Growth of the Ideal Generated by a Quadratic Boolean Function View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2010

AUTHORS

Jintai Ding , Timothy J. Hodges , Victoria Kruglov

ABSTRACT

We give exact formulas for the growth of the ideal Aλ for λ a quadratic element of the algebra of Boolean functions over the Galois field GF(2). That is, we calculate where Ak is the subspace of elements of degree less than or equal to k. These results clarify some of the assertions made in the article of Yang, Chen and Courtois [22,23] concerning the efficiency of the XL algorithm. More... »

PAGES

13-27

References to SciGraph publications

  • 2008-12. On solving sparse algebraic equations over finite fields in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2006. Cryptanalysis of Variants of UOV in INFORMATION SECURITY
  • 2009. Algebraic Techniques in Differential Cryptanalysis in FAST SOFTWARE ENCRYPTION
  • 2006. Multivariate Public Key Cryptosystems in NONE
  • 2004. Theoretical Analysis of XL over Small Fields in INFORMATION SECURITY AND PRIVACY
  • 2006. Algebraic Attacks on Clock-Controlled Cascade Ciphers in PROGRESS IN CRYPTOLOGY - INDOCRYPT 2006
  • 2008. On the Number of Linearly Independent Equations Generated by XL in SEQUENCES AND THEIR APPLICATIONS - SETA 2008
  • 2004. The XL-Algorithm and a Conjecture from Commutative Algebra in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2004
  • 2003. Algebraic Attacks on Combiners with Memory in ADVANCES IN CRYPTOLOGY - CRYPTO 2003
  • 2005. An Analysis of the XSL Algorithm in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2005
  • 2004. Comparison Between XL and Gröbner Basis Algorithms in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2004
  • 2003-02-28. About the XL Algorithm over GF(2) in TOPICS IN CRYPTOLOGY — CT-RSA 2003
  • 2007. Analysis of QUAD in FAST SOFTWARE ENCRYPTION
  • 2002. Cryptanalysis of Block Ciphers with Overdefined Systems of Equations in ADVANCES IN CRYPTOLOGY — ASIACRYPT 2002
  • 2004. On Asymptotic Security Estimates in XL and Gröbner Bases-Related Algebraic Cryptanalysis in INFORMATION AND COMMUNICATIONS SECURITY
  • 2005. All in the XL Family: Theory and Practice in INFORMATION SECURITY AND CRYPTOLOGY – ICISC 2004
  • 2000. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2000
  • Book

    TITLE

    Post-Quantum Cryptography

    ISBN

    978-3-642-12928-5
    978-3-642-12929-2

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-12929-2_2

    DOI

    http://dx.doi.org/10.1007/978-3-642-12929-2_2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1029294350


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