A proof complexity perspective on effectively zero-knowledge proofs

2026-07-15

AI Summary

This work reinterprets efficient zero-knowledge (EZK) proofs from the perspective of proof complexity, establishing their core properties—particularly indistinguishability from real interactions—as derivable consequences rather than definitional assumptions. By employing logical formalization, the paper provides a concise proof of the existence of EZK protocols and their indistinguishability property. Furthermore, under the common reference string model and assuming the hardness of certain generators, it leverages generator theory from proof complexity to transform EZK into genuine zero-knowledge proofs. This approach not only streamlines existing existence arguments but also opens a new pathway toward achieving true zero knowledge under standard complexity-theoretic assumptions.

Abstract

Ilango (FOCS 2025) invented effectively zero-knowledge proofs, a new variant of zero-knowledge. We reformulate it in the language of logic and give simple proofs (under the same assumptions as Ilango (FOCS 2025)) of its existence and of the key property defined in Ilango (FOCS 2025) that it is "indistinguishable from true" (that property is in Ilango (FOCS 2025) a part of the definition of the prover, not its consequence). Using the theory of proof complexity generators we show that the concept can be turned it into a genuinely zero-knowledge proofs, assuming a conjecture from the theory about the existence of a hard generator and allowing the parties to share a common random string.

Problem

• zero-knowledge proofs
• proof complexity
• effectively zero-knowledge
• hard generator
• common random string

Innovation

• effectively zero-knowledge proofs
• proof complexity
• hard generator
• common random string
• indistinguishability