Multivariate public key cryptosystems. ([2020])

• Record Type: Book
• Further Information: Note: Jintai Ding, Albrecht Petzoldt, Dieter S. Schmidt.
• Authors: Ding, Jintai; Petzoldt, Albrecht; Schmidt, Dieter S
• 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
• Edition: Second edition
• Publisher Details: New York, NY : Springer
• Publication Date: 2020
• Extent: 1 online resource
• Subjects: 005.82; Computers -- Access control; Data encryption (Computer science); Computer security; Electronic books
• Languages: English
• ISBNs: 9781071609873; 1071609874
• Related ISBNs: 1071609858; 9781071609859
• Notes: Note: Includes bibliographical references and index.; Note: Description based on online resource; title from digital title page (viewed on November 25, 2020).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.