At the heart of modern cryptographic algorithms lies computational number theory. Written by a number theorist and practicing cryptographer, this book takes readers from basic number theory through the inner workings of ciphers and protocols, to their strengths and weaknesses.

This is the first book to take readers all the way from basic number theory through the inner workings of ciphers and protocols to their strengths and weaknesses. It is also the first book that does the number theory correctly and presents cryptosystems as practical workable algorithms. The author shows readers how to break ciphers and how to design ones that are hard to break. The book includes numerous examples of ciphers in use today and describes many algorithms in pseudocode that allows easy programming. This book will have a broad and eager audience, from those in the military to the Internet administrator and from e-commerce practitioners to hackers.

"This book contains a nice introduction to modern cryptography, with emphasis laid on the ciphers based on computational number theory. ? The reader learns to deal with large numbers in a computer and to analyze the complexity of the most basic algorithms. ? [T]he reader is not just confronted with a list of algorithms, but he/she is given the clues to assimilate the ideas behind the results ? . The book contains more than 200 interesting exercises that test the reader's understanding of the text." - Zentralblatt MATH, 1045 "The book provides an excellent text concerning cryptanalysis. ? masterly and carefully written. As the proofs are given with full details ? I can recommend it also to students." - Monatshefte fur Mathematik