Integer Algorithms in Cryptology and Information Assurance

Integer Algorithms in Cryptology and Information Assurance is a collection of the author's own innovative approaches in algorithms and protocols for secret and reliable communication. It concentrates on the "what" and "how" behind implementing the proposed cryptographic algorithms rather than on formal proofs of "why" these algorithms work. The book consists of five parts (in 28 chapters) and describes the author's research results in: Innovative methods in cryptography (secret communication between initiated parties); Cryptanalysis (how to break the encryption algorithms based on computational complexity of integer factorization and discrete logarithm problems); How to provide a reliable transmission of information via unreliable communication channels and; How to exploit a synergetic effect that stems from combining the cryptographic and information assurance protocols. This text contains innovative cryptographic algorithms; computationally efficient algorithms for information assurance; new methods to solve the classical problem of integer factorization, which plays a key role in cryptanalysis; and numerous illustrative examples and tables that facilitate the understanding of the proposed algorithms. The fundamental ideas contained within are not based on temporary advances in technology, which might become obsolete in several years. The problems addressed in the book have their own intrinsic computational complexities, and the ideas and methods described in the book will remain important for years to come.