High Order Linearization Equation (HOLE) Attack on Multivariate Public Key Cryptosystems View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2007

AUTHORS

Jintai Ding , Lei Hu , Xuyun Nie , Jianyu Li , John Wagner

ABSTRACT

In the CT-track of the 2006 RSA conference, a new multivariate public key cryptosystem, which is called the Medium Field Equation (MFE) multivariate public key cryptosystem, is proposed by Wang, Yang, Hu and Lai. We use the second order linearization equation attack method by Patarin to break MFE. Given a ciphertext, we can derive the plaintext within 223 \(\mathbb {F}_{2^{16}}\)-multiplications, after performing once for any given public key a computation of complexity less than 252. We also propose a high order linearization equation (HOLE) attack on multivariate public key cryptosystems, which is a further generalization of the (first and second order) linearization equation (LE). This method can be used to attack extensions of the current MFE. More... »

PAGES

233-248

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. Cryptanalysis of the TTM Cryptosystem in ADVANCES IN CRYPTOLOGY — ASIACRYPT 2000
  • 2005. Building Secure Tame-like Multivariate Public-Key Cryptosystems: The New TTS in INFORMATION SECURITY AND PRIVACY
  • 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
  • 1995. Cryptanalysis of the Matsumoto and Imai Public Key Scheme of Eurocrypt’88 in ADVANCES IN CRYPTOLOGY — CRYPT0’ 95
  • 2004. Comparison Between XL and Gröbner Basis Algorithms in ADVANCES IN CRYPTOLOGY - ASIACRYPT 2004
  • 2006. Inoculating Multivariate Schemes Against Differential Attacks in PUBLIC KEY CRYPTOGRAPHY - PKC 2006
  • 2006. A “Medium-Field” Multivariate Public-Key Encryption Scheme in TOPICS IN CRYPTOLOGY – CT-RSA 2006
  • 2003. A Fast and Secure Implementation of Sflash 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
  • 2004. A New Variant of the Matsumoto-Imai Cryptosystem through Perturbation in PUBLIC KEY CRYPTOGRAPHY – PKC 2004
  • 2002. Cryptanalysis of Block Ciphers with Overdefined Systems of Equations in ADVANCES IN CRYPTOLOGY — ASIACRYPT 2002
  • 2000. Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations in ADVANCES IN CRYPTOLOGY — EUROCRYPT 2000
  • Book

    TITLE

    Public Key Cryptography – PKC 2007

    ISBN

    978-3-540-71676-1
    978-3-540-71677-8

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-540-71677-8_16

    DOI

    http://dx.doi.org/10.1007/978-3-540-71677-8_16

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1002694957


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