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The Elliptic Curve Digital Signature Algorithm (ECDSA)
, 1999
"... 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 consideratio ..."
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Cited by 107 (5 self)
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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 ordinary discrete logarithm problem and the integer factorization problem, no subexponentialtime algorithm is known for the elliptic curve discrete logarithm problem. For this reason, the strengthperkeybit 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.
Algorithms in algebraic number theory
 Bull. Amer. Math. Soc
, 1992
"... 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 ..."
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Cited by 42 (4 self)
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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.
Answers To Frequently Asked Questions About Today's Cryptography
, 1993
"... 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 agre ..."
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Cited by 9 (0 self)
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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.
Towards Practical NonInteractive PublicKey Cryptosystems Using NonMaximal Imaginary Quadratic Orders
, 2001
"... Abstract. We present a new noninteractive publickey distribution system based on the class group of a nonmaximal imaginary quadratic order ClðDpÞ. The main advantage of our system over earlier proposals based on ðZ=nZÞ [25,27] is that embedding id information into group elements in a cyclic subgr ..."
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Abstract. We present a new noninteractive publickey distribution system based on the class group of a nonmaximal imaginary quadratic order ClðDpÞ. The main advantage of our system over earlier proposals based on ðZ=nZÞ [25,27] is that embedding id information into group elements in a cyclic subgroup of the class group is easy (straightforward embedding into prime ideals suffices) and secure, since the entire class group is cyclic with very high probability. Computational results demonstrate that a key generation center (KGC) with modest computational resources can set up a key distribution system using reasonably secure public system parameters. In order to compute discrete logarithms in the class group, the KGC needs to know the prime factorization of Dp D1p 2. We present an algorithm for computing discrete logarithms in ClðDpÞ by reducing the problem to computing discrete logarithms in ClðD1Þ and either F p or F p 2. Our algorithm is a specific case of the more general algorithm used in the setting of ray class groups [5]. We prove—for arbitrary nonmaximal orders—that this reduction to discrete logarithms in the maximal order and a small number of finite fields has polynomial complexity if the factorization of the conductor is known.
unknown title
"... The discrete logarithm problem has played an important role in the construction of some cryptographic protocols. Hence, many of the most widely used public key cryptosystems are based on the assumption that the discrete logarithm is indeed hard to compute. In this thesis, we discuss the security of ..."
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The discrete logarithm problem has played an important role in the construction of some cryptographic protocols. Hence, many of the most widely used public key cryptosystems are based on the assumption that the discrete logarithm is indeed hard to compute. In this thesis, we discuss the security of some cryptosystems based on discrete logarithm, such as Ghodosi and Saeednia’s selfcertified grouporiented cryptosystem and Seo and Sweeney’s simple authenticated key agreement protocol. In addition, we further construct a practical model that embeds the concept of an IDBased system into all of the cryptosystems based on the discrete logarithm, while maintaining the original security level. We not only design a transformation process to provide solutions rather than to reinvent a new scheme but also keep all the advantages of IdentityBased system such as the publickey forgeries prevention and identification
Data Security  CM 0321
, 2001
"... 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 0138690170. Fills in many aspects of the present course and goes on to discuss mail and intern ..."
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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 0138690170. 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 0131857940. 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 nontechnical 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
MODULE: Data Security
, 1996
"... Overhead slides are posted on: Overhead notes will be issued. ..."