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Isogeny-Based Multi-signature Scheme

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Information Security Practice and Experience (ISPEC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14341))

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Abstract

Multi-signatures are protocols that allow multiple signers to produce a joint signature on the same message. They are used in areas such as blockchains for cryptocurrencies. In recent years, multi-signature schemes have been proposed in lattice-based cryptography as well as pairing-based cryptography but there are currently no multi-signature schemes in isogeny-based cryptography.

In this paper, we propose a multi-signature scheme by extending the Commutative Supersingular Isogeny based Fiat-Shamir signature (CSI-FiSh), as well as its variant CSI-FiSh with Sharing-friendly Keys (CSI-SharK) to the multiple signers setting. To adapt our scheme to the isogeny setting, we use a round-robin during both the key aggregation and the signature aggregation. We also prove the security of our scheme in the Random Oracle Model (ROM) by using the Double Forking Lemma Technique.

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References

  1. Atapoor, S., Baghery, K., Cozzo, D., Pedersen, R.: CSI-SharK: CSI-FiSh with sharing-friendly keys. In: IACR Cryptol. ePrint Arch, p. 1189 (2022)

    Google Scholar 

  2. Bellare, M., Neven, G.: Multi-signatures in the plain public-key model and a general forking lemma, pp. 390–399 (2006)

    Google Scholar 

  3. Beullens, W., Kleinjung, T., Vercauteren, F.: CSI-FiSh: efficient isogeny based signatures through class group computations. In: IACR Cryptol. ePrint Arch, p. 498 (2019)

    Google Scholar 

  4. Boschini, C., Takahashi, A., Tibouchi, M.: MuSig-L: lattice-based multi-signature with single-round online phase. Cryptology ePrint Archive, Paper 2022/1036 (2022)

    Google Scholar 

  5. Castryck, W., Decru, T.: An efficient key recovery attack on SIDH (preliminary version). In: IACR Cryptol. ePrint Arch, p. 975 (2022)

    Google Scholar 

  6. Castryck, W., Lange, T., Martindale, C., Panny, L., Renes, J.: CSIDH: an efficient post-quantum commutative group action. In: IACR Cryptol. ePrint Arch, p. 383 (2018)

    Google Scholar 

  7. Childs, A.M., Jao, D., Soukharev, V.: Constructing elliptic curve isogenies in quantum subexponential time. J. Math. Cryptol. 8(1), 1–29 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Couveignes, J.M.: Hard homogeneous spaces. In: IACR Cryptol. ePrint Arch, p. 291 (2006)

    Google Scholar 

  9. Couveignes, J.M.: Hard homogeneous spaces. Cryptology ePrint Archive, Paper 2006/291 (2006)

    Google Scholar 

  10. Cozzo, D., Smart, N.P.: Sashimi: cutting up CSI-FiSh secret keys to produce an actively secure distributed signing protocol. In: Ding, J., Tillich, J.-P. (eds.) PQCrypto 2020. LNCS, vol. 12100, pp. 169–186. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-44223-1_10

    Chapter  Google Scholar 

  11. Drijvers, M., Gorbunov, S., Neven, G., Wee, H.: Pixel: multi-signatures for consensus. In: 29th USENIX Security Symposium (USENIX Security 2020), pp. 2093–2110. USENIX Association (2020)

    Google Scholar 

  12. Feo, L.D.: Mathematics of isogeny based cryptography. CoRR abs/1711.04062 (2017)

    Google Scholar 

  13. De Feo, L., Galbraith, S.D.: SeaSign: compact isogeny signatures from class group actions. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11478, pp. 759–789. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_26

    Chapter  Google Scholar 

  14. Feo, L.D., Jao, D., Plut, J.: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. J. Math. Cryptol. 8(3), 209–247 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Feo, L.D., Meyer, M.: Threshold schemes from isogeny assumptions. IACR Cryptol. ePrint Arch, p. 1288 (2019)

    Google Scholar 

  16. Jao, D., De Feo, L.: Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies. In: Yang, B.-Y. (ed.) PQCrypto 2011. LNCS, vol. 7071, pp. 19–34. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25405-5_2

    Chapter  MATH  Google Scholar 

  17. Kojima, R., Yamamoto, D., Shimoyama, T., Yasaki, K., Nimura, K.: A new schnorr multi-signatures to support both multiple messages signing and key aggregation. J. Inf. Process. 29, 525–536 (2021)

    Google Scholar 

  18. Maino, L., Martindale, C.: An attack on SIDH with arbitrary starting curve. In: IACR Cryptol. ePrint Arch, p. 1026 (2022)

    Google Scholar 

  19. Maxwell, G., Poelstra, A., Seurin, Y., Wuille, P.: Simple schnorr multi-signatures with applications to bitcoin. Cryptology ePrint Archive, Paper 2018/068 (2018)

    Google Scholar 

  20. Robert, D.: Breaking SIDH in polynomial time. In: IACR Cryptol. ePrint Arch, p. 1038 (2022)

    Google Scholar 

  21. Rostovtsev, A., Stolbunov, A.: Public-key cryptosystem based on isogenies. In: IACR Cryptol. ePrint Arch, p. 145 (2006)

    Google Scholar 

  22. Stolbunov, A.: Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves. Adv. Math. Commun. 4(2), 215–235 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Stolbunov, A.: Cryptographic schemes based on isogenies. Ph.D. thesis (2012)

    Google Scholar 

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Acknowledgment

This work is partially supported by JSPS KAKENHI Grant Number JP21H03443 and SECOM Science and Technology Foundation.

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Authors and Affiliations

  1. Osaka University, Osaka, Japan

    Mathieu de Goyon & Atsuko Miyaji

  2. Japan Advanced Institute of Technology, Ishikawa, Japan

    Atsuko Miyaji

Authors
  1. Mathieu de Goyon
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  2. Atsuko Miyaji
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Corresponding author

Correspondence to Mathieu de Goyon .

Editor information

Editors and Affiliations

  1. Technical University of Denmark, Kongens Lyngby, Denmark

    Weizhi Meng

  2. Xidian University, Xi'an, China

    Zheng Yan

  3. University of Milan, Milan, Italy

    Vincenzo Piuri

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© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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de Goyon, M., Miyaji, A. (2023). Isogeny-Based Multi-signature Scheme. In: Meng, W., Yan, Z., Piuri, V. (eds) Information Security Practice and Experience. ISPEC 2023. Lecture Notes in Computer Science, vol 14341. Springer, Singapore. https://doi.org/10.1007/978-981-99-7032-2_28

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  • DOI: https://doi.org/10.1007/978-981-99-7032-2_28

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-7031-5

  • Online ISBN: 978-981-99-7032-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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