Multivariate public key cryptosystems /

Saved in:

Bibliographic Details
Author / Creator:	Ding, Jintai, author.
Edition:	Second edition.
Imprint:	New York, NY : Springer, [2020]
Description:	1 online resource (269 p.).
Language:	English
Series:	Advances in Information Security ; volume 80 Advances in information security ; v. 80.
Subject:	Computers -- Access control. Data encryption (Computer science) Computer security. Computer security. Computers -- Access control. Data encryption (Computer science) Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12608352

Hidden Bibliographic Details
Other authors / contributors:	Petzoldt, Albrecht, author. Schmidt, Dieter S., author.
ISBN:	9781071609873 1071609874 1071609858 9781071609859
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references and index. Description based on online resource; title from digital title page (viewed on November 25, 2020).
Summary:	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.
Other form:	Print version: Ding, Jintai Multivariate Public Key Cryptosystems New York, NY : Springer,c2020 9781071609859
Standard no.:	10.1007/978-1-0716-0987-3

Table of Contents:

Intro
Preface
Changes to the Previous Edition
Contents
Notations
List of Algorithms
List of Figures
List of Tables
1 Introduction
1.1 Cryptography
1.2 Public Key Cryptography
1.3 Post-Quantum Cryptography
References
2 Multivariate Cryptography
2.1 Multivariate Polynomials
2.1.1 Matrix Representation
2.1.2 Symmetric Matrices Corresponding to a Multivariate Quadratic Polynomial
2.2 Construction Methods for MPKC's
2.2.1 The Bipolar Construction
2.2.1.1 Encryption Schemes ( m ≥n)
2.2.1.2 Signature Schemes ( m ≤n)
2.2.2 Mixed Systems
2.2.2.1 Encryption Schemes (m ≥n)
2.2.2.2 Signature Schemes ( m ≤n)
2.2.3 IP Based Identification
2.2.4 MQ Based Identification
2.3 Underlying Problems
2.3.1 The MQ Problem
2.3.2 The IP Problem
2.4 Security and Standard Attacks
2.4.1 Security Categories
2.5 Advantages and Disadvantages
References
3 The Matsumoto-Imai Cryptosystem
3.1 The Basic Matsumoto-Imai Cryptosystem
3.1.1 MI as an Encryption Scheme
3.1.2 MI as a Signature Scheme
3.1.3 Degree of the Public Key Components
3.1.4 Key Sizes and Efficiency
3.1.5 Toy Example
3.2 The Linearization Equations Attack
3.2.1 Linearization Equations Attack on Matsumoto-Imai
3.2.2 Toy Example
3.3 Encryption Schemes Based on MI
3.3.1 Internal Perturbation
3.3.2 Differential Attack on PMI
3.3.3 Preventing the Differential Attack and PMI+
3.3.4 Toy Example
3.4 Signature Schemes Based on MI
3.4.1 The Minus Variation and SFlash
3.4.2 Toy Example
3.4.3 Differential Attack on SFlash
3.4.3.1 Skew Symmetric Maps
3.4.3.2 The Multiplicative Symmetry
3.4.4 Preventing the Differential Attack and PFlash
3.4.5 Toy Example
References
4 Hidden Field Equations
4.1 The Basic HFE Cryptosystem
4.1.1 HFE as an Encryption Scheme
4.1.2 HFE as a Signature Scheme
4.1.3 Key Sizes and Efficiency
4.1.4 Toy Example
4.2 Attacks on HFE
4.2.1 The Direct Attack on HFE
4.2.2 Rank Attacks of the Kipnis-Shamir Type
4.2.2.1 The Notion of Q-Rank
4.2.2.2 The Case of HFE
4.2.2.3 Kipnis-Shamir Modeling
4.2.2.4 Minors Modeling
4.2.3 Summary of the Security of HFE
4.3 Encryption Schemes Based on HFE
4.3.1 The IPHFE+ Encryption Scheme
4.3.2 Security and Efficiency
4.3.3 The ZHFE Encryption Scheme
4.3.4 Key Sizes and Efficiency
4.3.5 Cryptanalysis of ZHFE
4.4 Signature Schemes Based on HFE
4.4.1 The HFEv- Signature Scheme
4.4.2 Key Sizes and Efficiency
4.4.3 Toy Example
4.4.4 Security of HFEv-
4.4.4.1 Direct Attacks
4.4.4.2 The Kipnis-Shamir Attack on HFEv-
4.4.5 The Gui Signature Scheme
4.4.6 Security
4.4.7 Key Sizes and Efficiency
References
5 Oil and Vinegar
5.1 The Oil and Vinegar Signature Scheme
5.1.1 Properties of the Central Map
5.1.2 Key Sizes and Efficiency
5.1.3 Toy Example

Multivariate public key cryptosystems /

Similar Items