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### A quantum algorithm for computing the unit group of a number field and connections to post-quantum cryptography

**Algebra & Discrete Mathematics**

Speaker: | Kirsten Eisenträger, Penn State U |

Related Webpage: | http://www.personal.psu.edu/kxe8/ |

Location: | Zoom lecture |

Start time: | Thu, Nov 5 2020, 10:00AM |

Computing the group of units in a number field is one of the central tasks of computational algebraic number theory. It is believed to be hard classically, which is of interest for cryptography. In the quantum setting, efficient algorithms were previously only known for number fields of constant degree. We will give a quantum algorithm that is polynomial in the degree of the field and the logarithm of its discriminant and discuss connections to post-quantum cryptography.

Joint work with Sean Hallgren, Alexei Kitaev, and Fang Song.

All meetings this quarter will be by Zoom. Please see announcements or contact organizers for the passcode. Slides for the talk are also available.

Stay afterwards for a brief, informal reception. Refreshments will be self-provided.