Document Open Access Logo

New Constructions of Pseudorandom Codes

Authors Surendra Ghentiyala , Venkatesan Guruswami

PDF

File

Thumbnail PDF
PDF
LIPIcs.APPROX-RANDOM.2025.54.pdf
  • Filesize: 1.42 MB
  • 22 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • Error-correcting codes
  • Watermarking
  • Pseudorandomness

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

Introduced in [Christ and Gunn, 2024], pseudorandom error-correcting codes (PRCs) are a new cryptographic primitive with applications in watermarking generative AI models. These are codes where a collection of polynomially many codewords is computationally indistinguishable from random for an adversary that does not have the secret key, but anyone with the secret key is able to efficiently decode corrupted codewords. In this work, we examine the assumptions under which PRCs with robustness to a constant error rate exist.  
1) We show that if both the planted hyperloop assumption introduced in [Andrej Bogdanov et al., 2023] and security of a version of Goldreich’s PRG hold, then there exist public-key PRCs for which no efficient adversary can distinguish a polynomial number of codewords from random with better than o(1) advantage. 
2) We revisit the construction of [Christ and Gunn, 2024] and show that it can be based on a wider range of assumptions than presented in [Christ and Gunn, 2024]. To do this, we introduce a weakened version of the planted XOR assumption which we call the weak planted XOR assumption and which may be of independent interest. 
3) We initiate the study of PRCs which are secure against space-bounded adversaries. We show how to construct secret-key PRCs of length O(n) which are unconditionally indistinguishable from random by poly(n) time, O(n^{1.5-ε}) space adversaries.

Cite As Get BibTex

Surendra Ghentiyala and Venkatesan Guruswami. New Constructions of Pseudorandom Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 54:1-54:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2025.54

Author Details

Surendra Ghentiyala
  • Cornell University, Ithaca, NY, USA
Venkatesan Guruswami
  • Simons Institute for the Theory of Computing and Department of EECS and Mathematics, University of California, Berkeley, CA, USA

Funding

  • Ghentiyala, Surendra: This work is supported in part by the NSF under Grants Nos. CCF-2122230 and CCF-2312296, a Packard Foundation Fellowship, and a generous gift from Google. This work was done while the author was visiting the Simons Institute for the Theory of Computing.
  • Guruswami, Venkatesan: Research supported in part by a Simons Investigator award, and NSF grant CCF-2211972.

Acknowledgements

The authors would like to thank Yinuo Zhang for helpful discussion. They would also like to thank Sam Gunn and Noah Stephens-Davidowitz for reviewing early drafts of this work. We also wish to thank Miranda Christ for the observation that our warmup implies that secret-key PRCs with ω(1) alphabet size and robustness to constant rate errors is trivial to achieve.

References

  1. Scott Aaronson. My AI safety lecture for UT effective altruism, 2022. URL: https://scottaaronson.blog/?p=6823.
  2. Shweta Agrawal, Sagnik Saha, Nikolaj Ignatieff Schwartzbach, Akhil Vanukuri, and Prashant Nalini Vasudevan. k-SUM in the sparse regime. Cryptology ePrint Archive, Paper 2023/488, 2023. URL: https://eprint.iacr.org/2023/488.
  3. Michael Alekhnovich. More on average case vs approximation complexity. In FOCS, pages 298-307, 2003. URL: https://doi.org/10.1109/SFCS.2003.1238204.
  4. Benny Applebaum, Boaz Barak, and Avi Wigderson. Public-key cryptography from different assumptions. In Proceedings of the Forty-Second ACM Symposium on Theory of Computing, STOC '10, pages 171-180, New York, NY, USA, 2010. Association for Computing Machinery. URL: https://doi.org/10.1145/1806689.1806715.
  5. Benny Applebaum, David Cash, Chris Peikert, and Amit Sahai. Fast cryptographic primitives and circular-secure encryption based on hard learning problems. In Shai Halevi, editor, Advances in Cryptology - CRYPTO 2009, pages 595-618, Berlin, Heidelberg, 2009. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-642-03356-8_35.
  6. Andrej Bogdanov, Pravesh Kothari, and Alon Rosen. Public-key encryption, local pseudorandom generators, and the low-degree method. Cryptology ePrint Archive, Paper 2023/1049, 2023. URL: https://eprint.iacr.org/2023/1049.
  7. Christian Cachin and Ueli Maurer. Unconditional security against memory-bounded adversaries. In Burton S. Kaliski, editor, Advances in Cryptology - CRYPTO '97, pages 292-306, Berlin, Heidelberg, 1997. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/BFB0052243.
  8. Herman Chernoff. A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations. The Annals of Mathematical Statistics, 23(4):493-507, 1952. URL: https://doi.org/10.1214/aoms/1177729330.
  9. Miranda Christ and Sam Gunn. Pseudorandom error-correcting codes. In Leonid Reyzin and Douglas Stebila, editors, Advances in Cryptology - CRYPTO 2024, pages 325-347, Cham, 2024. Springer Nature Switzerland. URL: https://doi.org/10.1007/978-3-031-68391-6_10.
  10. Miranda Christ, Sam Gunn, and Or Zamir. Undetectable watermarks for language models. In The Thirty Seventh Annual Conference on Learning Theory, pages 1125-1139. PMLR, 2024. URL: https://proceedings.mlr.press/v247/christ24a.html.
  11. Geoffroy Couteau, Aurélien Dupin, Pierrick Meaux, Mélissa Rossi, and Yann Rotella. On the Concrete Security of Goldreich’s Pseudorandom Generator: 24th International Conference on the Theory and Application of Cryptology and Information Security, Brisbane, QLD, Australia, December 2–6, 2018, Proceedings, Part II, pages 96-124. Springer, 2018. URL: https://doi.org/10.1007/978-3-030-03329-3_4.
  12. Yan Zong Ding. Oblivious transfer in the bounded storage model. In Joe Kilian, editor, Advances in Cryptology - CRYPTO 2001, pages 155-170, Berlin, Heidelberg, 2001. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/3-540-44647-8_9.
  13. Yevgeniy Dodis, Willy Quach, and Daniel Wichs. Speak much, remember little: Cryptography in the bounded storage model, revisited. In Carmit Hazay and Martijn Stam, editors, Advances in Cryptology - EUROCRYPT 2023, pages 86-116, Cham, 2023. Springer Nature Switzerland. URL: https://doi.org/10.1007/978-3-031-30545-0_4.
  14. Sumegha Garg, Pravesh K. Kothari, Pengda Liu, and Ran Raz. Memory-sample lower bounds for learning parity with noise, 2021. URL: https://arxiv.org/abs/2107.02320.
  15. Dmitry Gavinsky, Shachar Lovett, Michael E. Saks, and Srikanth Srinivasan. A tail bound for read‐k families of functions. Random Structures & Algorithms, 47, 2012. URL: https://api.semanticscholar.org/CorpusID:14447567.
  16. Surendra Ghentiyala and Venkatesan Guruswami. New constructions of pseudorandom codes, 2024. URL: https://doi.org/10.48550/arXiv.2409.07580.
  17. Oded Goldreich. Candidate One-Way Functions Based on Expander Graphs, pages 76-87. Springer Berlin Heidelberg, Berlin, Heidelberg, 2011. URL: https://doi.org/10.1007/978-3-642-22670-0_10.
  18. Noah Golowich and Ankur Moitra. Edit distance robust watermarks for language models, 2024. URL: https://doi.org/10.48550/arXiv.2406.02633.
  19. Wassily Hoeffding. Probability Inequalities for sums of Bounded Random Variables, pages 409-426. Springer New York, New York, NY, 1994. URL: https://doi.org/10.1007/978-1-4612-0865-5_26.
  20. John Kirchenbauer, Jonas Geiping, Yuxin Wen, Jonathan Katz, Ian Miers, and Tom Goldstein. A watermark for large language models. In International Conference on Machine Learning, pages 17061-17084. PMLR, 2023. URL: https://proceedings.mlr.press/v202/kirchenbauer23a.html.
  21. Gillat Kol, Ran Raz, and Avishay Tal. Time-space hardness of learning sparse parities. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2017, pages 1067-1080, New York, NY, USA, 2017. Association for Computing Machinery. URL: https://doi.org/10.1145/3055399.3055430.
  22. Alex Lombardi and Vinod Vaikuntanathan. Minimizing the complexity of goldreich’s pseudorandom generator. Cryptology ePrint Archive, Paper 2017/277, 2017. URL: https://eprint.iacr.org/2017/277.
  23. Ueli M. Maurer. Conditionally-perfect secrecy and a provably-secure randomized cipher. Journal of Cryptology, 5(1):53-66, 1992. URL: https://doi.org/10.1007/BF00191321.
  24. Igor C. Oliveira, Rahul Santhanam, and Roei Tell. Expander-based cryptography meets natural proofs. computational complexity, 31(1):4, 2022. URL: https://doi.org/10.1007/s00037-022-00220-x.
  25. Ran Raz. Fast learning requires good memory: A time-space lower bound for parity learning. J. ACM, 66(1), December 2018. URL: https://doi.org/10.1145/3186563.
  26. Umesh V. Vazirani and Vijay V. Vazirani. Trapdoor pseudo-random number generators, with applications to protocol design. In 24th Annual Symposium on Foundations of Computer Science (sfcs 1983), pages 23-30, 1983. URL: https://doi.org/10.1109/SFCS.1983.78.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact