Multivariate public key cryptosystems (MPKC) is a fast-developing area in cryptography. This book systematically presents the subject matter for a broad audience and is the first book to focus on this exciting new topic. Information security experts in industry can use the book as a guide for understanding what is needed to implement these cryptosystems for practical applications, and researchers in both computer science and mathematics will find it a good starting point for exploring this new field. It is also suitable as a textbook for advanced-level students.

This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others. Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories. This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.

This book constitutes the refereed proceedings of the 6th International Workshop on Post-Quantum Cryptography, PQCrypto 2014, held in Waterloo, ON, Canada, in October 2014. The 16 revised full papers presented were carefully reviewed and selected from 37 submissions. The papers cover all technical aspects of cryptographic research related to the future world with large quantum computers such as code-based cryptography, lattice-based cryptography, multivariate cryptography, isogeny-based cryptography, security proof frameworks, cryptanalysis and implementations.

This book discusses the current research concerning public key cryptosystems. It begins with an introduction to the basic concepts of multivariate cryptography and the history of this field. The authors provide a detailed description and security analysis of the most important multivariate public key schemes, including the four multivariate signature schemes participating as second round candidates in the NIST standardization process for post-quantum cryptosystems. Furthermore, this book covers the Simple Matrix encryption scheme, which is currently the most promising multivariate public key encryption scheme. This book also covers the current state of security analysis methods for Multivariate Public Key Cryptosystems including the algorithms and theory of solving systems of multivariate polynomial equations over finite fields. Through the book’s website, interested readers can find source code to the algorithms handled in this book. In 1994, Dr. Peter Shor from Bell Laboratories proposed a quantum algorithm solving the Integer Factorization and the Discrete Logarithm problem in polynomial time, thus making all of the currently used public key cryptosystems, such as RSA and ECC insecure. Therefore, there is an urgent need for alternative public key schemes which are resistant against quantum computer attacks. Researchers worldwide, as well as companies and governmental organizations have put a tremendous effort into the development of post-quantum public key cryptosystems to meet this challenge. One of the most promising candidates for this are Multivariate Public Key Cryptosystems (MPKCs). The public key of an MPKC is a set of multivariate polynomials over a small finite field. Especially for digital signatures, numerous well-studied multivariate schemes offering very short signatures and high efficiency exist. The fact that these schemes work over small finite fields, makes them suitable not only for interconnected computer systems, but also for small devices with limited resources, which are used in ubiquitous computing. This book gives a systematic introduction into the field of Multivariate Public Key Cryptosystems (MPKC), and presents the most promising multivariate schemes for digital signatures and encryption. Although, this book was written more from a computational perspective, the authors try to provide the necessary mathematical background. Therefore, this book is suitable for a broad audience. This would include researchers working in either computer science or mathematics interested in this exciting new field, or as a secondary textbook for a course in MPKC suitable for beginning graduate students in mathematics or computer science. Information security experts in industry, computer scientists and mathematicians would also find this book valuable as a guide for understanding the basic mathematical structures necessary to implement multivariate cryptosystems for practical applications.

Algebraic Cryptanalysis bridges the gap between a course in cryptography, and being able to read the cryptanalytic literature. This book is divided into three parts: Part One covers the process of turning a cipher into a system of equations; Part Two covers finite field linear algebra; Part Three covers the solution of Polynomial Systems of Equations, with a survey of the methods used in practice, including SAT-solvers and the methods of Nicolas Courtois. Topics include: Analytic Combinatorics, and its application to cryptanalysis The equicomplexity of linear algebra operations Graph coloring Factoring integers via the quadratic sieve, with its applications to the cryptanalysis of RSA Algebraic Cryptanalysis is designed for advanced-level students in computer science and mathematics as a secondary text or reference book for self-guided study. This book is suitable for researchers in Applied Abstract Algebra or Algebraic Geometry who wish to find more applied topics or practitioners working for security and communications companies.

This volume consists of invited papers written by eminent researchers working in the areas of theoretical computer science. The contents of the papers reflect the current trend of research being carried out in each of the areas. Some of the areas featured are petri-nets, distributed systems, map-generating systems, Lindenmayer systems, logic, cryptography, graph grammars, probabilistic automata, array grammars and pattern recognition. Many of these areas contain open problems and it is hoped that younger research workers will be motivated to work on them. In addition, some of the models designed, constructed and presented are suitable for practical applications such as in computer graphics, cryptography and distributed computing.