### Abstract

Multivariate polynomials over finite fields have found applications in Public Key Cryptography (PKC) where the hardness to find solutions provides the "one-way function" indispensable to such cryptosystems. Several schemes for both encryption and signature have been proposed, many of which are using quadratic (degree 2) polynomials. Finding a solution to such systems in general is called MQ problem, which easiest "generic" instances are NP-hard. An important feature of this Multivariate Pubic Key Cryptography (MPKC) is the resistance to quantum computers: no faster quantum algorithm than classical ones to solve MQ problem is known. Besides being thereby a candidate for Post-Quantum Cryptography, signatures are much shorter than to other candidates. We have established an open public "MQ Challenge" (https://www.mqchallenge.org) to stimulate progress in the design of efficient algorithms to solve MQ problem, and thus test limit parameters guaranteeing security of MPKC.

Original language | English |
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Pages (from-to) | 105-107 |

Number of pages | 3 |

Journal | ACM Communications in Computer Algebra |

Volume | 49 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*ACM Communications in Computer Algebra*,

*49*(3), 105-107. https://doi.org/10.1145/2850449.2850462