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

National Institute of Standards and Technology における超伝導研究及び生活

The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.

[서평]「Applied Cryptography」

Fast Fourier Transform

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 an algorithm for computing elliptic scalar multiplications on non-supersingular elliptic curves defined over GF(2m). The algorithm is an optimized version of a method described in [1], which is based on Montgomery's method [8]. Our algorithm is easy to implement in both hardware and software, works for any elliptic curve over GF(2m), requires no precomputed multiples of a point, and is faster on average than the addition-subtraction method described in draft standard IEEE P1363. In addition, the method requires less memory than projective schemes and the amount of computation needed for a scalar multiplication is fixed for all multipliers of the same binary length. Therefore, the improved method possesses many desirable features for implementing elliptic curves in restricted environments.

/pdf/fast-multiplication-on-elliptic-curves-over-gf-2m-without-1af428080e.pdf

Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation

By using Elliptic Curve Cryptography (ECC), it has been recently shown that Public-Key Cryptography (PKC) is indeed feasible on resource-constrained nodes This feasibility, however, does not necessarily mean attractiveness, as the obtained results are still not satisfactory enough In this paper, we present results on implementing ECC, as well as the related emerging field of Pairing-Based Cryptography (PBC), on two of the most popular sensor nodes By doing that, we show that PKC is not only viable, but in fact attractive for WSNs As far as we know pairing computations presented in this paper are the most efficient results on the MICA2 (8-bit/73828-MHz ATmega128L) and Tmote Sky (16-bit/8192-MHz MSP-430) nodes

/pdf/nanoecc-testing-the-limits-of-elliptic-curve-cryptography-in-1ruhlxqrax.pdf

NanoECC: testing the limits of elliptic curve cryptography in sensor networks

This paper describes three contributions for efficient implementation of elliptic curve cryptosystems in GF(2n) The first is a new method for doubling an elliptic curve point, which is simpler to implement than the fastest known method, due to Schroeppel, and which favors sparse elliptic curve coefficients The second is a generalized and improved version of the Guajardo and Paar's formulas for computing repeated doubling points The third contribution consists of a new kind of projective coordinates that provides the fastest known arithmetic on elliptic curves The algorithms resulting from this new formulation lead to a running time improvement for computing a scalar multiplication of about 17% over previous projective coordinate methods

/pdf/improved-algorithms-for-elliptic-curve-arithmetic-in-gf-2n-3kvnp2p9cv.pdf

Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)

Clustered sensor networks have been shown to increase system throughput, decrease system delay, and save energy. While those with rotating cluster heads, such as LEACH, have also advantages in terms of security, the dynamic nature of their communication makes most existing security solutions inadequate for them. In this paper, we show how random key predistribution, widely studied in the context of flat networks, can be used to secure communication in hierarchical (cluster-based) protocols such as LEACH. To our knowledge, it is the first work that investigates random key predistribution as applied to hierarchical WSNs.

/pdf/secleach-a-random-key-distribution-solution-for-securing-596xfur1kn.pdf

Ricardo Dahab

Papers

Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation

NanoECC: testing the limits of elliptic curve cryptography in sensor networks

Improved Algorithms for Elliptic Curve Arithmetic in GF(2n)

SecLEACH - A Random Key Distribution Solution for Securing Clustered Sensor Networks

TinyPBC: Pairings for authenticated identity-based non-interactive key distribution in sensor networks