Recovering Short Generators of Principal Fractional Ideals in Cyclotomic Fields of Conductor p^a * q^b

20.04.2017 11:00-12:00

Recovering Short Generators of Principal Fractional Ideals in Cyclotomic Fields of Conductor p^a * q^b

20.04.2017, 11:00 – 12:00

Speaker: Patrick Holzer, TU Darmstadt | Location: Mornewegstraße 32 (S4|14), Room 5.3.01, Darmstadt

Organizer: Prof. Johannes Buchmann, Moritz Horsch

Abstract

Some recent cryptographic schemes rely on the hardness of finding a shortest generator of a principal (fractional) ideal in an algebraic number field K in the logarithmic embedding with some guaranteed small generator. Cramer, Ducas Peikert and Regev have shown that one can efficiently recover short generators in cyclotomic fields of prime power conductor with quantum computers. In my thesis I generalized their results to the case, that m is the product of two prime powers. Hence, one can efficiently recover short generators under some conditions in this case.

zur Liste