Multivariate public key cryptosystems
著者
書誌事項
Multivariate public key cryptosystems
（Advances in information security, 80）
Springer, 2020
2nd ed
大学図書館所蔵 全5件
注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
1 IntroductionReferences 2 Multivariate Cryptography 2.1 Multivariate Polynomials 2.2 Construction Methods for MPKC's2.3 Underlying Problems2.4 Security and Standard Attacks 2.5 Advantages and Disadvantages References 3 The Matsumoto-Imai Cryptosystem 3.1 The Basic Matsumoto-Imai Cryptosystem3.2 The Linearization Equations Attack3.3 Encryption Schemes Based on MI3.4 Signature Schemes Based on MI References 4 Hidden Field Equations 4.1 The Basic HFE Cryptosystem 4.2 Attacks on HFE 4.3 Encryption Schemes Based on HFE4.4 Signature Schemes Based on HFE References5 Oil and Vinegar 5.1 The Oil and Vinegar Signature Scheme5.2 Cryptanalysis of Balanced Oil and Vinegar and UOV5.3 Other Attacks on UOV 5.4 The Rainbow Signature Scheme5.5 Attacks on Rainbow 5.6 Reducing the Public Key Size5.7 Efficient Key Generation of Rainbow References 6 MQDSS 6.1 The MQ Based Identification Scheme 6.2 The Fiat-Shamir Transformation 6.3 The MQDSS Signature Scheme References7 The SimpleMatrix Encryption Scheme 7.1 The Basic SimpleMatrix Encryption Scheme 7.2 The Rectangular SimpleMatrix Encryption Scheme 7.3 Attacks on SimpleMatrix References 8 Solving Polynomial Systems 8.1 History of Solving Polynomial Equations 8.2 Solving Univariate Polynomials of High Degree 8.3 The XL-Algorithm8.4 Grobner Bases 8.5 Buchberger's Algorithm and F4 8.6 Estimating the Degree of Regularity8.7 Solving Over- and Underdetermined Systems ReferencesIndex List of Toy Examples Software
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