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Darrel Hankerson

Bio: Darrel Hankerson is an academic researcher from Auburn University. The author has contributed to research in topics: Elliptic curve cryptography & Elliptic curve point multiplication. The author has an hindex of 19, co-authored 35 publications receiving 5026 citations.

Papers
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Book
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

Book ChapterDOI
17 Aug 2000
TL;DR: This paper presents an extensive and careful study of the software implementation on workstations of the NIST-recommended elliptic curves over binary fields and the results of the implementation in C on a Pentium II 400MHz workstation.
Abstract: This paper presents an extensive and careful study of the software implementation on workstations of the NIST-recommended elliptic curves over binary fields. We also present the results of our implementation in C on a Pentium II 400MHz workstation.

436 citations

Journal Article
TL;DR: In this article, the authors present an extensive and careful study of the software implementation on workstations of the NIST-recommended elliptic curves over binary fields, and present the results of their implementation in C on a Pentium II 400MHz workstation.
Abstract: This paper presents an extensive and careful study of the software implementation on workstations of the NIST-recommended elliptic curves over binary fields. We also present the results of our implementation in C on a Pentium II 400MHz workstation.

425 citations

Book ChapterDOI
08 Apr 2001
TL;DR: This paper presents an extensive study of the software implementation on workstations of the NIST-recommended elliptic curves over prime fields in C and assembler on a Pentium II 400MHz workstation.
Abstract: This paper presents an extensive study of the software implementation on workstations of the NIST-recommended elliptic curves over prime fields. We present the results of our implementation in C and assembler on a Pentium II 400MHz workstation. We also provide a comparison with the NIST-recommended curves over binary fields.

287 citations

Journal ArticleDOI
TL;DR: A careful analysis of elliptic curve point multiplication methods that use the point halving technique of Knudsen and Schroeppel is presented and an algorithm of Knuth is adapted to allow efficient use of projective coordinates with halving-based windowing methods for point multiplication.
Abstract: We present a careful analysis of elliptic curve point multiplication methods that use the point halving technique of Knudsen and Schroeppel and compare these methods to traditional algorithms that use point doubling. The performance advantage of halving methods is clearest in the case of point multiplication kP, where P is not known in advance and smaller field inversion to multiplication ratios generally favor halving. Although halving essentially operates on affine coordinate representations, we adapt an algorithm of Knuth to allow efficient use of projective coordinates with halving-based windowing methods for point multiplication.

189 citations


Cited by
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Proceedings ArticleDOI
11 May 2003
TL;DR: The random-pairwise keys scheme is presented, which perfectly preserves the secrecy of the rest of the network when any node is captured, and also enables node-to-node authentication and quorum-based revocation.
Abstract: Key establishment in sensor networks is a challenging problem because asymmetric key cryptosystems are unsuitable for use in resource constrained sensor nodes, and also because the nodes could be physically compromised by an adversary. We present three new mechanisms for key establishment using the framework of pre-distributing a random set of keys to each node. First, in the q-composite keys scheme, we trade off the unlikeliness of a large-scale network attack in order to significantly strengthen random key predistribution's strength against smaller-scale attacks. Second, in the multipath-reinforcement scheme, we show how to strengthen the security between any two nodes by leveraging the security of other links. Finally, we present the random-pairwise keys scheme, which perfectly preserves the secrecy of the rest of the network when any node is captured, and also enables node-to-node authentication and quorum-based revocation.

3,125 citations

Book
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

Journal ArticleDOI
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

Proceedings ArticleDOI
23 Sep 2002
TL;DR: a secure on-demand routing protocol for ad hoc networks that can be used to connect ad-hoc networks to each other without disrupting existing networks.
Abstract: An ad hoc network is a group of wireless mobile computers (or nodes), in which individual nodes cooperate by forwarding packets for each other to allow nodes to communicate beyond direct wireless transmission range. Prior research in ad hoc networking has generally studied the routing problem in a non-adversarial setting, assuming a trusted environment. In this paper, we present attacks against routing in ad hoc networks, and we present the design and performance evaluation of a new secure on-demand ad hoc network routing protocol, called Ariadne. Ariadne prevents attackers or compromised nodes from tampering with uncompromised routes consisting of uncompromised nodes, and also prevents a large number of types of Denial-of-Service attacks. In addition, Ariadne is efficient, using only highly efficient symmetric cryptographic primitives.

1,829 citations

Proceedings ArticleDOI
09 Jul 2003
TL;DR: A new, general mechanism, called packet leashes, is presented for detecting and thus defending against wormhole attacks, and a specific protocol is presented, called TIK, that implements leashes.
Abstract: As mobile ad hoc network applications are deployed, security emerges as a central requirement. In this paper, we introduce the wormhole attack, a severe attack in ad hoc networks that is particularly challenging to defend against. The wormhole attack is possible even if the attacker has not compromised any hosts, and even if all communication provides authenticity and confidentiality. In the wormhole attack, an attacker records packets (or bits) at one location in the network, tunnels them (possibly selectively) to another location, and retransmits them there into the network. The wormhole attack can form a serious threat in wireless networks, especially against many ad hoc network routing protocols and location-based wireless security systems. For example, most existing ad hoc network routing protocols, without some mechanism to defend against the wormhole attack, would be unable to find routes longer than one or two hops, severely disrupting communication. We present a new, general mechanism, called packet leashes, for detecting and thus defending against wormhole attacks, and we present a specific protocol, called TIK, that implements leashes.

1,667 citations