Elliptic Curve Cryptography

Hankerson, Darrel; Menezes, Alfred

doi:10.1007/0-387-23483-7_131

Cited by 805 publications

(1,665 citation statements)

References 5 publications

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“…Reference over multiplication in ONB can be found in (Reyhani, 2003;2006). According to (Hankerson et al, 2004), an elliptic curve over a finite field F 2 m is defined as the set of points that satisfies the following equation:…”

Section: Elliptic Curvesmentioning

confidence: 99%

Using Petri Net for Modeling and Analysis of a Encryption Scheme for Wireless Sensor Networks

Rodríguez¹,

Carvajal²,

Ontiveros³

et al. 2010

Petri Nets Applications

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Section: Elliptic Curvesmentioning

confidence: 99%

Using Petri Net for Modeling and Analysis of a Encryption Scheme for Wireless Sensor Networks

Rodríguez¹,

Carvajal²,

Ontiveros³

et al. 2010

Petri Nets Applications

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“…Most practical ECC implementations use special types of finite fields to improve performance; among these special field types are binary extension fields GF(2 m ), prime fields GF(p), and optimal extension fields (OEFs), i.e. extension fields GF(p m ) whose characteristic p and extension degree m are specifically selected [13]. The latter two field types allow for efficient software implementation, especially on processors equipped with a fast integer multiplier.…”

Section: Elliptic Curve Cryptographymentioning

confidence: 99%

“…The set of all points, together with a special point O (referred to as the "point at infinity"), allows to form an Abelian group with O acting as identity element. The group operation is the addition of points, which can be performed through arithmetic operations (addition, multiplication, squaring, and inversion) in the underlying field GF(2 m ) according to well-defined formulae [13]. A basic building block of all elliptic curve cryptosystems is scalar multiplication, an operation of the form k · P where k is an integer and P is a point on the curve.…”

Section: Elliptic Curve Cryptographymentioning

confidence: 99%

“…A special property of the LD scalar multiplication algorithm is the fact that it performs exactly one Madd and one Mdouble operation for each bit of the scalar k. Consequently, the total number of Madd/Mdouble operations depends only on the bitlength of k, but not on its Hamming weight, i.e. the number of "0" and "1" bits in the binary representation of k. This property helps to prevent certain side-channel attacks like simple power analysis (SPA) attacks and timing attacks [13].…”

Section: Elliptic Curve Cryptographymentioning

confidence: 99%

“…Therefore, some kind of hardware acceleration of the performance-critical operations carried out in ECC is necessary. Elliptic curve cryptography offers a multitude of implementation options for both field and curve (group) arithmetic, respectively [13]. In addition, a number of different boundaries between hardware and software are possible, which allows a system designer to find the proper trade-off between performance and silicon area.…”

Section: Introductionmentioning

confidence: 99%

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Hardware/Software Co-design of Elliptic Curve Cryptography on an 8051 Microcontroller

Koschuch

Lechner

Weitzer

et al. 2006

Lecture Notes in Computer Science

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Abstract. 8-bit microcontrollers like the 8051 still hold a considerable share of the embedded systems market and dominate in the smart card industry. The performance of 8-bit microcontrollers is often too poor for the implementation of public-key cryptography in software. In this paper we present a minimalist hardware accelerator for enabling elliptic curve cryptography (ECC) on an 8051 microcontroller. We demonstrate the importance of removing system-level performance bottlenecks caused by the transfer of operands between hardware accelerator and external RAM. The integration of a small direct memory access (DMA) unit proves vital to exploit the full potential of the hardware accelerator. Our design allows to perform a scalar multiplication over the binary extension field GF(2 191 ) in 118 msec at a clock frequency of 12 MHz. Considering performance and hardware cost, our system compares favorably with previous work on similar 8-bit platforms.

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Parallel Computers

2011

Algorithms and Parallel Computing

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Elliptic Curve Cryptography

Cited by 805 publications

References 5 publications

Using Petri Net for Modeling and Analysis of a Encryption Scheme for Wireless Sensor Networks

Using Petri Net for Modeling and Analysis of a Encryption Scheme for Wireless Sensor Networks

Hardware/Software Co-design of Elliptic Curve Cryptography on an 8051 Microcontroller

Parallel Computers

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