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, D\"ottling, 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.
Category / Keywords: foundations / obfuscation, LWE Date: received 25 Aug 2020, last revised 10 Oct 2020 Contact author: giulio malavolta at hotmail it Available format(s): PDF | BibTeX Citation Version: 20201010:062504 (All versions of this report) Short URL: ia.cr/2020/1024