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Investigation into the Cryptographic Properties of Elliptic Curves Defined over a Prime Field

Forensics, language: English, abstract: Elliptic curves, as used in cryptography, are essentially points bounded by a finite prime field which;

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Elliptic Curves

approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves;

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Algebraic Geometry And Its Applications

elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions;

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Elliptic Curves. (MN-40), Volume 40

analytic functions in the upper half plane with certain transformation laws and growth properties. The two subjects--elliptic curves and modular;

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Ranks of Elliptic Curves and Random Matrix Theory

, statistical properties of families of elliptic curves and their associated L-functions and the emerging uses of random matrix theory in this field;

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The Large Sieve and Its Applications

, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials;

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Algebraic Curves in Cryptography

, including algebraic geometry codes, and provide an introduction to elliptic curves. Each chapter in the remainder of the book deals with a selected;

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Algebraic Geometry

, elliptic curves, the zeta function of a curve over a finite field, and the Riemann hypothesis for elliptic curves.;

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Handbook of Elliptic and Hyperelliptic Curve Cryptography

The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The;

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Advanced Topics in the Arithmetic of Elliptic Curves

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that the theory;

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The Arithmetic of Elliptic Curves

geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and;

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Elliptic Curves

plane curve defined by a cubic polynomial. Although the problem of finding the rational points on an elliptic curve has fascinated;

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Modern Cryptography and Elliptic Curves

to gain an understanding of the arithmetic of elliptic curves over finite fields and their applications to modern cryptography. This gradual;

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Twisted L-Functions and Monodromy. (AM-150), Volume 150

of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still;

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Progress in Cryptology - LATINCRYPT 2010

selected from 62 submissions. The topics covered are encryption, elliptic curves, implementation of pairings, implementation of cryptographic;

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Arithmetic Of Elliptic Curves

of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and;

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The Arithmetic of Elliptic Curves

of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and;

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Elliptic curves and functions

An introduction in the theory of elliptic functions and elliptic curves. Both are a priori different mathematical subjects. However, there;

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Jacobi Forms Finite Quadratic Modules and Weil Representations over Number Fiel

arithmetic theory of Hilbert modular forms, its L-series, and into elliptic curves over number fields. This work is inspired by the classical theory;

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Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59

curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and;

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Complex Multiplication

of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the;

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Elementary Number Theory

This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out;

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Mordell Weil Lattices

the theory of Mordell-Weil lattices in detail, notably, relevant portions of lattice theory, elliptic curves, and algebraic surfaces. After;

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Elliptic Curves, Modular Forms and Iwasawa Theory

collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois;

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Elliptic Curves

quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the;

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Elliptic Curves

quadratic field, and on elliptic curves. Requiring only a first acquaintance with complex function theory, this book is an ideal introduction to the;

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Elliptic Curves and Big Galois Representations

The arithmetic properties of modular forms and elliptic curves lie at the heart of modern number theory. This book develops a;

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