Known constructions of ZAPs from trapdoor permutations or bilinear maps are only computationally WI (and statistically sound). Two recent results of Badrinarayanan-Fernando-Jain-Khurana-Sahai and Goyal-Jain-Jin-Malavolta [EUROCRYPT '20] construct the first statistical ZAP arguments, which are statistically WI (and computationally sound), from the quasi-polynomial LWE assumption. Here, we construct statistical ZAPR arguments from the quasi-polynomial decision-linear (DLIN) assumption on groups with a bilinear map. Our construction relies on a combination of several tools, including the Groth-Ostrovsky-Sahai NIZK and NIWI [EUROCRYPT '06, CRYPTO '06, JACM '12], ``sometimes-binding statistically hiding commitments'' [Kalai-Khurana-Sahai, EUROCRYPT '18] and the ``MPC-in-the-head'' technique [Ishai-Kushilevitz-Ostrovsky-Sahai, STOC '07].
Category / Keywords: cryptographic protocols / ZAPs, Statistical Witness Indistinguishability Original Publication (with minor differences): IACR-EUROCRYPT-2020 Date: received 25 Feb 2020, last revised 25 Feb 2020 Contact author: alexjl at mit edu Available format(s): PDF | BibTeX Citation Version: 20200225:204549 (All versions of this report) Short URL: ia.cr/2020/256