Building Secure Tame-like Multivariate Public-Key Cryptosystems: The New TTS

  • Bo-Yin Yang
  • Jiun-Ming Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3574)


Multivariate public-key cryptosystems (sometimes polynomial-based PKC’s or just multivariates) handle polynomials of many variables over relatively small fields instead of elements of a large ring or group. The “tame-like” or “sparse” class of multivariates are distinguished by the relatively few terms that they have per central equation. We explain how they differ from the “big-field” type of multivariates, represented by derivatives of C  ∗  and HFE, how they are better, and give basic security criteria for them. The last is shown to be satisfied by efficient schemes called “Enhanced TTS” which is built on a combination of the Oil-and-Vinegar and Triangular ideas. Their security levels are estimated. In this process we summarize and in some cases, improve rank-based attacks, which seek linear combinations of certain matrices at given ranks. These attacks are responsible for breaking many prior multivariate designs.


Smart Card Signature Scheme Central Equation Digital Signature Scheme Multivariate Signature Scheme 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Bo-Yin Yang
    • 1
  • Jiun-Ming Chen
    • 2
  1. 1.Dept. of MathematicsTamkang UniversityTamsuiTaiwan
  2. 2.Chinese Data Security, Inc., & Nat’l Taiwan U.Taipei

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