Author: Vasyl Ustimenko

The book deals with various issues of post-quantum cryptography, a study of cryptosystems with resistance to attacks of adversaries by means of quantum cryptanalysis. It should be noted that the most popular classic cryptographic public key algorithms, which were based on the ideas of number theory (such as RSA, Diffie-Hellman and others), were broken using techniques based on a hypothetical quantum computer. Additionally, the use of quantum computers is theoretically justified by the possibility of breaking the popular number theoretical El Gamal algorithm .

The book belongs to a special direction of Noncommutative Cryptography based on algebraic structures such as groups, semigroups and noncommutative rings.. It contains materials relating to constructions of new protocols onon-commutative cryptography and their extensions in forms of cryptosystems similar to the combination of Diffie-Hellman algorithm with symmetric encryption procedure or classical El Gamal algorithm. Most of the book is dedicated to the study of certain subgroups or subsemigroups of affine Cremona semigroup CSn(K) of dimension n ≥ 2, where K is  a finite commutative ring as platforms of Noncommutative Cryptography. These subsemigroups are defined in terms of Algebraic Graphs given by equations over K. This class of graphs has some other applications to cryptography and coding theory. Therefore, this monograph delves into a very important special topic of modern cryptography, an intersection of Multivariate Cryptography in a wide sense with Noncommutative Cryptography.

The book is intended for scientists working in mathematics, and cryptography as well as lecturers, graduate and post graduate students of Mathematics and Computer science departments. Selected chapters of this book can be used for special courses or monographic lectures in Applied Mathematics and Computer Science. The book can be especially very useful for students working on their Master Theses in Computer Science, Applied Mathematics and Cryptography.