### Abstract

In this paper, we propose a post-quantum public-key encryption scheme whose security depends on a problem arising from a multivariate non-linear indeterminate equation. The security of lattice cryptosystems, which are considered to be the most promising candidate for a post-quantum cryptosystem, is based on the shortest vector problem or the closest vector problem in the discrete linear solution spaces of simultaneous equations. However, several improved attacks for the underlying problems have recently been developed by using approximation methods, which result in requiring longer key sizes. As a scheme to avoid such attacks, we propose a public-key encryption scheme based on the “smallest” solution problem in the non-linear solution spaces of multivariate indeterminate equations that was developed from the algebraic surface cryptosystem. Since no efficient algorithm to find such a smallest solution is currently known, we introduce a new computational assumption under which proposed scheme is proven to be secure in the sense of IND-CPA. Then, we perform computational experiments based on known attack methods and evaluate that the key size of our scheme is able to be much shorter than those of previous lattice cryptosystems.

Original language | English |
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Title of host publication | Selected Areas in Cryptography – SAC 2017 - 24th International Conference, Revised Selected Papers |

Editors | Carlisle Adams, Jan Camenisch |

Publisher | Springer Verlag |

Pages | 215-234 |

Number of pages | 20 |

ISBN (Print) | 9783319725642 |

DOIs | |

Publication status | Published - Jan 1 2018 |

Event | 24th International Conference on Selected Areas in Cryptography, SAC 2017 - Ottawa, Canada Duration: Aug 16 2017 → Aug 18 2017 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10719 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 24th International Conference on Selected Areas in Cryptography, SAC 2017 |
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Country | Canada |

City | Ottawa |

Period | 8/16/17 → 8/18/17 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Selected Areas in Cryptography – SAC 2017 - 24th International Conference, Revised Selected Papers*(pp. 215-234). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10719 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-72565-9_11