A New Variant of the Matsumoto-Imai Cryptosystem through Perturbation View Full Text


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Chapter Info

DATE

2004

AUTHORS

Jintai Ding

ABSTRACT

Though the multivariable cryptosystems first suggested by Matsumoto and Imai was defeated by the linearization method of Patarin due to the special properties of the Matsumoto-Imai (MI) cryptosystem, many variants and extensions of the MI system were suggested mainly by Patarin and his collaborators. In this paper, we propose a new variant of the MI system, which was inspired by the idea of “perturbation”. This method uses a set of r (a small number) linearly independent linear functions \(z_i=\sum_{j=1}^n \alpha_{ij} x_j+\beta_i,\) i=1,..,r, over the variables x i , which are variables of the MI system. The perturbation is performed by adding random quadratic function of z i to the MI systems. The difference between our idea and a very similar idea of the Hidden Field Equation and Oil-Vinegar system is that our perturbation is internal, where we do not introduce any new variables, while the Hidden Field Equation and Oil-Vinegar system is an “external” perturbation of the HFE system, where a few extra (external) new variables are introduced to perform the perturbation. A practical implementation example of 136 bits, its security analysis and efficiency analysis are presented. The attack complexity of this perturbed Matsumoto-Imai cryptosystem is estimated. More... »

PAGES

305-318

References to SciGraph publications

  • 2001-07-13. Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): Two New Families of Asymmetric Algorithms in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’96
  • 2000-06. Cryptanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt'98 in DESIGNS, CODES AND CRYPTOGRAPHY
  • 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
  • 1988. Public Quadratic Polynomial-Tuples for Efficient Signature-Verification and Message-Encryption in ADVANCES IN CRYPTOLOGY — EUROCRYPT ’88
  • 2001-07-13. Efficient Signature Schemes Based on Birational Permutations in ADVANCES IN CRYPTOLOGY — CRYPTO’ 93
  • 2001. The Security of Hidden Field Equations (HFE) in TOPICS IN CRYPTOLOGY — CT-RSA 2001
  • 2003. A Fast and Secure Implementation of Sflash in PUBLIC KEY CRYPTOGRAPHY — PKC 2003
  • 2003. On the Security of HFE, HFEv- and Quartz in PUBLIC KEY CRYPTOGRAPHY — PKC 2003
  • 1999. Cryptanalysis of the HFE Public Key Cryptosystem by Relinearization in ADVANCES IN CRYPTOLOGY — CRYPTO’ 99
  • 2001. FLASH, a Fast Multivariate Signature Algorithm in TOPICS IN CRYPTOLOGY — CT-RSA 2001
  • 2003-02-28. About the XL Algorithm over GF(2) in TOPICS IN CRYPTOLOGY — CT-RSA 2003
  • 2001. QUARTZ, 128-Bit Long Digital Signatures in TOPICS IN CRYPTOLOGY — CT-RSA 2001
  • 2000. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2000
  • Book

    TITLE

    Public Key Cryptography – PKC 2004

    ISBN

    978-3-540-21018-4
    978-3-540-24632-9

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-540-24632-9_22

    DOI

    http://dx.doi.org/10.1007/978-3-540-24632-9_22

    DIMENSIONS

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