Takagi, Hideyuki; Morozov, Kirill

Mathematics of Post-Quantum Cryptography

This book serves as an introduction to post-quantum cryptography for students, engineers and researchers in the field of information security. It opens with an explanation on the impact of quantum algorithms to hardness of some mathematical problems underlying modern cryptosystems. It is shown that Shor's quantum algorithm solves factoring and discrete logarithm problems in polynomial time, while the best known quantum algorithm (Grover's search) to solve general decoding problem, multivariate quadratic equations and some problems on lattices still requires exponential time. Subsequently, this book presents constructions and security evaluation of identification, digital signature and public-key encryption schemes based on the later three problems that resist quantum attacks. Each chapter contains notes on the recent results with references.The distinguishable feature and importance of this book is the comprehensive description of fundamental mathematical concepts underlying the security of post-quantum cryptographic schemes. It contains a summary of the basic results in the covered areas, hereby serving as a guidance for students and researchers who begin to study this prospective area of cryptography.