Paper 2015/971
Attacks on Search RLWE
Hao Chen, Kristin Lauter, and Katherine E. Stange
Abstract
We describe a new attack on the Search Ring Learning-With-Errors (RLWE) problem based on the chi-square statistical test, and give examples of RLWE instances in Galois number fields which are vulnerable to our attack. We prove a search-to-decision reduction for Galois fields which applies for any unramified prime modulus $q$, regardless of the residue degree $f$ of $q$, and we use this in our attacks. The time complexity of our attack is $O(q^{2f})$, where $f$ is the {\it residue degree} of $q$ in $K$. We also show an attack on the RLWE problem in general cyclotomic rings (non $2$-power cyclotomic rings) which works when the modulus is a ramified prime. We demonstrate the attacks in practice by finding many vulnerable instances and successfully attacking them. We include the code for all attacks.
Note: Under submission elsewhere.
Metadata
- Available format(s)
- Category
- Secret-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- RLWEAttacksCryptanalysis
- Contact author(s)
- chenh123 @ uw edu
- History
- 2017-10-09: last of 2 revisions
- 2015-10-09: received
- See all versions
- Short URL
- https://ia.cr/2015/971
- License
-
CC BY