International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Nick Wadleigh

Publications

Year
Venue
Title
2021
EUROCRYPT
On the ideal shortest vector problem over random rational primes
Yanbin Pan Jun Xu Nick Wadleigh Qi Cheng
Any non-zero ideal in a number field can be factored into a product of prime ideals. In this paper 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 popular in lattice based cryptosystems, 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. Although the shortest vector problem of ideal lattices underpins the security of the Ring-LWE cryptosystem, this work does not break Ring-LWE, since the security reduction is from the worst case ideal SVP to the average case Ring-LWE, and it is one-way.

Coauthors

Qi Cheng (1)
Yanbin Pan (1)
Jun Xu (1)