We construct an adaptively-sound succinct non-interactive argument (SNARG) for \(\textsf{NP}\) in the CRS model from sub-exponentially-secure indistinguishability obfuscation ( \(i\mathcal {O} \) ) and sub-exponentially-secure one-way functions. Previously, Waters and Wu (STOC 2024), and subsequently, Waters and Zhandry (CRYPTO 2024) showed how to construct adaptively-sound SNARGs for \(\textsf{NP}\) by relying on sub-exponentially-secure indistinguishability obfuscation, one-way functions, and an additional algebraic assumption (i.e., discrete log, factoring, or learning with errors). In this work, we show that no additional algebraic assumption is needed and vanilla (sub-exponentially-secure) one-way functions already suffice in combination with \(i\mathcal {O} \) .

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A Pure Indistinguishability Obfuscation Approach to Adaptively-Sound SNARGs for  \(\textsf{NP}\)

  • Brent Waters,
  • David J. Wu

摘要

We construct an adaptively-sound succinct non-interactive argument (SNARG) for \(\textsf{NP}\) in the CRS model from sub-exponentially-secure indistinguishability obfuscation ( \(i\mathcal {O} \) ) and sub-exponentially-secure one-way functions. Previously, Waters and Wu (STOC 2024), and subsequently, Waters and Zhandry (CRYPTO 2024) showed how to construct adaptively-sound SNARGs for \(\textsf{NP}\) by relying on sub-exponentially-secure indistinguishability obfuscation, one-way functions, and an additional algebraic assumption (i.e., discrete log, factoring, or learning with errors). In this work, we show that no additional algebraic assumption is needed and vanilla (sub-exponentially-secure) one-way functions already suffice in combination with \(i\mathcal {O} \) .