Multivariate Public Key Cryptosystems

By Dieter Schmidt, Jintai Ding, Jason E Gower, et al.

Book Overview

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 Gr]obner 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

• Format: Hardcover
• Language: English
• ISBN: 1071609858
• ISBN13: 9781071609859
• Release Date: October 2020
• Publisher: Springer
• Length: 253 Pages
• Weight: 1.25 lbs.
• Dimensions: 0.7" x 6.1" x 9.2"