In these lecture notes I consider one remarkable system of differential equations that
appeared in the papers of physicists on two-dimensional topological field theory (TFT) in the …

Since the introduction of public-key cryptography by Diffie and Hellman in 1976, the
potential for the use of the discrete logarithm problem in public-key cryptosystems has been …

A bstract Recent developments involving JT gravity in two dimensions indicate that under
some conditions, a gravitational path integral is dual to an average over an ensemble of …

This is the second edition of Understanding Cryptography. Ever since we released the first
edition in 2009, we have been humbled by the many positive responses we received from …

This book studies when a prime p can be written in the form x2+ ny2. It begins at an
elementary level with results of Fermat and Euler and then discusses the work of Lagrange …

The theory of elliptic curves is distinguished by its long history and by the diversity of the
methods that have been used in its study. This book treats the arithmetic theory of elliptic …

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 …

The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag,
1986), I observed that" the theory of elliptic curves is rich, varied, and amazingly vast," and …

Differential geometry and topology have become essential tools for many theoretical
physicists. In particular, they are indispensable in theoretical studies of condensed matter …