DROPS

Document

DOI: 10.4230/LIPIcs.ITC.2026.5

Weak Zero-Knowledge and One-Way Functions

Authors: Rohit Chatterjee, Yunqi Li, and Prashant Nalini Vasudevan

Published in: LIPIcs, Volume 385, 7th Conference on Information-Theoretic Cryptography (ITC 2026)

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

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)

Copy BibTex To Clipboard

@InProceedings{chatterjee_et_al:LIPIcs.ITC.2026.5,
  author =	{Chatterjee, Rohit and Li, Yunqi and Vasudevan, Prashant Nalini},
  title =	{{Weak Zero-Knowledge and One-Way Functions}},
  booktitle =	{7th Conference on Information-Theoretic Cryptography (ITC 2026)},
  pages =	{5:1--5:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-426-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{385},
  editor =	{Dodis, Yevgeniy},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2026.5},
  URN =		{urn:nbn:de:0030-drops-270987},
  doi =		{10.4230/LIPIcs.ITC.2026.5},
  annote =	{Keywords: One-way functions, zero-knowledge}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.23

Decoding Balanced Linear Codes with Preprocessing

Authors: Andrej Bogdanov, Rohit Chatterjee, Yunqi Li, and Prashant Nalini Vasudevan

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

Prange’s information set algorithm is a well-known decoding algorithm for linear codes. It decodes corrupted codewords of most 𝔽₂-linear codes C of message length n up to relative error rate O(log n / n) in poly(n) time. We show that the error rate can be improved to O((log n)² / n), provided: (1) the decoder has access to a polynomial-length advice string that depends on C only, and (2) C is n^{-Ω(1)}-balanced. As a consequence we improve the error tolerance in decoding random linear codes if inefficient preprocessing of the code is allowed. This reveals potential vulnerabilities in cryptographic applications of Learning Noisy Parities with low noise rate. Our main technical result is that the Hamming weight of Hw, where the rows of H are a random sample of short dual codewords, measures the proximity of a received word w to the code in the regime of interest. Given such H as advice, our algorithm corrects errors by locally minimizing this measure. We show that for most codes, the error rate tolerated by our decoder is asymptotically optimal among all algorithms whose decision is based on thresholding Hw for an arbitrary polynomial-size advice matrix H.

Cite as

Andrej Bogdanov, Rohit Chatterjee, Yunqi Li, and Prashant Nalini Vasudevan. Decoding Balanced Linear Codes with Preprocessing. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 23:1-23:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{bogdanov_et_al:LIPIcs.ITCS.2026.23,
  author =	{Bogdanov, Andrej and Chatterjee, Rohit and Li, Yunqi and Vasudevan, Prashant Nalini},
  title =	{{Decoding Balanced Linear Codes with Preprocessing}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{23:1--23:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.23},
  URN =		{urn:nbn:de:0030-drops-253107},
  doi =		{10.4230/LIPIcs.ITCS.2026.23},
  annote =	{Keywords: Linear codes, nearest codeword problem, learning parity with noise}
}

Document

DOI: 10.4230/LIPIcs.CCC.2025.2

Hardness Amplification for Real-Valued Functions

Authors: Yunqi Li and Prashant Nalini Vasudevan

Published in: LIPIcs, Volume 339, 40th Computational Complexity Conference (CCC 2025)

Abstract

Given an integer-valued function f:{0,1}ⁿ → {0,1,… , m-1} that is mildly hard to compute on instances drawn from some distribution D over {0,1}ⁿ, we show that the function g(x_1, … , x_t) = f(x_1) + ⋯ + f(x_t) is strongly hard to compute on instances (x_1,… ,x_t) drawn from the product distribution D^t. We also show the same for the task of approximately computing real-valued functions f:{0,1}ⁿ → [0,m). Our theorems immediately imply hardness self-amplification for several natural problems including Max-Clique and Max-SAT, Approximate #SAT, Entropy Estimation, etc..

Cite as

Yunqi Li and Prashant Nalini Vasudevan. Hardness Amplification for Real-Valued Functions. In 40th Computational Complexity Conference (CCC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 339, pp. 2:1-2:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{li_et_al:LIPIcs.CCC.2025.2,
  author =	{Li, Yunqi and Vasudevan, Prashant Nalini},
  title =	{{Hardness Amplification for Real-Valued Functions}},
  booktitle =	{40th Computational Complexity Conference (CCC 2025)},
  pages =	{2:1--2:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-379-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{339},
  editor =	{Srinivasan, Srikanth},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2025.2},
  URN =		{urn:nbn:de:0030-drops-236967},
  doi =		{10.4230/LIPIcs.CCC.2025.2},
  annote =	{Keywords: Average-case complexity, hardness amplification}
}

Search Results

Documents authored by Li, Yunqi

Weak Zero-Knowledge and One-Way Functions

Abstract

Cite as

Decoding Balanced Linear Codes with Preprocessing

Abstract

Cite as

Hardness Amplification for Real-Valued Functions

Abstract

Cite as

Thanks for your feedback!

Could not send message