MQ Challenge: Hardness Evaluation of Solving Multivariate Quadratic Problems

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

Paper 2015/275

MQ Challenge: Hardness Evaluation of Solving Multivariate Quadratic Problems

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

Abstract

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.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: post-quantum cryptography multivariate public-key cryptosystem MQ problem
Contact author(s): yasuda @ isit or jp
History: 2015-05-29: last of 4 revisions; 2015-03-25: received; See all versions
Short URL: https://ia.cr/2015/275
License: CC BY

BibTeX

@misc{cryptoeprint:2015/275,
      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},
      url = {https://eprint.iacr.org/2015/275}
}