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.Contents:Introductory Notes on Security and ReliabilityEnhanced Algorithm for Modular Multiplicative InverseMultiplication of Large-Integers Based on Homogeneous PolynomialsDeterministic Algorithms for Primitive Roots and Cyclic Groups with Mutual GeneratorsPrimality Testing via Complex Integers and Pythagorean TripletsAlgorithm Generating Random PermutationExtractability of Square Roots and Divisibility TestsExtraction of Roots of Higher Order in Modular ArithmeticPublic-Key Cryptography Based on Square Roots and Complex ModulusCubic Roots of Complex Integers and Encryption with Digital IsotopesExponentiation-Free Accelerated Encryption/Decryption ProtocolCryptocol Based on Three-Dimensional Elliptic SurfaceMulti-Parametric Cryptography for Rapid Transmission of InformationScheme for Digital Signature that Always WorksHybrid Cryptographic Protocols Providing Digital SignatureControl Protocols Providing Information AssuranceInformation Assurance Based on Cubic Roots of IntegersSimultaneous Information Assurance and Encryption Based on Quintic RootsModular Equations and Integer FactorizationCounting Points on Hyper-Elliptic Curves and Integer FactorizationInteger Factorization via Constrained Discrete Logarithm ProblemDecomposability of Discrete Logarithm ProblemsDetecting Intervals and Order of Point on Elliptic CurveGeneralization of Gauss Theorem and Computation of Complex PrimesSpace Complexity of Algorithm for Modular Multiplicative InverseNew Algorithm Can Be ComputedSearch for Period of Odd FunctionOptimized Search for Maximum of Function on Large IntervalsTopological Design of Satellite Communication NetworksReadership: Integer Algorithms in Cryptology and Information Assurance would be a book of interest for researchers and developers working on telecommunication security and/or reliability, in industries such as business and banking, national security agencies, militaries, interplanetary space exploration, and telemedicine. Faculty members in Computer Science, Electrical Engineering, Information Technology, Bio-Engineering and Applied Mathematics Departments, who are planning to teach advanced courses in cryptography; graduate and PhD students; advanced undergraduate students of the same fields; and various national cryptographic societies would also find this book useful.