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\(\textsf{ReSolveD} \): Shorter Signatures from Regular Syndrome Decoding and VOLE-in-the-Head

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Public-Key Cryptography – PKC 2024 (PKC 2024)

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Abstract

We present \(\textsf{ReSolveD} \), a new candidate post-quantum signature scheme under the regular syndrome decoding (RSD) assumption for random linear codes, which is a well-established variant of the well-known syndrome decoding (SD) assumption. Our signature scheme is obtained by designing a new zero-knowledge proof for proving knowledge of a solution to the RSD problem in the recent VOLE-in-the-head framework using a sketching scheme to verify that a vector has weight exactly one. We achieve a signature size of 3.99 KB with a signing time of 27.3 ms and a verification time of 23.1 ms on a single core of a standard desktop for a 128-bit security level. Compared to the state-of-the-art code-based signature schemes, our signature scheme achieves \(1.5{\times }\)–\(2{\times }\) improvement in terms of the common “signature size + public-key size” metric, while keeping the computational efficiency competitive.

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Notes

  1. 1.

    This technique somewhat resembles the classical MPC-in-the-head technique.

  2. 2.

    We select the parameters of \(\textsf{ReSolveD} \)-128 and \(\textsf{ReSolveD} \)-L{1,3,5} independently, because the former targets at signatures with 128-bit security while the latter targets other NIST submissions.

  3. 3.

    We adapted the reference implementation of FAEST at https://github.com/faest-sign/faest-ref. We also note that OpenSSL is required to facilitate fast evaluation.

References

  1. Aguilar Melchor, C., Gama, N., Howe, J., Hülsing, A., Joseph, D., Yue, D.: The return of the SDitH. LNCS, vol. 14008, pp. 564–596. Springer, Heidelberg (2023). https://doi.org/10.1007/978-3-031-30589-4_20

  2. Alaoui, S.M.E.Y., Cayrel, P., Bansarkhani, R.E., Hoffmann, G.: Code-based identification and signature schemes in software. In: Cuzzocrea, A., Kittl, C., Simos, D.E., Weippl, E.R., Xu, L. (eds.) Security Engineering and Intelligence Informatics - CD-ARES 2013 Workshops: MoCrySEn and SeCIHD, Regensburg, Germany, 2–6 September 2013, Proceedings. LNCS, vol. 8128, pp. 122–136. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40588-4_9

  3. Aragon, N., Blazy, O., Gaborit, P., Hauteville, A., Zémor, G.: Durandal: a rank metric based signature scheme. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019, Part III. LNCS, vol. 11478, pp. 728–758. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-030-17659-4_25

  4. Augot, D., Finiasz, M., Sendrier, N.: A fast provably secure cryptographic hash function. Cryptology ePrint Archive, Report 2003/230 (2003). https://eprint.iacr.org/2003/230

  5. Barenghi, A., Biasse, J.F., Persichetti, E., Santini, P.: LESS-FM: fine-tuning signatures from the code equivalence problem. In: Cheon, J.H., Tillich, J.P. (eds.) Post-Quantum Cryptography - 12th International Workshop, PQCrypto 2021. LNCS, vol. 12841, pp. 23–43. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-030-81293-5_2

  6. Barg, S.: Some new NP-complete coding problems. Probl. Inf. Transm. 30(3), 209–214 (1994)

    MathSciNet  Google Scholar 

  7. Baum, C., Braun, L., Munch-Hansen, A., Razet, B., Scholl, P.: Appenzeller to Brie: efficient zero-knowledge proofs for mixed-mode arithmetic and Z2k. In: Vigna, G., Shi, E. (eds.) ACM CCS 2021, pp. 192–211. ACM Press, November 2021. https://doi.org/10.1145/3460120.3484812

  8. Baum, C., Braun, L., Munch-Hansen, A., Scholl, P.: Moz\(\mathbb{Z}_{2^k}\)arella: efficient vector-OLE and zero-knowledge proofs over \(\mathbb{Z}_{2^k}\). In: Dodis, Y., Shrimpton, T. (eds.) CRYPTO 2022, Part IV. LNCS, pp. 329–358. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-15985-5_12

  9. Baum, C., et al.: FAEST: algorithm specifications. Technical report, National Institute of Standards and Technology (2023). https://faest.info/faest-spec-v1.1.pdf

  10. Baum, C., et al.: Publicly verifiable zero-knowledge and post-quantum signatures from VOLE-in-the-Head. In: Handschuh, H., Lysyanskaya, A. (eds.) CRYPTO 2023, Part V. LNCS, vol. 14085, pp. 581–615. Springer, Heidelberg (2023). https://doi.org/10.1007/978-3-031-38554-4_19

  11. Baum, C., Malozemoff, A.J., Rosen, M.B., Scholl, P.: Mac’n’Cheese: zero-knowledge proofs for boolean and arithmetic circuits with nested disjunctions. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021, Part IV. LNCS, vol. 12828, pp. 92–122. Springer, Heidelberg (2021). Virtual Event, https://doi.org/10.1007/978-3-030-84259-8_4

  12. Bendlin, R., Damgård, I., Orlandi, C., Zakarias, S.: Semi-homomorphic encryption and multiparty computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169–188. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_11

  13. Berlekamp, E.R., McEliece, R.J., van Tilborg, H.C.A.: On the inherent intractability of certain coding problems (Corresp.). IEEE Trans. Inf. Theory 24(3), 384–386 (1978). https://doi.org/10.1109/TIT.1978.1055873

  14. Biasse, J.F., Micheli, G., Persichetti, E., Santini, P.: LESS is more: code-based signatures without syndromes. In: Nitaj, A., Youssef, A.M. (eds.) AFRICACRYPT 2020. LNCS, vol. 12174, pp. 45–65. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-51938-4_3

  15. Bidoux, L., Gaborit, P., Kulkarni, M., Mateu, V.: Code-based signatures from new proofs of knowledge for the syndrome decoding problem. Des. Codes Cryptogr. 91(2), 497–544 (2023). https://doi.org/10.1007/s10623-022-01114-3

    Article  MathSciNet  Google Scholar 

  16. Boyle, E., Gilboa, N., Ishai, Y.: Function secret sharing: improvements and extensions. In: Weippl, E.R., Katzenbeisser, S., Kruegel, C., Myers, A.C., Halevi, S. (eds.) ACM CCS 2016, pp. 1292–1303. ACM Press, October 2016. https://doi.org/10.1145/2976749.2978429

  17. Briaud, P., Øygarden, M.: A new algebraic approach to the regular syndrome decoding problem and implications for PCG constructions. In: Hazay, C., Stam, M. (eds.) Advances in Cryptology – EUROCRYPT 2023. LNCS, vol. 14008, pp. 391–422. Springer, Heidelberg (2023). https://doi.org/10.1007/978-3-031-30589-4_14

  18. Carozza, E., Couteau, G., Joux, A.: Short signatures from regular syndrome decoding in the head. In: Hazay, C., Stam, M. (eds.) Advances in Cryptology – EUROCRYPT 2023. LNCS, vol. 14008, pp. 532–563. Springer, Heidelberg (2023). https://doi.org/10.1007/978-3-031-30589-4_19

  19. Cascudo, I., Damgård, I., David, B., Döttling, N., Dowsley, R., Giacomelli, I.: Efficient UC commitment extension with homomorphism for free (and applications). In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019, Part II. LNCS, vol. 11922, pp. 606–635. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-030-34621-8_22

  20. Cayrel, P., Véron, P., Alaoui, S.M.E.Y.: A zero-knowledge identification scheme based on the q-ary syndrome decoding problem. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 171–186. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-19574-7_12

  21. Chou, T., Persichetti, E., Santini, P.: On linear equivalence, canonical forms, and digital signatures. Cryptology ePrint Archive, Paper 2023/1533 (2023). https://eprint.iacr.org/2023/1533

  22. Debris-Alazard, T., Sendrier, N., Tillich, J.P.: Wave: a new family of trapdoor one-way preimage sampleable functions based on codes. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019, Part I. LNCS, vol. 11921, pp. 21–51. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-030-34578-5_2

  23. Dittmer, S., Ishai, Y., Lu, S., Ostrovsky, R.: Improving line-point zero knowledge: two multiplications for the price of one, pp. 829–841. ACM Press (2022). https://doi.org/10.1145/3548606.3559385

  24. Dittmer, S., Ishai, Y., Ostrovsky, R.: Line-point zero knowledge and its applications. In: 2nd Conference on Information-Theoretic Cryptography (2021)

    Google Scholar 

  25. Esser, A., Santini, P.: Not just regular decoding: asymptotics and improvements of regular syndrome decoding attacks. Cryptology ePrint Archive, Paper 2023/1568 (2023). https://eprint.iacr.org/2023/1568

  26. Feneuil, T., Joux, A., Rivain, M.: Syndrome decoding in the head: shorter signatures from zero-knowledge proofs. In: CRYPTO 2022, Part II, pp. 541–572. LNCS, Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-15979-4_19

  27. Feneuil, T., Joux, A., Rivain, M.: Shared permutation for syndrome decoding: new zero-knowledge protocol and code-based signature. Des. Codes Cryptogr. 91(2), 563–608 (2023). https://doi.org/10.1007/s10623-022-01116-1, First appeared online at https://eprint.iacr.org/2021/1576

  28. Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987). https://doi.org/10.1007/3-540-47721-7_12

  29. Gaborit, P., Girault, M.: Lightweight code-based identification and signature. In: IEEE International Symposium on Information Theory, ISIT 2007, Nice, France, 24–29 June 2007, pp. 191–195. IEEE (2007). https://doi.org/10.1109/ISIT.2007.4557225

  30. Gueron, S., Persichetti, E., Santini, P.: Designing a practical code-based signature scheme from zero-knowledge proofs with trusted setup. Cryptography 6(1), 5 (2022). https://doi.org/10.3390/cryptography6010005

  31. Guo, C., Katz, J., Wang, X., Yu, Y.: Efficient and secure multiparty computation from fixed-key block ciphers. In: 2020 IEEE Symposium on Security and Privacy, pp. 825–841. IEEE Computer Society Press, May 2020. https://doi.org/10.1109/SP40000.2020.00016

  32. Guo, X., et al.: Half-Tree: halving the cost of tree expansion in COT and DPF. In: Hazay, C., Stam, M. (eds.) EUROCRYPT 2023, Part I. LNCS, vol. 14004, pp. 330–362. Springer, Heidelberg (2023). https://doi.org/10.1007/978-3-031-30545-0_12

  33. Hazay, C., Orsini, E., Scholl, P., Soria-Vazquez, E.: TinyKeys: a new approach to efficient multi-party computation. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part III. LNCS, vol. 10993, pp. 3–33. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-319-96878-0_1

  34. Hülsing, A., et al.: SPHINCS+. Technical report, National Institute of Standards and Technology (2022). https://csrc.nist.gov/Projects/post-quantum-cryptography/selected-algorithms-2022

  35. Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Zero-knowledge from secure multiparty computation. In: Johnson, D.S., Feige, U. (eds.) 39th ACM STOC, pp. 21–30. ACM Press, June 2007. https://doi.org/10.1145/1250790.1250794

  36. Kales, D., Zaverucha, G.: Improving the performance of the Picnic signature scheme. IACR TCHES 2020(4), 154–188 (2020). https://doi.org/10.13154/tches.v2020.i4.154-188, https://tches.iacr.org/index.php/TCHES/article/view/8680

  37. Keller, M., Orsini, E., Scholl, P.: Actively secure OT extension with optimal overhead. In: Gennaro, R., Robshaw, M.J.B. (eds.) CRYPTO 2015, Part I. LNCS, vol. 9215, pp. 724–741. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6_35

  38. Liu, H., Wang, X., Yang, K., Yu, Y.: The hardness of LPN over any integer ring and field for PCG applications. Cryptology ePrint Archive, Report 2022/712 (2022). https://eprint.iacr.org/2022/712

  39. Lyubashevsky, V., et al.: CRYSTALS-DILITHIUM. Technical report, National Institute of Standards and Technology (2022). https://csrc.nist.gov/Projects/post-quantum-cryptography/selected-algorithms-2022

  40. Melchor, C.A., et al.: The Syndrome Decoding in the Head (SD-in-the-Head) signature scheme. Technical report, National Institute of Standards and Technology (2023). https://csrc.nist.gov/csrc/media/Projects/pqc-dig-sig/documents/round-1/spec-files/SDitH-spec-web.pdf

  41. Melchor, C.A., Gaborit, P., Schrek, J.: A new zero-knowledge code based identification scheme with reduced communication. In: 2011 IEEE Information Theory Workshop, ITW 2011, Paraty, Brazil, 16–20 October 2011, pp. 648–652. IEEE (2011). https://doi.org/10.1109/ITW.2011.6089577

  42. Melchor, C.A., Hülsing, A., Joseph, D., Majenz, C., Ronen, E., Yue, D.: SDitH in the QROM. In: Guo, J., Steinfeld, R. (eds.) ASIACRYPT 2023, Part VII. LNCS, vol. 14444, pp. 317–350. Springer, Heidelberg (2023). https://doi.org/10.1007/978-981-99-8739-9_11

  43. Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A new approach to practical active-secure two-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 681–700. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_40

  44. NIST: Call for additional digital signature schemes for the post-quantum cryptography standardization process (2022). https://csrc.nist.gov/csrc/media/Projects/pqc-dig-sig/documents/call-for-proposals-dig-sig-sept-2022.pdf

  45. Orrù, M., Orsini, E., Scholl, P.: Actively secure 1-out-of-N OT extension with application to private set intersection. In: Handschuh, H. (ed.) CT-RSA 2017. LNCS, vol. 10159, pp. 381–396. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-319-52153-4_22

  46. Patra, A., Sarkar, P., Suresh, A.: Fast actively secure OT extension for short secrets. In: NDSS 2017. The Internet Society, February/March 2017

    Google Scholar 

  47. Persichetti, E., Santini, P.: A new formulation of the linear equivalence problem and shorter less signatures. Cryptology ePrint Archive, Paper 2023/847 (2023). https://eprint.iacr.org/2023/847

  48. Prest, T., et al.: FALCON. Technical report, National Institute of Standards and Technology (2022). https://csrc.nist.gov/Projects/post-quantum-cryptography/selected-algorithms-2022

  49. Roy, L.: SoftSpokenOT: quieter OT extension from small-field silent VOLE in the minicrypt model. In: CRYPTO 2022, Part I. LNCS, vol. 13507, pp. 657–687. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-15802-5_23

  50. Schwartz, J.T.: Fast probabilistic algorithms for verification of polynomial identities. J. ACM 27(4), 701–717 (1980). https://doi.org/10.1145/322217.322225

    Article  MathSciNet  Google Scholar 

  51. Stern, J.: A new identification scheme based on syndrome decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 13–21. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48329-2_2

  52. Véron, P.: Improved identification schemes based on error-correcting codes. Appl. Algebra Eng. Commun. Comput. 8(1), 57–69 (1996). https://doi.org/10.1007/s002000050053

  53. Weng, C., Yang, K., Katz, J., Wang, X.: Wolverine: fast, scalable, and communication-efficient zero-knowledge proofs for boolean and arithmetic circuits. In: 2021 IEEE Symposium on Security and Privacy, pp. 1074–1091. IEEE Computer Society Press, May 2021. https://doi.org/10.1109/SP40001.2021.00056

  54. Weng, C., Yang, K., Xie, X., Katz, J., Wang, X.: Mystique: efficient conversions for zero-knowledge proofs with applications to machine learning. In: Bailey, M., Greenstadt, R. (eds.) USENIX Security 2021, pp. 501–518. USENIX Association, August 2021

    Google Scholar 

  55. Weng, C., Yang, K., Yang, Z., Xie, X., Wang, X.: AntMan: interactive zero-knowledge proofs with sublinear communication, pp. 2901–2914. ACM Press (2022). https://doi.org/10.1145/3548606.3560667

  56. Yang, K., Sarkar, P., Weng, C., Wang, X.: QuickSilver: efficient and affordable zero-knowledge proofs for circuits and polynomials over any field. In: Vigna, G., Shi, E. (eds.) ACM CCS 2021, pp. 2986–3001. ACM Press, November 2021. https://doi.org/10.1145/3460120.3484556

  57. Zaverucha, G., et al.: Picnic. Technical report, National Institute of Standards and Technology (2020). https://csrc.nist.gov/projects/post-quantum-cryptography/post-quantum-cryptography-standardization/round-3-submissions

  58. Zhang, K., Cui, H., Yu, Y.: SPHINCS-alpha. Technical report, National Institute of Standards and Technology (2023). https://csrc.nist.gov/Projects/pqc-dig-sig/round-1-additional-signatures

  59. Zippel, R.: Probabilistic algorithms for sparse polynomials. In: Ng, E.W. (ed.) Symbolic and Algebraic Computation, EUROSAM 1979, An International Symposium on Symbolic and Algebraic Computation, Marseille, France, June 1979, Proceedings. LNCS, vol. 72, pp. 216–226. Springer, Heidelberg (1979). https://doi.org/10.1007/3-540-09519-5_73

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Acknowledgements

We thank anonymous reviewers for their helpful comments. Yu Yu is supported by the National Key Research and Development Program of China (Grant No. 2020YFA0309705), the National Natural Science Foundation of China (Grant Nos. 62125204 and 92270201), and the Major Program of Guangdong Basic and Applied Research (Grant No. 2019B030302008). Yu Yu also acknowledges the support from the XPLORER PRIZE. Kang Yang is supported by the National Natural Science Foundation of China (Grant Nos. 62102037 and 61932019).

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Authors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Hongrui Cui, Yu Yu & Kaiyi Zhang

  2. Shanghai Qi Zhi Institute, Shanghai, China

    Hanlin Liu & Yu Yu

  3. State Key Laboratory of Cryptology, Beijing, China

    Di Yan & Kang Yang

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  1. The University of Sydney, Sydney, NSW, Australia

    Qiang Tang

  2. The Australian National University, Acton, ACT, Australia

    Vanessa Teague

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Cui, H., Liu, H., Yan, D., Yang, K., Yu, Y., Zhang, K. (2024). \(\textsf{ReSolveD} \): Shorter Signatures from Regular Syndrome Decoding and VOLE-in-the-Head. In: Tang, Q., Teague, V. (eds) Public-Key Cryptography – PKC 2024. PKC 2024. Lecture Notes in Computer Science, vol 14601. Springer, Cham. https://doi.org/10.1007/978-3-031-57718-5_8

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