Cryptology ePrint Archive: Report 2020/1351

Tight State-Restoration Soundness in the Algebraic Group Model

Ashrujit Ghoshal and Stefano Tessaro

Abstract: Most efficient zero-knowledge arguments lack a concrete security analysis, making parameter choices and efficiency comparisons challenging. This is even more true for non-interactive versions of these systems obtained via the Fiat-Shamir transform, for which the security guarantees generically derived from the interactive protocol are often too weak, even when assuming a random oracle.

This paper initiates the study of state-restoration soundness in the algebraic group model (AGM) of Fuchsbauer, Kiltz, and Loss (CRYPTO '18). This is a stronger notion of soundness for an interactive proof or argument which allows the prover to rewind the verifier, and which is tightly connected with the concrete soundness of the non-interactive argument obtained via the Fiat-Shamir transform.

We propose a general methodology to prove tight bounds on state-restoration soundness, and apply it to variants of Bulletproofs (Bootle et al, S&P '18) and Sonic (Maller et al., CCS '19). To the best of our knowledge, our analysis of Bulletproofs gives the first non-trivial concrete security analysis for a non-constant round argument combined with the Fiat-Shamir transform.

Category / Keywords: foundations / Zero-knowledge proof systems, concrete security, Fiat-Shamir transform, Algebraic Group Model, state-restoration soundness.

Date: received 26 Oct 2020, last revised 13 Jan 2021

Contact author: ashrujit at cs washington edu

Available format(s): PDF | BibTeX Citation

Note: Typos fixed

Version: 20210113:170317 (All versions of this report)

Short URL: ia.cr/2020/1351