Paper 2020/1024
Factoring and Pairings are not Necessary for iO: Circular-Secure LWE Suffices
Zvika Brakerski, Nico Döttling, Sanjam Garg, and Giulio Malavolta
Abstract
We construct indistinguishability obfuscation (iO) solely under circular-security properties of encryption schemes based on the Learning with Errors (LWE) problem. Circular-security assumptions were used before to construct (non-leveled) fully-homomorphic encryption (FHE), but our assumption is stronger and requires circular randomness-leakage-resilience. In contrast with prior works, this assumption can be conjectured to be post-quantum secure; yielding the first provably secure iO construction that is (plausibly) post-quantum secure. Our work follows the high-level outline of the recent work of Gay and Pass [ePrint 2020], who showed a way to remove the heuristic step from the homomorphic-encryption based iO approach of Brakerski, Döttling, Garg, and Malavolta [EUROCRYPT 2020]. They thus obtain a construction proved secure under circular security assumption of natural homomorphic encryption schemes --- specifically, they use homomorphic encryption schemes based on LWE and DCR, respectively. In this work we show how to remove the DCR assumption and remain with a scheme based on the circular security of LWE alone. Along the way we relax some of the requirements in the Gay-Pass blueprint and thus obtain a scheme that is secure under a relaxed assumption. Specifically, we do not require security in the presence of a key-cycle, but rather only in the presence of a key-randomness cycle.
Note: Update on the writeup and new results on XiO.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint. MINOR revision.
- Keywords
- obfuscationLWE
- Contact author(s)
- giulio malavolta @ hotmail it
- History
- 2022-03-28: last of 5 revisions
- 2020-08-27: received
- See all versions
- Short URL
- https://ia.cr/2020/1024
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2020/1024, author = {Zvika Brakerski and Nico Döttling and Sanjam Garg and Giulio Malavolta}, title = {Factoring and Pairings are not Necessary for {iO}: Circular-Secure {LWE} Suffices}, howpublished = {Cryptology {ePrint} Archive, Paper 2020/1024}, year = {2020}, url = {https://eprint.iacr.org/2020/1024} }