Speaker：Qi Cheng (The University of Oklahoma)

Time：2023-7-13, 10:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus

Abstract:

Any non-zero ideal in a number field can be factored into a product of prime ideals. In this talk we report a surprising connection between the complexity of the shortest vector problem (SVP) of prime ideals in number fields and their decomposition groups. When applying the result to number fields, such as power-of-two cyclotomic fields, we show that a majority of rational primes lie under prime ideals admitting a polynomial time algorithm for SVP. This is a joint work with Yanbin Pan, Jun Xu and Nick Wadleigh.