Document Open Access Logo

Mutable Batch Arguments and Applications

Author Rishab Goyal

PDF

File

Thumbnail PDF
PDF
LIPIcs.ICALP.2026.101.pdf
  • Filesize: 0.9 MB
  • 24 pages

Document Identifiers

Related Versions

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
Keywords
  • BARGs
  • Mutable proofs

Metrics

Abstract

We put forth a new concept of mutability for batch arguments (BARGs), called mutable batch arguments. Our goal is to re-envision how we view and use BARGs. Traditionally, a BARG proof π is an immutable encoding of k NP witness ω_1, …, ω_k. A mutable BARG system captures the notion of computations over BARGs, where each proof string π is treated as a mutable encoding of original witnesses. We also study strong privacy notions for mutable BARGs, with the goal of hiding all non-trivial information about witnesses from a mutated proof. Such mutable BARGs are a naturally good fit for many privacy sensitive applications. Our main contributions include introducing the concept of mutable BARGs, identifying non-trivial classes of feasible mutations, designing mutable BARGs with varying capabilities satisfying mutation privacy from standard cryptographic assumptions, and enabling new applications while improving state-of-the-art known for many signature systems.

Cite As Get BibTex

Rishab Goyal. Mutable Batch Arguments and Applications. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 101:1-101:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ICALP.2026.101

Author Details

Rishab Goyal
  • University of Wisconsin-Madison, WI, USA

Funding

  • Goyal, Rishab: Support for this research was provided by OVCRGE at UW-Madison with funding from the Wisconsin Alumni Research Foundation.

References

  1. Tolga Acar and Lan Nguyen. Homomorphic proofs and applications, 2011. Google Scholar
  2. Abtin Afshar, Jiaqi Cheng, and Rishab Goyal. Leveled fully-homomorphic signatures from batch arguments. Cryptology ePrint Archive, Paper 2024/931, 2024. URL: https://eprint.iacr.org/2024/931.
  3. Shweta Agrawal and Dan Boneh. Homomorphic macs: Mac-based integrity for network coding. In Applied Cryptography and Network Security: 7th International Conference, ACNS 2009, Paris-Rocquencourt, France, June 2-5, 2009. Proceedings 7, pages 292-305. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-01957-9_18.
  4. Prabhanjan Ananth, Apoorvaa Deshpande, Yael Tauman Kalai, and Anna Lysyanskaya. Fully homomorphic nizk and niwi proofs. In Theory of Cryptography Conference, pages 356-385. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-36033-7_14.
  5. Prabhanjan Ananth, Vipul Goyal, and Omkant Pandey. Interactive proofs under continual memory leakage. In Advances in Cryptology-CRYPTO 2014: 34th Annual Cryptology Conference, Santa Barbara, CA, USA, August 17-21, 2014, Proceedings, Part II 34, pages 164-182. Springer, 2014. URL: https://doi.org/10.1007/978-3-662-44381-1_10.
  6. Gaspard Anthoine, David Balbás, and Dario Fiore. Fully-succinct multi-key homomorphic signatures from standard assumptions. In Annual International Cryptology Conference, pages 317-351. Springer, 2024. URL: https://doi.org/10.1007/978-3-031-68382-4_10.
  7. Karim Baghery, Markulf Kohlweiss, Janno Siim, and Mikhail Volkhov. Another look at extraction and randomization of groth’s zk-snark. In Nikita Borisov and Claudia Diaz, editors, Financial Cryptography and Data Security, pages 457-475, Berlin, Heidelberg, 2021. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-662-64322-8_22.
  8. Mira Belenkiy, Jan Camenisch, Melissa Chase, Markulf Kohlweiss, Anna Lysyanskaya, and Hovav Shacham. Randomizable proofs and delegatable anonymous credentials. In Advances in Cryptology-CRYPTO 2009: 29th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 16-20, 2009. Proceedings, pages 108-125. Springer, 2009. URL: https://doi.org/10.1007/978-3-642-03356-8_7.
  9. Eli Ben-Sasson, Iddo Bentov, Yinon Horesh, and Michael Riabzev. Scalable, transparent, and post-quantum secure computational integrity. Cryptology ePrint Archive, 2018. Google Scholar
  10. Nir Bitansky, Ran Canetti, Alessandro Chiesa, Shafi Goldwasser, Huijia Lin, Aviad Rubinstein, and Eran Tromer. The hunting of the SNARK. J. Cryptol., 30(4):989-1066, 2017. URL: https://doi.org/10.1007/s00145-016-9241-9.
  11. Nir Bitansky, Ran Canetti, Alessandro Chiesa, and Eran Tromer. From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again. In Shafi Goldwasser, editor, Innovations in Theoretical Computer Science 2012, Cambridge, MA, USA, January 8-10, 2012, pages 326-349. ACM, 2012. URL: https://doi.org/10.1145/2090236.2090263.
  12. Nir Bitansky, Ran Canetti, Alessandro Chiesa, and Eran Tromer. Recursive composition and bootstrapping for SNARKS and proof-carrying data. In Dan Boneh, Tim Roughgarden, and Joan Feigenbaum, editors, Symposium on Theory of Computing Conference, STOC'13, Palo Alto, CA, USA, June 1-4, 2013, pages 111-120. ACM, 2013. URL: https://doi.org/10.1145/2488608.2488623.
  13. Nir Bitansky, Ran Canetti, Omer Paneth, and Alon Rosen. On the existence of extractable one-way functions. In Proceedings of the forty-sixth annual ACM symposium on Theory of computing, pages 505-514, 2014. URL: https://doi.org/10.1145/2591796.2591859.
  14. Nir Bitansky, Alessandro Chiesa, Yuval Ishai, Rafail Ostrovsky, and Omer Paneth. Succinct non-interactive arguments via linear interactive proofs. In Amit Sahai, editor, Theory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Tokyo, Japan, March 3-6, 2013. Proceedings, volume 7785 of Lecture Notes in Computer Science, pages 315-333. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-36594-2_18.
  15. Dan Boneh, David Freeman, Jonathan Katz, and Brent Waters. Signing a linear subspace: Signature schemes for network coding. In Stanisław Jarecki and Gene Tsudik, editors, Public Key Cryptography - PKC 2009, pages 68-87, Berlin, Heidelberg, 2009. Springer Berlin Heidelberg. Google Scholar
  16. Dan Boneh and David Mandell Freeman. Linearly homomorphic signatures over binary fields and new tools for lattice-based signatures. In International Workshop on Public Key Cryptography, 2011. Google Scholar
  17. Dan Boneh, Craig Gentry, Ben Lynn, and Hovav Shacham. Aggregate and verifiably encrypted signatures. In Eurocrypt, 2003. Google Scholar
  18. Dan Boneh, Yuval Ishai, Amit Sahai, and David J Wu. Lattice-based snargs and their application to more efficient obfuscation. In Advances in Cryptology-EUROCRYPT 2017: 36th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Paris, France, April 30-May 4, 2017, Proceedings, Part III, pages 247-277. Springer, 2017. URL: https://doi.org/10.1007/978-3-319-56617-7_9.
  19. Dan Boneh, Gil Segev, and Brent Waters. Targeted malleability: homomorphic encryption for restricted computations. In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, pages 350-366, 2012. URL: https://doi.org/10.1145/2090236.2090264.
  20. Dan Boneh and Brent Waters. Constrained pseudorandom functions and their applications. In ASIACRYPT 2013, 2013. Google Scholar
  21. Elette Boyle, Shafi Goldwasser, and Ioana Ivan. Functional signatures and pseudorandom functions. In PKC 2014, 2014. Google Scholar
  22. Eli Bradley, Brent Waters, and David J Wu. Batch arguments to nizks from one-way functions. Cryptology ePrint Archive, 2023. Google Scholar
  23. Zvika Brakerski, Maya Farber Brodsky, Yael Tauman Kalai, Alex Lombardi, and Omer Paneth. Snargs for monotone policy batch np. In Annual International Cryptology Conference, pages 252-283. Springer, 2023. URL: https://doi.org/10.1007/978-3-031-38545-2_9.
  24. Zvika Brakerski, Justin Holmgren, and Yael Kalai. Non-interactive delegation and batch np verification from standard computational assumptions. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pages 474-482, 2017. Google Scholar
  25. Maya Farber Brodsky, Arka Rai Choudhuri, Abhishek Jain, and Omer Paneth. Monotone-policy aggregate signatures. In EUROCRYPT. Springer-Verlag, 2024. Google Scholar
  26. Mike Burmester, Yvo G Desmedt, Toshiya Itoh, Kouichi Sakurai, and Hiroki Shizuya. Divertible and subliminal-free zero-knowledge proofs for languages. Journal of cryptology, 12:197-223, 1999. URL: https://doi.org/10.1007/S001459900053.
  27. Dario Catalano and Dario Fiore. Practical homomorphic macs for arithmetic circuits. In Annual International Conference on the Theory and Applications of Cryptographic Techniques, pages 336-352. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-38348-9_21.
  28. Dario Catalano, Dario Fiore, and Bogdan Warinschi. Homomorphic signatures with efficient verification for polynomial functions. In Annual Cryptology Conference, pages 371-389. Springer, 2014. URL: https://doi.org/10.1007/978-3-662-44371-2_21.
  29. Jeffrey Champion and David J. Wu. Non-interactive zero-knowledge from non-interactive batch arguments. Cryptology ePrint Archive, Paper 2023/695, 2023. Google Scholar
  30. Melissa Chase, Markulf Kohlweiss, Anna Lysyanskaya, and Sarah Meiklejohn. Malleable proof systems and applications. In Advances in Cryptology-EUROCRYPT 2012: 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Cambridge, UK, April 15-19, 2012. Proceedings 31, pages 281-300. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-29011-4_18.
  31. Melissa Chase, Markulf Kohlweiss, Anna Lysyanskaya, and Sarah Meiklejohn. Malleable signatures: Complex unary transformations and delegatable anonymous credentials. Cryptology ePrint Archive, 2013. Google Scholar
  32. Melissa Chase, Markulf Kohlweiss, Anna Lysyanskaya, and Sarah Meiklejohn. Succinct malleable nizks and an application to compact shuffles. In Theory of Cryptography Conference, pages 100-119. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-36594-2_6.
  33. Alessandro Chiesa, Yuncong Hu, Mary Maller, Pratyush Mishra, Noah Vesely, and Nicholas Ward. Marlin: Preprocessing zksnarks with universal and updatable srs. In Advances in Cryptology-EUROCRYPT 2020: 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10-14, 2020, Proceedings, Part I 39, pages 738-768. Springer, 2020. URL: https://doi.org/10.1007/978-3-030-45721-1_26.
  34. Alessandro Chiesa, Dev Ojha, and Nicholas Spooner. Fractal: Post-quantum and transparent recursive proofs from holography. In Advances in Cryptology - EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10-14, 2020, Proceedings, Part I, pages 769-793, 2020. URL: https://doi.org/10.1007/978-3-030-45721-1_27.
  35. Alessandro Chiesa and Eran Tromer. Proof-carrying data and hearsay arguments from signature cards. In Innovations in Computer Science - ICS 2010, Tsinghua University, Beijing, China, January 5-7, 2010. Proceedings, pages 310-331, 2010. URL: http://conference.iiis.tsinghua.edu.cn/ICS2010/content/papers/25.html.
  36. Arka Rai Choudhuri, Sanjam Garg, Abhishek Jain, Zhengzhong Jin, and Jiaheng Zhang. Correlation intractability and snargs from sub-exponential ddh. Cryptology ePrint Archive, 2022. Google Scholar
  37. Arka Rai Choudhuri, Abhihsek Jain, and Zhengzhong Jin. Snargs for p from lwe. In 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS), pages 68-79. IEEE, 2021. Google Scholar
  38. Arka Rai Choudhuri, Abhishek Jain, and Zhengzhong Jin. Non-interactive batch arguments for NP from standard assumptions. In Tal Malkin and Chris Peikert, editors, Advances in Cryptology - CRYPTO 2021 - 41st Annual International Cryptology Conference, CRYPTO 2021, Virtual Event, August 16-20, 2021, Proceedings, Part IV, volume 12828 of Lecture Notes in Computer Science, pages 394-423. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-84259-8_14.
  39. Ivan Damgård, Sebastian Faust, and Carmit Hazay. Secure two-party computation with low communication. In Theory of Cryptography: 9th Theory of Cryptography Conference, TCC 2012, Taormina, Sicily, Italy, March 19-21, 2012. Proceedings 9, pages 54-74. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-28914-9_4.
  40. Alfredo De Santis and Moti Yung. Cryptographic applications of the non-interactive metaproof and many-prover systems. In Advances in Cryptology-CRYPTO’90: Proceedings 10, pages 366-377. Springer, 1991. Google Scholar
  41. Alfredo De Santis and Moti Yung. "Metaproofs" (and their cryptographic applications). Cryptology ePrint Archive, 2012. Google Scholar
  42. David Derler, Stephan Krenn, and Daniel Slamanig. Signer-anonymous designated-verifier redactable signatures for cloud-based data sharing. In CANS, 2016. Google Scholar
  43. David Derler, Henrich C Pöhls, Kai Samelin, and Daniel Slamanig. A general framework for redactable signatures and new constructions. In ICISC, 2015. Google Scholar
  44. Lalita Devadas, Rishab Goyal, Yael Kalai, and Vinod Vaikuntanathan. Rate-1 non-interactive arguments for batch-np and applications. In 63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022, 2022. Google Scholar
  45. Yevgeniy Dodis, Kristiyan Haralambiev, Adriana López-Alt, and Daniel Wichs. Cryptography against continuous memory attacks. In 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, pages 511-520. IEEE, 2010. URL: https://doi.org/10.1109/FOCS.2010.56.
  46. Dario Fiore, Aikaterini Mitrokotsa, Luca Nizzardo, and Elena Pagnin. Multi-key homomorphic authenticators. In International conference on the theory and application of cryptology and information security, pages 499-530. Springer, 2016. URL: https://doi.org/10.1007/978-3-662-53890-6_17.
  47. Rachit Garg, Kristin Sheridan, Brent Waters, and David J Wu. Fully succinct batch arguments for np from indistinguishability obfuscation. In Theory of Cryptography: 20th International Conference, TCC 2022, Chicago, IL, USA, November 7-10, 2022, Proceedings, Part I, pages 526-555. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-22318-1_19.
  48. Rosario Gennaro, Craig Gentry, Bryan Parno, and Mariana Raykova. Quadratic span programs and succinct nizks without pcps. In Advances in Cryptology-EUROCRYPT 2013: 32nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, Athens, Greece, May 26-30, 2013. Proceedings 32, pages 626-645. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-38348-9_37.
  49. Craig Gentry and Daniel Wichs. Separating succinct non-interactive arguments from all falsifiable assumptions. In Proceedings of the forty-third annual ACM symposium on Theory of computing, pages 99-108, 2011. URL: https://doi.org/10.1145/1993636.1993651.
  50. S. Goldwasser, S. Micali, and C. Rackoff. The knowledge complexity of interactive proof systems. SIAM J. Comput., 18(1):186-208, February 1989. URL: https://doi.org/10.1137/0218012.
  51. Sergey Gorbunov, Vinod Vaikuntanathan, and Daniel Wichs. Leveled fully homomorphic signatures from standard lattices. In Proceedings of the forty-seventh annual ACM symposium on Theory of computing, pages 469-477, 2015. URL: https://doi.org/10.1145/2746539.2746576.
  52. Rishab Goyal and Vinod Vaikuntanathan. Locally verifiable signature and key aggregation. In Advances in Cryptology - CRYPTO 2022 - 42nd Annual International Cryptology Conference, 2022. Google Scholar
  53. Jens Groth. Short pairing-based non-interactive zero-knowledge arguments. In Asiacrypt, volume 6477, pages 321-340. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-17373-8_19.
  54. Jens Groth. On the size of pairing-based non-interactive arguments. In Advances in Cryptology-EUROCRYPT 2016: 35th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Vienna, Austria, May 8-12, 2016, Proceedings, Part II 35, pages 305-326. Springer, 2016. URL: https://doi.org/10.1007/978-3-662-49896-5_11.
  55. Pavel Hubacek and Daniel Wichs. On the communication complexity of secure function evaluation with long output. In Proceedings of the 2015 Conference on Innovations in Theoretical Computer Science, pages 163-172, 2015. Google Scholar
  56. James Hulett, Ruta Jawale, Dakshita Khurana, and Akshayaram Srinivasan. Snargs for p from sub-exponential ddh and qr. In Advances in Cryptology-EUROCRYPT 2022: 41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Trondheim, Norway, May 30-June 3, 2022, Proceedings, Part II, pages 520-549. Springer, 2022. URL: https://doi.org/10.1007/978-3-031-07085-3_18.
  57. Robert Johnson, David Molnar, Dawn Song, and David Wagner. Homomorphic signature schemes. In CT-RSA, 2002. Google Scholar
  58. Yael Kalai, Alex Lombardi, Vinod Vaikuntanathan, and Daniel Wichs. Boosting batch arguments and ram delegation. In STOC, 2023. Google Scholar
  59. Yael Tauman Kalai, Alex Lombardi, and Vinod Vaikuntanathan. Snargs and ppad hardness from the decisional diffie-hellman assumption. Cryptology ePrint Archive, 2022. Google Scholar
  60. Yael Tauman Kalai, Omer Paneth, and Lisa Yang. How to delegate computations publicly. In Moses Charikar and Edith Cohen, editors, Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019, Phoenix, AZ, USA, June 23-26, 2019, pages 1115-1124. ACM, 2019. URL: https://doi.org/10.1145/3313276.3316411.
  61. Yael Tauman Kalai, Vinod Vaikuntanathan, and Rachel Yun Zhang. Somewhere statistical soundness, post-quantum security, and snargs. In Kobbi Nissim and Brent Waters, editors, Theory of Cryptography - 19th International Conference, TCC 2021, Raleigh, NC, USA, November 8-11, 2021, Proceedings, Part I, volume 13042 of Lecture Notes in Computer Science, pages 330-368. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-90459-3_12.
  62. Aggelos Kiayias, Stavros Papadopoulos, Nikos Triandopoulos, and Thomas Zacharias. Delegatable pseudorandom functions and applications. In Proceedings of the 2013 ACM SIGSAC Conference on Computer & Communications Security, CCS '13, pages 669-684, New York, NY, USA, 2013. ACM. URL: https://doi.org/10.1145/2508859.2516668.
  63. Joe Kilian. A note on efficient zero-knowledge proofs and arguments. In Proceedings of the twenty-fourth annual ACM symposium on Theory of computing, pages 723-732, 1992. Google Scholar
  64. Benoît Libert, Somindu C Ramanna, and Moti Yung. Functional commitment schemes: From polynomial commitments to pairing-based accumulators from simple assumptions. In 43rd International Colloquium on Automata, Languages and Programming (ICALP 2016), 2016. Google Scholar
  65. Helger Lipmaa. Succinct non-interactive zero knowledge arguments from span programs and linear error-correcting codes. In Advances in Cryptology-ASIACRYPT 2013: 19th International Conference on the Theory and Application of Cryptology and Information Security, Bengaluru, India, December 1-5, 2013, Proceedings, Part I 19, pages 41-60. Springer, 2013. URL: https://doi.org/10.1007/978-3-642-42033-7_3.
  66. Silvio Micali. CS proofs (extended abstracts). In 35th Annual Symposium on Foundations of Computer Science, Santa Fe, New Mexico, USA, 20-22 November 1994, pages 436-453. IEEE Computer Society, 1994. URL: https://doi.org/10.1109/SFCS.1994.365746.
  67. Moni Naor. On cryptographic assumptions and challenges. In Advances in Cryptology-CRYPTO 2003: 23rd Annual International Cryptology Conference, Santa Barbara, California, USA, August 17-21, 2003. Proceedings 23, pages 96-109. Springer, 2003. URL: https://doi.org/10.1007/978-3-540-45146-4_6.
  68. Shafik Nassar, Brent Waters, and David J Wu. Monotone policy bargs from bargs and additively homomorphic encryption. Cryptology ePrint Archive, 2023. Google Scholar
  69. Tatsuaki Okamoto, Krzysztof Pietrzak, Brent Waters, and Daniel Wichs. New realizations of somewhere statistically binding hashing and positional accumulators. In International Conference on the Theory and Application of Cryptology and Information Security, pages 121-145. Springer, 2015. URL: https://doi.org/10.1007/978-3-662-48797-6_6.
  70. Omer Paneth and Rafael Pass. Incrementally verifiable computation via rate-1 batch arguments. In 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS), pages 1045-1056. IEEE, 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00102.
  71. Bryan Parno, Jon Howell, Craig Gentry, and Mariana Raykova. Pinocchio: Nearly practical verifiable computation. Communications of the ACM, 59(2):103-112, 2016. URL: https://doi.org/10.1145/2856449.
  72. Oded Regev. On lattices, learning with errors, random linear codes, and cryptography. In STOC, 2005. Google Scholar
  73. Omer Reingold, Guy N Rothblum, and Ron D Rothblum. Constant-round interactive proofs for delegating computation. In Proceedings of the forty-eighth annual ACM symposium on Theory of Computing, pages 49-62, 2016. URL: https://doi.org/10.1145/2897518.2897652.
  74. Amit Sahai and Brent Waters. How to use indistinguishability obfuscation: deniable encryption, and more. In Symposium on Theory of Computing, STOC 2014, New York, NY, USA, May 31 - June 03, 2014, pages 475-484, 2014. URL: https://doi.org/10.1145/2591796.2591825.
  75. Srinath Setty. Spartan: Efficient and general-purpose zksnarks without trusted setup. In Advances in Cryptology-CRYPTO 2020: 40th Annual International Cryptology Conference, CRYPTO 2020, Santa Barbara, CA, USA, August 17-21, 2020, Proceedings, Part III, pages 704-737. Springer, 2020. URL: https://doi.org/10.1007/978-3-030-56877-1_25.
  76. Ron Steinfeld, Laurence Bull, and Yuliang Zheng. Content extraction signatures. In ICISC, 2001. Google Scholar
  77. Paul Valiant. Incrementally verifiable computation or proofs of knowledge imply time/space efficiency. In Theory of Cryptography, Fifth Theory of Cryptography Conference, TCC 2008, New York, USA, March 19-21, 2008, pages 1-18, 2008. URL: https://doi.org/10.1007/978-3-540-78524-8_1.
  78. Brent Waters and David J. Wu. Batch arguments for NP and more from standard bilinear group assumptions. IACR Cryptol. ePrint Arch., page 336, 2022. URL: https://eprint.iacr.org/2022/336.
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
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact