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Weak Zero-Knowledge and One-Way Functions

Authors Rohit Chatterjee , Yunqi Li , Prashant Nalini Vasudevan

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ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • One-way functions
  • zero-knowledge

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Abstract

We study the implications of the existence of weak Zero-Knowledge (ZK) protocols for worst-case hard languages. These are protocols that have completeness, soundness, and zero-knowledge errors (denoted ε_c, ε_s, and ε_z, respectively) that might not be negligible. Under the assumption that there are worst-case hard languages in NP, we show the following:  
1) If all languages in NP have NIZK proofs or arguments satisfying ε_c+ε_s+ε_z < 1, then One-Way Functions (OWFs) exist. This covers all possible non-trivial values for these error rates. It additionally implies that if all languages in NP have such NIZK proofs and ε_c is negligible, then they also have NIZK proofs where all errors are negligible. Previously, these results were known under the more restrictive condition ε_c+√{ε_s}+ε_z < 1 [Chakraborty et al., CRYPTO 2025]. 
2) If all languages in NP have k-round public-coin ZK proofs or arguments satisfying ε_c+ε_s+(2k-1)⋅ε_z < 1, then OWFs exist.
3) If, for some constant k, all languages in NP have k-round public-coin ZK proofs or arguments satisfying ε_c+ε_s+k⋅ε_z < 1, then infinitely-often OWFs exist.

Cite As Get BibTex

Rohit Chatterjee, Yunqi Li, and Prashant Nalini Vasudevan. Weak Zero-Knowledge and One-Way Functions. In 7th Conference on Information-Theoretic Cryptography (ITC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 385, pp. 5:1-5:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITC.2026.5

Author Details

Rohit Chatterjee
  • Department of Computer Science, National University of Singapore, Singapore
Yunqi Li
  • Department of Computer Science, National University of Singapore, Singapore
Prashant Nalini Vasudevan
  • Department of Computer Science, National University of Singapore, Singapore

Funding

This work was supported by the National Research Foundation, Singapore, under its NRF Fellowship programme, award no. NRF-NRFF14-2022-0010.

Acknowledgements

We thank the anonymous reviewers for their comments.

References

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