Paper 2015/275

MQ Challenge: Hardness Evaluation of Solving Multivariate Quadratic Problems

Takanori Yasuda, Xavier Dahan, Yun-Ju Huang, Tsuyoshi Takagi, and Kouichi Sakurai


Multivariate Quadratic polynomial (MQ) problem serve as the basis of security for potentially post-quantum cryptosystems. The hardness of solving MQ problem depends on a number of parameters, most importantly the number of variables and the degree of the polynomials, as well as the number of equations, the size of the base field etc. We investigate the relation among these parameters and the hardness of solving MQ problem, in order to construct hard instances of MQ problem. These instances are used to create a challenge, which may be helpful in determining appropriate parameters for multivariate public key cryptosystems, and stimulate further the research in solving MQ problem.

Note: Revised version contains description of the range of parameters of MQ challenge and correction of errors.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
post-quantum cryptographymultivariate public-key cryptosystemMQ problem
Contact author(s)
yasuda @ isit or jp
2015-05-29: last of 4 revisions
2015-03-25: received
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Creative Commons Attribution


      author = {Takanori Yasuda and Xavier Dahan and Yun-Ju Huang and Tsuyoshi Takagi and Kouichi Sakurai},
      title = {MQ Challenge: Hardness Evaluation of Solving Multivariate Quadratic Problems},
      howpublished = {Cryptology ePrint Archive, Paper 2015/275},
      year = {2015},
      note = {\url{}},
      url = {}
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