We investigate the question of whether this compiler can be proven to work under standard cryptographic assumptions. We prove:
(i) If FHEs or PIR systems exist, then there is a sound interactive proof protocol that, when run through the compiler, results in a protocol that is not sound.
(ii) If the verifier in the original protocol runs in logarithmic space and has no ``long-term'' secret memory (a generalization of public coins), then the compiled protocol is sound. This yields a succinct two-message argument system for any language in NC, where the verifier's work is linear (or even polylog if the input is coded appropriately). This is the first (non trivial) two-message succinct argument system that is based on a standard polynomial-time hardness assumption.Category / Keywords: foundations / Arguments, Interactive Proofs Date: received 15 Mar 2016 Contact author: rothblum at alum mit edu Available format(s): PDF | BibTeX Citation Version: 20160317:161658 (All versions of this report) Short URL: ia.cr/2016/291 Discussion forum: Show discussion | Start new discussion