# Cryptanalysis of the bisectional MQ equations system

Zhou, Xiaoyi, Ma, Jixin, Du, Wencai, Zhao, Bo, Chen, Mingrui and Zhao, Youngzhe
(2010)
*Cryptanalysis of the bisectional MQ equations system.*
In: Proceedings - 10th IEEE International Conference on Computer and Information Technology, CIT-2010, 7th IEEE International Conference on Embedded Software and Systems, ICESS-2010, ScalCom-2010.
IEEE Computer Society, Piscataway, USA, pp. 1038-1043.
ISBN 9781424475476
(doi:10.1109/CIT.2010.190)

## Abstract

The security of many recently proposed cryptosystems is mainly based on the difficulty of solving large multivariate quadratic equations systems. Apart from UOV schemes with proper parameter values, the basic types of these schemes can be broken without great difficulty. Moreover, there are some shortages lying in some of these examined schemes. This paper proposes a bisectional multivariate quadratic equation (BMQE) system over a finite field of degree q (denoted as ). The BMQE system is analyzed by Kipnis & Shamir’s relinearization, and it is shown that the number of the variables n, together with the number of the equations m and the number of the degree q of , have a great impact on the complexity of the BMQE system. If they are properly set, relinearization cannot be used to solve this system.

Item Type: | Conference Proceedings |
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Title of Proceedings: | Proceedings - 10th IEEE International Conference on Computer and Information Technology, CIT-2010, 7th IEEE International Conference on Embedded Software and Systems, ICESS-2010, ScalCom-2010 |

Additional Information: | This paper forms part of the proceedings of 10th IEEE International Conference on Computer and Information Technology, CIT-2010, 7th IEEE International Conference on Embedded Software and Systems, ICESS-2010, 10th IEEE Int. Conf. Scalable Computing and Communications, ScalCom-2010 June 29, 2010 - July 1, 2010 Bradford, United kingdom |

Uncontrolled Keywords: | multivariate quadratic, finite field, relinearization, cryptanalysis, public key cryptosystems |

Subjects: | Q Science > QA Mathematics |

Pre-2014 Departments: | School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Department of Computer Science School of Computing & Mathematical Sciences > Department of Computing and Information Systems School of Computing & Mathematical Sciences > Department of Smart Systems Technologies |

Related URLs: | |

Last Modified: | 14 Oct 2016 09:10 |

URI: | http://gala.gre.ac.uk/id/eprint/3884 |

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