Inverting HFE Systems Is Quasi-Polynomial for All Fields View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2011

AUTHORS

Jintai Ding , Timothy J. Hodges

ABSTRACT

In this paper, we present and prove the first closed formula bounding the degree of regularity of an HFE system over an arbitrary finite field. Though these bounds are not necessarily optimal, they can be used to deduce if D, the degree of the corresponding HFE polynomial, and q, the size of the corresponding finite field, are fixed, inverting HFE system is polynomial for all fields; if D is of the scale O(nα) where n is the number of variables in an HFE system, and q is fixed, inverting HFE systems is quasi-polynomial for all fields. if D, the degree of the corresponding HFE polynomial, and q, the size of the corresponding finite field, are fixed, inverting HFE system is polynomial for all fields; if D is of the scale O(nα) where n is the number of variables in an HFE system, and q is fixed, inverting HFE systems is quasi-polynomial for all fields. We generalize and prove rigorously similar results by Granboulan, Joux and Stern in the case when q = 2 that were communicated at Crypto 2006. More... »

PAGES

724-742

References to SciGraph publications

  • 2003. Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases in ADVANCES IN CRYPTOLOGY - CRYPTO 2003
  • 1963. Introduction to Quadratic Forms in NONE
  • 2004. Theoretical Analysis of XL over Small Fields in INFORMATION SECURITY AND PRIVACY
  • 1988. Public Quadratic Polynomial-Tuples for Efficient Signature-Verification and Message-Encryption in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’88
  • 2011. Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants in PUBLIC KEY CRYPTOGRAPHY – PKC 2011
  • 2008. Algebraic Attack on HFE Revisited in INFORMATION SECURITY
  • 1995. Cryptanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt’88 in ADVANCES IN CRYPTOLOGY — CRYPT0’ 95
  • 2006. Inverting HFE Is Quasipolynomial in ADVANCES IN CRYPTOLOGY - CRYPTO 2006
  • 1999. Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization in ADVANCES IN CRYPTOLOGY — CRYPTO’ 99
  • 2010. The Degree of Regularity of HFE Systems in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2010
  • 2010. Growth of the Ideal Generated by a Quadratic Boolean Function in POST-QUANTUM CRYPTOGRAPHY
  • 2010. MXL3: An Efficient Algorithm for Computing Gröbner Bases of Zero-Dimensional Ideals in INFORMATION, SECURITY AND CRYPTOLOGY – ICISC 2009
  • Book

    TITLE

    Advances in Cryptology – CRYPTO 2011

    ISBN

    978-3-642-22791-2
    978-3-642-22792-9

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-22792-9_41

    DOI

    http://dx.doi.org/10.1007/978-3-642-22792-9_41

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1038551007


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