Multivariate Public Key Cryptosystems

Beschreibung

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.
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.
Due to the fast development in MPKC, this second edition has been totally rewritten with many more new ideas and research results Presents the essential ideas, methods, and examples, so that readers will not be distracted by technical details, which can be found in the references provided Relevant software for this book is available for public use located at the book’s website, which provides interested readers a starting point to further develop their understanding and computational intuition by experimenting with the software

Autor*in

Jintai Ding

Themen in »Multivariate Public Key Cryptosystems«

Post-quantum Cryptograpy public key cryptography public key encryption digital signatures quantum computing Shor’s Algorithm quantum-resistant quantum-proof multivariate polynomials multivariate quadratic polynomials Groebner Basis XL algorithm Degree of regularity Min-Rank problem Unbalanced Oil-Vinegar Signature

Stimmen zu »Multivariate Public Key Cryptosystems«

“The book is a well-assorted collection of cryptosystems based on the problem of solving non-linear systems of polynomial equations over finite fields … . The book, in most of its contents, provides a sufficiently self-contained introduction to the design and the cryptanalysis of MPKCs and some of the chapters of the book can undoubtedly represent a useful resource for an advanced course in public-key cryptography.” (Roberto Civino, zbMATH 1506.94001, 2023)
()

Details

Link teilen