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Paper 2020/1351

Tight State-Restoration Soundness in the Algebraic Group Model

Ashrujit Ghoshal and Stefano Tessaro


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.

Note: Major update with updated security definitions

Available format(s)
Publication info
A major revision of an IACR publication in CRYPTO 2021
Zero-knowledge proof systemsconcrete securityFiat-Shamir transformAlgebraic Group Modelstate-restoration soundness.
Contact author(s)
ashrujit @ cs washington edu
2021-06-25: last of 5 revisions
2020-10-29: received
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      author = {Ashrujit Ghoshal and Stefano Tessaro},
      title = {Tight State-Restoration Soundness in the Algebraic Group Model},
      howpublished = {Cryptology ePrint Archive, Paper 2020/1351},
      year = {2020},
      note = {\url{https://eprint.iacr.org/2020/1351}},
      url = {https://eprint.iacr.org/2020/1351}
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