### Abstract

In this paper, we propose a multivariate quadratic (MQ) equation system based on ergodic matrix (EM) over a finite field with q elements (denoted as Fq). The system actually implicates a problem which is equivalent to the famous Graph Coloring problem, and therefore is NP complete for attackers. The complexity of bisectional multivariate quadratic equation (BMQE) system is determined by the number of the variables, of the equations and of the elements of Fq, which is denoted as n, m, and q, respectively. The paper shows that, if the number of the equations is larger or equal to twice the number of the variables, and qn is large enough, the system is complicated enough to prevent attacks from most of the existing attacking schemes.

Original language | English |
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Title of host publication | Proceedings of the 2010 International Conference on Security and Cryptography (SECRYPT) |

Publisher | IEEE |

Pages | 431-435 |

Number of pages | 5 |

ISBN (Electronic) | 9789898425188 |

Publication status | Published - 1 Jan 2010 |

Event | Proceedings of the 2010 International Conference on Security and Cryptography (SECRYPT) - Athens, 26-28 July 2010 Duration: 1 Jan 2010 → … |

### Conference

Conference | Proceedings of the 2010 International Conference on Security and Cryptography (SECRYPT) |
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Period | 1/01/10 → … |

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## Cite this

Zhou, X., Ma, J., Du, W., Zhao, B., & Petridis, M. (2010). BMQE system - a MQ equations system based on Ergodic matrix. In

*Proceedings of the 2010 International Conference on Security and Cryptography (SECRYPT)*(pp. 431-435). IEEE. http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=5741641