signatures cannot be repudiated; i.e., the signer of a document cannot later disown it by claiming it was forged.

etwork security. Mandatory reading for aspiring system managers. Antonia J. Jones:18 December 2001 2 W. Stallings. Cryptography and Network Security: Principles and Practice. Prentice Hall. 1998. ISBN 0-13-869017-0. Fills in many aspects of the present course and goes on to discuss mail and internet security. C. P. Pfleeger. Security in Computing. Prentice Hall. 1997. ISBN 0-13-185794-0. Good general introduction. The classic 1,200 page definitive story of cryptography up to the late 1950's is: D. Kahn. The Codebreakers. Scribner, New York. 1996. A recent very interesting account including the history of RSA and PGP and a non-technical discussion of quantum cryptography is: S. Singh. The Code Book. Fourth Estate, London. 1999. Fiction: Neal Stephenson. Cryptonomicon. William Heinemann, London. 1999. Antonia J. Jones:18 December 2001 3 CONTENTS I G