Degree of Regularity for HFEv and HFEv- View Full Text


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Chapter Info

DATE

2013

AUTHORS

Jintai Ding , Bo-Yin Yang

ABSTRACT

where the parameters v, D, q, and a are parameters of the cryptosystem denoting respectively the number of vinegar variables, the degree of the HFE polynomial, the base field size, and the number of removed equations, and r is the “rank” paramter which in the general case is determined by D and q as \(r=\lfloor \log_q(D-1)\rfloor +1\). In particular, setting a = 0 gives us the case of HFEv where the degree of regularity is bound by This formula provides the first solid theoretical estimate of the complexity of algebraic cryptanalysis of the HFEv- signature scheme, and as a corollary bounds on the complexity of a direct attack against the QUARTZ digital signature scheme. Based on some experimental evidence, we evaluate the complexity of solving QUARTZ directly using F4/F5 or similar Gröbner methods to be around 292. More... »

PAGES

52-66

References to SciGraph publications

  • 2003. On the Security of HFE, HFEv- and Quartz in PUBLIC KEY CRYPTOGRAPHY — PKC 2003
  • 2011. Cryptanalysis of Multivariate and Odd-Characteristic HFE Variants in PUBLIC KEY CRYPTOGRAPHY – PKC 2011
  • 2001. The Security of Hidden Field Equations (HFE) in TOPICS IN CRYPTOLOGY — CT-RSA 2001
  • 2012. Solving Underdetermined Systems of Multivariate Quadratic Equations Revisited in PUBLIC KEY CRYPTOGRAPHY – PKC 2012
  • 2010. Fast Exhaustive Search for Polynomial Systems in in CRYPTOGRAPHIC HARDWARE AND EMBEDDED SYSTEMS, CHES 2010
  • 1999. Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization in ADVANCES IN CRYPTOLOGY — CRYPTO’ 99
  • 2000. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2000
  • 2002. Solving Underdefined Systems of Multivariate Quadratic Equations in PUBLIC KEY CRYPTOGRAPHY
  • 2003. Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases in ADVANCES IN CRYPTOLOGY - CRYPTO 2003
  • 2009. Cryptanalysis of the Square Cryptosystems in ADVANCES IN CRYPTOLOGY – ASIACRYPT 2009
  • 2009. Multivariate Public Key Cryptography in POST-QUANTUM CRYPTOGRAPHY
  • 2004. Theoretical Analysis of XL over Small Fields in INFORMATION SECURITY AND PRIVACY
  • 2009. Square, a New Multivariate Encryption Scheme in TOPICS IN CRYPTOLOGY – CT-RSA 2009
  • 1995. Cryptanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt’88 in ADVANCES IN CRYPTOLOGY — CRYPT0’ 95
  • 2004. The XL-Algorithm and a Conjecture from Commutative Algebra in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2004
  • 2001. QUARTZ, 128-Bit Long Digital Signatures in TOPICS IN CRYPTOLOGY — CT-RSA 2001
  • 2005. All in the XL Family: Theory and Practice in INFORMATION SECURITY AND CRYPTOLOGY – ICISC 2004
  • 2007. Cryptanalysis of HFE with Internal Perturbation in PUBLIC KEY CRYPTOGRAPHY – PKC 2007
  • 2010. The Degree of Regularity of HFE Systems in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2010
  • 2001-07-13. Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’96
  • 1999-04-15. Unbalanced Oil and Vinegar Signature Schemes in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’99
  • 2012. Public-Key Identification Schemes Based on Multivariate Cubic Polynomials in PUBLIC KEY CRYPTOGRAPHY – PKC 2012
  • 2006. Inverting HFE Is Quasipolynomial in ADVANCES IN CRYPTOLOGY - CRYPTO 2006
  • 1983. Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations in COMPUTER ALGEBRA
  • 2011. Inverting HFE Systems Is Quasi-Polynomial for All Fields in ADVANCES IN CRYPTOLOGY – CRYPTO 2011
  • 2011. Public-Key Identification Schemes Based on Multivariate Quadratic Polynomials in ADVANCES IN CRYPTOLOGY – CRYPTO 2011
  • Book

    TITLE

    Post-Quantum Cryptography

    ISBN

    978-3-642-38615-2
    978-3-642-38616-9

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-38616-9_4

    DOI

    http://dx.doi.org/10.1007/978-3-642-38616-9_4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1041359545


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