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LINEAR-ALGEBRA-BASED GB ALGORITHMS Built from an idea of Lazard, they are currently the most efficient They include F/5s, XL and its variants
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Multivariate Cryptography and Polynomial System Solving Complexity
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- 1 Intro
- 2 A CRYPTOGRAPHY PRIMER Main goal: Achieving privacy and security in communications
- 3 ONE-WAY TRAPDOOR FUNCTIONS M set of messages, set of cyphertexts Definition
- 4 POST-QUANTUM CRYPTOGRAPHY
- 5 MULTIVARIATE CRYPTOGRAPHY
- 6 THE MULTIVARIATE QUADRATIC PROBLEM AND GRÖNER BASES
- 7 THE IMPORTANCE OF BEING LEX Shape Lemma
- 8 LINEAR-ALGEBRA-BASED GB ALGORITHMS Built from an idea of Lazard, they are currently the most efficient They include F/5s, XL and its variants
- 9 COMPUTING A LEX GROBNER BASIS IN PRACTICE compute a drl Grobner basis using a linear algebra-based algorithm convertit into a lex one using the FGLM Algorithm For cryptographic system, the complexity…
- 10 BOUNDING THE SOLVING DEGREE
- 11 EXAMPLE - THE COMPLEXITY OF MINRANK MinRank Problem
- 12 RANDOM POLYNOMIAL SYSTEMS
- 13 HILBERT SERIES AND REGULAR SEQUENCES
- 14 REGULAR AND SEMIREGULAR SEQUENCES
- 15 SOLVING DEGREE OF SEMIREGULAR SEQUENCES
- 16 (RANDOM) REGULAR SEQUENCES OF QUADRICS
- 17 THE ABC CRYPTOSYSTEM
