Overview
- 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
Part of the book series: Advances in Information Security (ADIS, volume 80)
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About 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.
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Keywords
- 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
- Rainbow Signature
- Algebraic Attack
Table of contents (8 chapters)
Reviews
Authors and Affiliations
About the authors
Albrecht Petzoldt received a diploma in mathematics in 2009 from FAU Erlangen-Nuremberg and a PhD in Computer Science in 2013 from Technische Universität Darmstadt / Germany. Since then he worked for several academic and non academic institutions, including Kyushu University / Japan and the National Institute of Standards and Technology (NIST) / USA. Currently, he works as a lecturer at FAU Erlangen-Nuremberg / Germany.
His main research interests are located in the field of multivariate cryptography, and in particular in thedevelopment and improvement of multivariate signature schemes such as UOV and Rainbow.
In 1966 Dieter Schmidt received his “Diplom in Mathematik” from the Technische Hochschule Stuttgart, Germany. He then went to the University of Minnesota, where he received his PhD in Mathematics in 1970. During that time he also worked for Univac and gained valuable experience in computer programming.
After an initial appointment at the University of Maryland, he accepted a position in the Department of Mathematical Sciences at the University of Cincinnati. The department started offering courses in Computer Science in the late 1970's. It was natural for him to teach some of these courses and then to join the Department of Computer Science when it was formed in 1984.
In 2002 he started his collaboration with Jintai Ding. He offered his expertise in programming in order to create the software for cryptographic schemes or the code to attack them. Although Dieter Schmidt retired from the University of Cincinnati in 2011, he has continued the collaboration with Jintai Ding.
Bibliographic Information
Book Title: Multivariate Public Key Cryptosystems
Authors: Jintai Ding, Albrecht Petzoldt, Dieter S. Schmidt
Series Title: Advances in Information Security
DOI: https://doi.org/10.1007/978-1-0716-0987-3
Publisher: Springer New York, NY
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2020
Hardcover ISBN: 978-1-0716-0985-9Published: 01 October 2020
eBook ISBN: 978-1-0716-0987-3Published: 30 September 2020
Series ISSN: 1568-2633
Series E-ISSN: 2512-2193
Edition Number: 2
Number of Pages: XXV, 253
Number of Illustrations: 30 b/w illustrations
Topics: Cryptology, Quantum Computing, Systems and Data Security, Symbolic and Algebraic Manipulation, Theory of Computation