Cryptology nowadays is one of the most important areas of applied mathematics, building on deep results and methods from various areas of mathematics. This text is devoted to the study of stochastic aspects of cryptology.
Besides classical topics from cryptology, the author presents chapters on probabilistic prime number tests, factorization with quantum computers, random-number generators, pseudo-random-number generators, information theory, and the birthday paradox and meet-in-the-middle attack.
In the light of the vast literature on stochastic results relevant for cryptology, this book is intended as an invitation and introduction for students, researchers, and practitioners to probabilistic and statistical issues in cryptology.
1 Classical Polyalphabetic Substitution Ciphers.- 2 RSA and Probabilistic Prime Number Tests.- 3 Factorization with Quantum Computers: Shor's Algorithm.- 4 Physical Random-Number Generators.- 5 Pseudo-random Number Generators.- 6 An Information Theory Primer.- 7 Tests for (Pseudo-)Random Number Generators.- 8 Diffie-Hellman Key Exchange.- 9 Differential Cryptanalysis.- 10 Semantic Security.- 11 *Algorithmic Complexity.- 12 Birthday Paradox and Meet-in-the-Middle Attack.- 13 Quantum Cryptography.
From the reviews:
"This book presents a large number of probabilistic aspects of cryptographic systems ... . All the classical statistical tests on random sequences are motivated and precisely detailed here. This book is surely a valuable companion to the NIST standard reference ... ." (Jérémie Bourdon, Mathematical Reviews, 2005j)
"This is an introductory text devoted to the stochastic approach to cryptology. The author selects various results and techniques to cover several important aspects of the standard and contemporary cryptology and cryptanalysis. ... The book is worth reading and is written in a clear and lucid style ... . the book provides enough bibliographical information for further reading." (Stefan Porubský, Zentralblatt MATH, Vol. 1088 (14), 2006)
