At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols.
First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as...

Sums of Squares of Integers is the first book to combine elementary methods with analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares for any s and n. This book is also the first to give a proof of Szemeredi's theorem, an important result in modern number theory. It discusses how the modern theory of modular forms complements and clarifies the classical, fundamental results about sums of squares. This text includes applications to such...