The question of primitive points on an elliptic curve modulo p is discussed, and a theorem on nonsmoothness of the order of the cyclic subgroup generated by a global point is given.Expand

P-adic numbers p-adic interpolation of the reimann zeta-function p-adic power series rationality of the zeta-function of a set of equations over a finite field (Part contents).

The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book… Expand

Our purpose is to describe elliptic curves with complex multiplication which in characteristic 2 have the following useful properties for constructing Diffie-Hellman type cryptosystems: (1) they are… Expand

A source of finite abelian groups suitable for cryptosystems based on the presumed intractability of the discrete logarithm problem for these groups are the jacobians of hyperelliptic curves defined over finite fields.Expand

This paper surveys the development of elliptic curve cryptosystems from their inception in 1985 by Koblitz and Miller to present day implementations.Expand

1. Cryptography.- 1. Early History.; 2. The Idea of Public Key Cryptography.; 3. The RSA Cryptosystem.; 4. Diffie-Hellman and the Digital Signature Algorithm; 5. Secret Sharing, Coin Flipping, and Time Spent on Homework.; 6. Passwords, Signatures, and Ciphers; 7. Randomized Algorithms and Complexity Classes.Expand

The book is divided into two parts. Part I gives a vivid picture of the civil rights movement in Mississippi in the years 1961–1964. Moses not only conveys the drama of impoverished black… Expand

This paper examines the implications of heightened security needs for pairing-based cryptosystems and describes three different reasons why high-security users might have concerns about the long-term viability of these systems.Expand