Multivariate Cryptography and Polynomial System Solving Complexity

Multivariate Cryptography and Polynomial System Solving Complexity

Society for Industrial and Applied Mathematics via YouTube Direct link

EXAMPLE - THE COMPLEXITY OF MINRANK MinRank Problem

11 of 17

11 of 17

EXAMPLE - THE COMPLEXITY OF MINRANK MinRank Problem

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Multivariate Cryptography and Polynomial System Solving Complexity

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  1. 1 Intro
  2. 2 A CRYPTOGRAPHY PRIMER Main goal: Achieving privacy and security in communications
  3. 3 ONE-WAY TRAPDOOR FUNCTIONS M set of messages, set of cyphertexts Definition
  4. 4 POST-QUANTUM CRYPTOGRAPHY
  5. 5 MULTIVARIATE CRYPTOGRAPHY
  6. 6 THE MULTIVARIATE QUADRATIC PROBLEM AND GRÖNER BASES
  7. 7 THE IMPORTANCE OF BEING LEX Shape Lemma
  8. 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. 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. 10 BOUNDING THE SOLVING DEGREE
  11. 11 EXAMPLE - THE COMPLEXITY OF MINRANK MinRank Problem
  12. 12 RANDOM POLYNOMIAL SYSTEMS
  13. 13 HILBERT SERIES AND REGULAR SEQUENCES
  14. 14 REGULAR AND SEMIREGULAR SEQUENCES
  15. 15 SOLVING DEGREE OF SEMIREGULAR SEQUENCES
  16. 16 (RANDOM) REGULAR SEQUENCES OF QUADRICS
  17. 17 THE ABC CRYPTOSYSTEM

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