## Abstract

In the present paper, we suggest a new method of creating ID-based cryptosystems, which is based on the use the explicit pairing obtained in the papers [1,2]. The classical reciprocity law goes back to Pierre Fermat and is an explicit formula for the product of the power residues in a filed of algebraic numbers. In 1990, on the first congress of mathematics, Hilbert stated the 9th problem and suggested a plan of solving it. His idea was to reduce the problem to finding an explicit formula for the norm residue symbol. This problem was solved completely in 1978 (see [1]). In the present paper, we use the explicit Hilbert pairing for a protocol of authentication without disclosure (see Sec.3).

Original language | English |
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Title of host publication | 2016 15th International Symposium on Problems of Redundancy in Information and Control Systems, REDUNDANCY 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 175-176 |

Number of pages | 2 |

ISBN (Electronic) | 9781509042319 |

DOIs | |

State | Published - 9 Dec 2016 |

Event | 15th International Symposium on Problems of Redundancy in Information and Control Systems, REDUNDANCY 2016 - Saint-Petersburg, Russian Federation Duration: 26 Sep 2016 → 29 Sep 2016 |

### Conference

Conference | 15th International Symposium on Problems of Redundancy in Information and Control Systems, REDUNDANCY 2016 |
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Country | Russian Federation |

City | Saint-Petersburg |

Period | 26/09/16 → 29/09/16 |

## Scopus subject areas

- Computer Networks and Communications
- Information Systems
- Signal Processing