Extension Field Cancellation: A New Central Trapdoor for Multivariate Quadratic Systems View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2016

AUTHORS

Alan Szepieniec , Jintai Ding , Bart Preneel

ABSTRACT

This paper introduces a new central trapdoor for multivariate quadratic (MQ) public-key cryptosystems that allows for encryption, in contrast to time-tested MQ primitives such as Unbalanced Oil and Vinegar or Hidden Field Equations which only allow for signatures. Our construction is a mixed-field scheme that exploits the commutativity of the extension field to dramatically reduce the complexity of the extension field polynomial implicitly present in the public key. However, this reduction can only be performed by the user who knows concise descriptions of two simple polynomials, which constitute the private key. After applying this transformation, the plaintext can be recovered by solving a linear system. We use the minus and projection modifiers to inoculate our scheme against known attacks. A straightforward C++ implementation confirms the efficient operation of the public key algorithms. More... »

PAGES

182-196

References to SciGraph publications

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  • 2007. Cryptanalysis of SFLASH with Slightly Modified Parameters in ADVANCES IN CRYPTOLOGY - EUROCRYPT 2007
  • 2001. The Security of Hidden Field Equations (HFE) in TOPICS IN CRYPTOLOGY — CT-RSA 2001
  • 2013. Degree of Regularity for HFEv and HFEv- in POST-QUANTUM CRYPTOGRAPHY
  • 1999. Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization in ADVANCES IN CRYPTOLOGY — CRYPTO’ 99
  • 2005. Rainbow, a New Multivariable Polynomial Signature Scheme in ROBOCUP 2005: ROBOT SOCCER WORLD CUP IX
  • 2003. Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases in ADVANCES IN CRYPTOLOGY - CRYPTO 2003
  • 2002-09-24. C−+* and HM: Variations Around Two Schemes of T. Matsumoto and H. Imai in ADVANCES IN CRYPTOLOGY — ASIACRYPT’98
  • 1995. Cryptanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt’88 in ADVANCES IN CRYPTOLOGY — CRYPT0’ 95
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  • 2001-07-13. Efficient Signature Schemes Based on Birational Permutations in ADVANCES IN CRYPTOLOGY — CRYPTO’ 93
  • 2013-10. Cryptanalysis of HFE, multi-HFE and variants for odd and even characteristic in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2013. Simple Matrix Scheme for Encryption in POST-QUANTUM CRYPTOGRAPHY
  • 2012. Cryptanalysis of Enhanced TTS, STS and All Its Variants, or: Why Cross-Terms Are Important in PROGRESS IN CRYPTOLOGY - AFRICACRYPT 2012
  • 2001-07-13. Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’96
  • 1988. Public Quadratic Polynomial-Tuples for Efficient Signature-Verification and Message-Encryption in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’88
  • 2007. Practical Cryptanalysis of SFLASH in ADVANCES IN CRYPTOLOGY - CRYPTO 2007
  • 1999-04-15. Unbalanced Oil and Vinegar Signature Schemes in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’99
  • 1998. NTRU: A ring-based public key cryptosystem in ALGORITHMIC NUMBER THEORY
  • 2011. Inverting HFE Systems Is Quasi-Polynomial for All Fields in ADVANCES IN CRYPTOLOGY – CRYPTO 2011
  • 2010. Properties of the Discrete Differential with Cryptographic Applications in POST-QUANTUM CRYPTOGRAPHY
  • Book

    TITLE

    Post-Quantum Cryptography

    ISBN

    978-3-319-29359-2
    978-3-319-29360-8

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-29360-8_12

    DOI

    http://dx.doi.org/10.1007/978-3-319-29360-8_12

    DIMENSIONS

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