Download pdf elliptic curves and cryptography lawrence washington

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. The structure of the unit group of the integers modulo a prime explains RSA encryption, Pollard's method of factorization, Diffie—Hellman key exchange, and ElGamal encryption, while the group of points of an elliptic curve over a finite field motivates Lenstra's elliptic curve factorization method and ECC.

The only real prerequisite for this book is a course on one-variable calculus; other necessary mathematical topics are introduced on-the-fly. Numerous exercises further guide the exploration. 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.

Elliptic curves have been intensively studied in algebraic geometry and number theory. In recent years they have been used in devising efficient algorithms for factoring integers and primality proving, and in the construction of public key cryptosystems. Elliptic Curve Public Key Cryptosystems provides an up-to-date and self-contained treatment of elliptic curve-based public key cryptology.

Elliptic curve cryptosystems potentially provide equivalent security to the existing public key schemes, but with shorter key lengths.

Having short key lengths means smaller bandwidth and memory requirements and can be a crucial factor in some applications, for example the design of smart card systems. The book examines various issues which arise in the secure and efficient implementation of elliptic curve systems.

Elliptic Curve Public Key Cryptosystems is a valuable reference resource for researchers in academia, government and industry who are concerned with issues of data security.

Because of the comprehensive treatment, the book is also suitable for use as a text for advanced courses on the subject. 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.

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