We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure,… Expand

1: Some Topics in Elementary Number Theory. 2: Finite Fields and Quadratic Residues. 3: Cryptography. 4: Public Key. 5: Primality and Factoring. 6: Elliptic Curves.

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

We describe elliptic curves with complex multiplication which in characteristic 2 have the following useful properties for constructing Diffie-Hellman type cryptosystems: (1) they are nonsupersingular (so that one cannot use the Menezes-Okamoto-Vanstone reduction of discrete log to 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

We discuss a source of finite abelian groups suitable for cryptosystems based on the presumed intractability of the discrete logarithm problem for these groups.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