Elliptic Curves and Their Applications to Cryptography: An Introduction provides a comprehensive and self-contained introduction to elliptic curves and how they are employed to secure public key cryptosystems.
Even though the elegant mathematical theory underlying cryptosystems is considerably more involved than for other systems, this text requires the reader to have only an elementary knowledge of basic algebra. The text nevertheless leads to problems at the forefront of current research, featuring chapters on point counting algorithms and security issues. The Adopted unifying approach treats with equal care elliptic curves over fields of even characteristic, which are especially suited for hardware implementations, and curves over fields of odd characteristic, which have traditionally received more attention.
Elliptic Curves and Their Applications: An Introduction has been used successfully for teaching advanced undergraduate courses.
It will be of greatest interest to mathematicians, computer scientists, and engineers who are curious about elliptic curve cryptography in practice, without losing the beauty of the underlying mathematics. Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to.
Requiring only high school-level algebra, this book explains how to implement functioning state-of-the-art cryptographic algorithms in a minimal amount of time.
Moreover, it simplifies the math and offers detailed code examples. The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases.
Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings.
It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves. Get Books. This book explains the mathematics behind practical implementations of elliptic curve systems.
Advances in Elliptic Curve Cryptography. Authors: Ian F. Blake, Gadiel Seroussi, Nigel P. Since the appearance of the authors' first volume on elliptic curve cryptography in there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tate pairings have been applied in new and important ways. Elliptic Curves. Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications.
New to. This book summarises knowledge built up within Hewlett Packard over a number of years. Highly Influenced. View 4 excerpts, cites background. Elliptic curves EC are smooth algebraic curves of abelian variety, which form a commutative group using the multiplication operation.
Elliptic curves may be dened over a variety of elds, for … Expand. View 1 excerpt, cites background. Applications of elliptic curves in public key cryptography. The most popular public key cryptosystems are based on the problem of factorization of large integers and discrete logarithm problem in finite groups, in particular in the multiplicative group of … Expand.
Binary Edwards curves in elliptic curve cryptography. Edwards curves are a new normal form for elliptic curves that exhibit some cryptographically desirable properties and advantages over the typical Weierstrass form.
Because the group law on an Edwards … Expand. Number theoretic algorithms for elliptic curves. We present new algorithms related to both theoretical and practical questions in the area of elliptic curves and class field theory. The dissertation has two main parts, as described below. Let O be … Expand.
View 2 excerpts, cites background. Efficient computation of pairings on Jacobi quartic elliptic curves. Abstract We show that finding an efficiently computable injective homomorphism from the XTR subgroup into the group of points over GF p2 of a particular type of supersingular elliptic curve is at … Expand. View 1 excerpt, references methods. The discrete logarithm problem forms the basis of numerous cryptographic systems. The most effective attack on the discrete logarithm problem in the multiplicative group of a finite field is via the … Expand.
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