Topic

# Elliptic Curve Digital Signature Algorithm

About: Elliptic Curve Digital Signature Algorithm is a research topic. Over the lifetime, 2053 publications have been published within this topic receiving 45571 citations. The topic is also known as: ECDSA & Elliptic Curve DSA.

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IBM

^{1}TL;DR: In this paper, an analogue of the Diffie-Hellmann key exchange protocol was proposed, which appears to be immune from attacks of the style of Western, Miller, and Adleman.

Abstract: We discuss the use of elliptic curves in cryptography. In particular, we propose an analogue of the Diffie-Hellmann key exchange protocol which appears to be immune from attacks of the style of Western, Miller, and Adleman. With the current bounds for infeasible attack, it appears to be about 20% faster than the Diffie-Hellmann scheme over GF(p). As computational power grows, this disparity should get rapidly bigger.

4,004 citations

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01 Jan 2004

TL;DR: This guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment, as well as side-channel attacks and countermeasures.

Abstract: After two decades of research and development, elliptic curve cryptography now has widespread exposure and acceptance. Industry, banking, and government standards are in place to facilitate extensive deployment of this efficient public-key mechanism. Anchored by a comprehensive treatment of the practical aspects of elliptic curve cryptography (ECC), this guide explains the basic mathematics, describes state-of-the-art implementation methods, and presents standardized protocols for public-key encryption, digital signatures, and key establishment. In addition, the book addresses some issues that arise in software and hardware implementation, as well as side-channel attacks and countermeasures. Readers receive the theoretical fundamentals as an underpinning for a wealth of practical and accessible knowledge about efficient application. Features & Benefits: * Breadth of coverage and unified, integrated approach to elliptic curve cryptosystems * Describes important industry and government protocols, such as the FIPS 186-2 standard from the U.S. National Institute for Standards and Technology * Provides full exposition on techniques for efficiently implementing finite-field and elliptic curve arithmetic* Distills complex mathematics and algorithms for easy understanding* Includes useful literature references, a list of algorithms, and appendices on sample parameters, ECC standards, and software toolsThis comprehensive, highly focused reference is a useful and indispensable resource for practitioners, professionals, or researchers in computer science, computer engineering, network design, and network data security.

2,893 citations

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TL;DR: The ANSI X9.62 ECDSA is described and related security, implementation, and interoperability issues are discussed, and the strength-per-key-bit is substantially greater in an algorithm that uses elliptic curves.

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.

2,092 citations

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Hewlett-Packard

^{1}TL;DR: In the past few years elliptic curve cryptography has moved from a fringe activity to a major challenger to the dominant RSA/DSA systems as mentioned in this paper, and it has become all pervasive.

Abstract: In the past few years elliptic curve cryptography has moved from a fringe activity to a major challenger to the dominant RSA/DSA systems. Elliptic curves offer major advances on older systems such as increased speed, less memory and smaller key sizes. As digital signatures become more and more important in the commercial world the use of elliptic curve-based signatures will become all pervasive. This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.

1,697 citations

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TL;DR: A short signature scheme based on the Computational Diffie–Hellman assumption on certain elliptic and hyperelliptic curves is introduced for systems where signatures are typed in by a human or are sent over a low-bandwidth channel.

Abstract: We introduce a short signature scheme based on the Computational Diffie–Hellman assumption on certain elliptic and hyperelliptic curves. For standard security parameters, the signature length is about half that of a DSA signature with a similar level of security. Our short signature scheme is designed for systems where signatures are typed in by a human or are sent over a low-bandwidth channel. We survey a number of properties of our signature scheme such as signature aggregation and batch verification.

1,171 citations