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.

https://cdn.preterhuman.net/texts/cryptography/Hankerson,%20Menezes,%20Vanstone.%20Guide%20to%20elliptic%20curve%20cryptography%20(Springer,%202004)(ISBN%20038795273X)(332s)_CsCr_.pdf

Guide to Elliptic Curve Cryptography

We present the first known implementation of elliptic curve cryptography over F/sub 2p/ for sensor networks based on the 8-bit, 7.3828-MHz MICA2 mote. Through instrumentation of UC Berkeley's TinySec module, we argue that, although secret-key cryptography has been tractable in this domain for some time, there has remained a need for an efficient, secure mechanism for distribution of secret keys among nodes. Although public-key infrastructure has been thought impractical, we argue, through analysis of our own implementation for TinyOS of multiplication of points on elliptic curves, that public-key infrastructure is, in fact, viable for TinySec keys' distribution, even on the MICA2. We demonstrate that public keys can be generated within 34 seconds, and that shared secrets can be distributed among nodes in a sensor network within the same, using just over 1 kilobyte of SRAM and 34 kilobytes of ROM.

/pdf/a-public-key-infrastructure-for-key-distribution-in-tinyos-328hooh214.pdf

A public-key infrastructure for key distribution in TinyOS based on elliptic curve cryptography

This paper describes the Elliptic Curve Cryptography algorithm and its suitability for smart cards.

https://dl.acm.org/doi/pdf/10.1145/1386853.1378356

Elliptic curve cryptography

Introduction to Reconfigurable Computing provides a comprehensive study of the field Reconfigurable Computing. It provides an entry point to the novice willing to move in the research field reconfigurable computing, FPGA and system on programmable chip design. The book can also be used as teaching reference for a graduate course in computer engineering, or as reference to advance electrical and computer engineers. It provides a very strong theoretical and practical background to the field of reconfigurable computing, from the early Estrins machine to the very modern architecture like coarse-grained reconfigurable device and the embedded logic devices. Apart from the introduction and the conclusion, the main chapters of the book are Architecture of reconfigurable systems, Design and implementation, High-Level Synthesis for Reconfigurable Devices, Temporal placement, On-line and Dynamic Interconnection, Designing a reconfigurable application on Xilinx Virtex FPGA, System on programmable chip, Applications.

Introduction to Reconfigurable Computing: Architectures, Algorithms, and Applications

The performance of elliptic curve based public key cryptosystems is mainly appointed by the efficiency of the underlying finite field arithmetic. This work describes two generic and scalable architectures of finite field coprocessors, which are implemented within the latest family of Field Programmable System Level Integrated Circuits FPSLIC from Atmel, Inc. The HW architectures are adapted from Karatsuba's divide and conquer algorithm and allow for a reasonable speedup of the top-level elliptic curve algorithms. The VHDL hardware models are automatically generated based on an eligible operand size, which permits the optimal utilization of a particular FPSLIC device.

/pdf/a-reconfigurable-system-on-chip-implementation-for-elliptic-3zptduhdrr.pdf

A Reconfigurable System on Chip Implementation for Elliptic Curve Cryptography over GF(2n)

The performance of elliptic curve based public key cryptosystems is mainly appointed by the efficiency of the underlying finite field arithmetic. This work describes two generic and scalable architectures of finite field coprocessors, which are implemented within the latest family of Field Programmable System Level Integrated Circuits FPSLIC from Atmel, Inc. The HW architectures are adapted from Karatsuba’s divide and conquer algorithm and allow for a reasonable speedup of the top-level elliptic curve algorithms. The VHDL hardware models are automatically generated based on an eligible operand size, which permits the optimal utilization of a particular FPSLIC device.

/pdf/a-reconfigurable-system-on-chip-implementation-for-elliptic-1zssljqo6w.pdf

A Reconfigurable System on Chip Implementation for Elliptic Curve Cryptography over \mathbb{G}\mathbb{F}\left( {2^n } \right)

This contribution describes a methodology used to efficiently implement elliptic curves (EC) over GF(p) on the 16-bit TI MSP430x33x family of low-cost microcontrollers. We show that it is possible to implement EC cryptosystems in highly constrained embedded systems and still obtain acceptable performance at low cost. We modified the EC point addition and doubling formulae to reduce the number of intermediate variables while at the same time allowingfor flexibility. We used a Generalized-Mersenne prime to implement the arithmetic in the underlying field. We take advantage of the special form of the moduli to minimize the number of precomputations needed to implement inversion via Fermat's Little theorem and the k-ary method of exponentiation. We apply these ideas to an implementation of an elliptic curve system over GF(p), where p = 2128 - 297 - 1. We show that a scalar point multiplication can be achieved in 3.4 seconds without any stored/precomputed values and the processor clocked at 1 MHz.

/pdf/efficient-implementation-of-elliptic-curve-cryptosystems-on-267l53ls1w.pdf

Efficient Implementation of Elliptic Curve Cryptosystems on the TI MSP 430x33x Family of Microcontrollers

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A Reconfigurable System on Chip Implementation for Elliptic Curve Cryptography over GF(2n)

A Reconfigurable System on Chip Implementation for Elliptic Curve Cryptography over \mathbb{G}\mathbb{F}\left( {2^n } \right)

Efficient Implementation of Elliptic Curve Cryptosystems on the TI MSP 430x33x Family of Microcontrollers