#### Conference abstracts

Session A3 - Computational Number Theory

July 11, 15:30 ~ 16:20 - Room B6

## Short generators without quantum computers: the case of multiquadratics

### Daniel J. Bernstein

### University of Illinois at Chicago, United States - conference-34e5ec3b68733@box.cr.yp.to

Finding a short element $g$ of a number field, given the ideal generated by $g$, is a classic problem in computational algebraic number theory. Solving this problem recovers the private key in cryptosystems introduced by Gentry, Smart--Vercauteren, Gentry--Halevi, Garg--Gentry--Halevi, et al. Work over the last few years has shown that for some number fields this problem has a surprisingly low *post-quantum* security level. The point of this talk is that for some number fields this problem has a surprisingly low *pre-quantum* security level.

Joint work with Jens Bauch, Henry de Valence, Tanja Lange and Christine van Vredendaal.