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2024 | OriginalPaper | Buchkapitel

Publicly Verifiable Secret Sharing Over Class Groups and Applications to DKG and YOSO

verfasst von : Ignacio Cascudo, Bernardo David

Erschienen in: Advances in Cryptology – EUROCRYPT 2024

Verlag: Springer Nature Switzerland

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Abstract

Publicly Verifiable Secret Sharing (PVSS) allows a dealer to publish encrypted shares of a secret so that parties holding the corresponding decryption keys may later reconstruct it. Both dealing and reconstruction are non-interactive and any verifier can check their validity. PVSS finds applications in randomness beacons, distributed key generation (DKG) and in YOSO MPC (Gentry et al. CRYPTO’21), when endowed with suitable publicly verifiable re-sharing as in YOLO YOSO (Cascudo et al. ASIACRYPT’22).

We introduce a PVSS scheme over class groups that achieves similar efficiency to state-of-the art schemes that only allow for reconstructing a function of the secret, while our scheme allows the reconstruction of the original secret. Our construction generalizes the DDH-based scheme of YOLO YOSO to operate over class groups, which poses technical challenges in adapting the necessary NIZKs in face of the unknown group order and the fact that efficient NIZKs of knowledge are not as simple to construct in this setting.

Building on our PVSS scheme’s ability to recover the original secret, we propose two DKG protocols for discrete logarithm key pairs: a biasable 1-round protocol, which improves on the concrete communication/computational complexities of previous works; and a 2-round unbiasable protocol, which improves on the round complexity of previous works. We also add publicly verifiable resharing towards anonymous committees to our PVSS, so that it can be used to efficiently transfer state among committees in the YOSO setting. Together with a recent construction of MPC in the YOSO model based on class groups (Braun et al. CRYPTO’23), this results in the most efficient full realization (i.e. without assuming receiver anonymous channels) of YOSO MPC based on the CDN framework with transparent setup.

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Vorheriges Kapitel Garbled Circuit Lookup Tables with Logarithmic Number of Ciphertexts

Nächstes Kapitel Bulletproofs++: Next Generation Confidential Transactions via Reciprocal Set Membership Arguments

Up to a constant due to the time for group operations and size for group elements in class groups being higher than those for DDH-hard groups based on elliptic curves.

In coding-theoretic this set is the dual code to the Reed-Solomon code formed by the evaluations of polynomials of degree \(\le d\).

As well as for using the ZK proof protocol from [6] which we show in next section.

The proofs were in fact introduced for slightly more involved relations, but for simplicity we adapt them for just proving knowledge of discrete logarithm.

Notation: To avoid confusion with the group \(G^q\) of q-th powers of elements from G, we denote the direct product of m copies of G, for \(m\in \mathbb {N}\), as \((G)^m\).

Recall, that by definition of \(\textrm{Lag}_{}\), \(L_i(X)=\prod _{j\in \mathcal {T}'\setminus \{i\}}\frac{X-\alpha _j}{\alpha _i-\alpha _j}\).

In practice we consider \(\kappa =40\) is reasonable.

Acharya, A., Hazay, C., Kolesnikov, V., Prabhakaran, M.: SCALES - MPC with small clients and larger ephemeral servers. In: Kiltz, E., Vaikuntanathan, V. (eds.) TCC 2022. LNCS, vol. 13748, pp. 502–531. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-22365-5_18CrossRef

Bayer, S., Groth, J.: Efficient zero-knowledge argument for correctness of a shuffle. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 263–280. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_17CrossRef

Benhamouda, F., et al.: Can a public blockchain keep a secret? In: Pass, R., Pietrzak, K. (eds.) TCC 2020. LNCS, vol. 12550, pp. 260–290. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-64375-1_10CrossRef

Boudot, F., Traoré, J.: Efficient publicly verifiable secret sharing schemes with fast or delayed recovery. In: Varadharajan, V., Yi, M. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 87–102. Springer, Heidelberg (1999). https://doi.org/10.1007/978-3-540-47942-0_8CrossRef

Bouvier, C., Castagnos, G., Imbert, L., Laguillaumie, F.: I want to ride my BICYCL : BICYCL implements cryptography in class groups. J. Cryptol. 36(3), 17 (2023)MathSciNetCrossRef

Braun, L., Damgård, I., Orlandi, C.: Secure multiparty computation from threshold encryption based on class groups. In: Handschuh, H., Lysyanskaya, A., (eds.) Advances in Cryptology - CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Santa Barbara, CA, USA, August 20-24, 2023, Proceedings, Part I, vol. 14081. LNCS, pp. 613–645. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-38557-5_20

Campanelli, M., David, B., Khoshakhlagh, H., Konring, A., Nielsen, J.B.: Encryption to the future - a paradigm for sending secret messages to future (anonymous) committees. In: Agrawal, S., Lin, D. (eds.) ASIACRYPT 2022. LNCS, vol. 13793, pp. 151–180. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-22969-5_6CrossRef

Cascudo, I., David, B.: SCRAPE: scalable randomness attested by public entities. In: Gollmann, D., Miyaji, A., Kikuchi, H. (eds.) ACNS 17. LNCS, vol. 10355, pp. 537–556. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-319-61204-1_27CrossRef

Cascudo, I., David, B.: ALBATROSS: publicly attestable batched randomness based on secret sharing. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12493, pp. 311–341. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-64840-4_11CrossRef

10.

Cascudo, I., David, B.: Publicly verifiable secret sharing over class groups and applications to DKG and YOSO. Cryptology ePrint Archive, Paper 2023/1651 (2023). https://eprint.iacr.org/2023/1651

11.

Cascudo, I., David, B., Garms, L., Konring, A.: YOLO YOSO: fast and simple encryption and secret sharing in the YOSO model. In: Agrawal, S., Lin, D. (eds.) ASIACRYPT 2022. LNCS, vol. 13791, pp. 651–680. Springer, Heidelberg (2022)CrossRef

12.

Cascudo, I., David, B., Shlomovits, O., Varlakov, D.: Mt. random: multi-tiered randomness beacons. In: Tibouchi, M., Wang, X., (eds.) Applied Cryptography and Network Security - 21st International Conference, ACNS 2023, Kyoto, Japan, June 19-22, 2023, Proceedings, Part II, vol. 13906, LNCS, pages 645–674. Springer, Cham (2023.) https://doi.org/10.1007/978-3-031-33491-7_24

13.

Castagnos, G., Catalano, D., Laguillaumie, F., Savasta, F., Tucker, I.: Two-party ECDSA from hash proof systems and efficient instantiations. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 191–221. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-030-26954-8_7CrossRef

14.

Castagnos, G., Catalano, D., Laguillaumie, F., Savasta, F., Tucker, I.: Bandwidth-efficient threshold EC-DSA. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020. LNCS, vol. 12111, pp. 266–296. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-45388-6_10CrossRef

15.

Castagnos, G., Imbert, L., Laguillaumie, F.: Encryption switching protocols revisited: Switching modulo \(p\). In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 255–287. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-319-63688-7_9CrossRef

16.

Castagnos, G., Laguillaumie, F.: Linearly homomorphic encryption from DDH. In: Nyberg, K., (ed.) Topics in Cryptology - CT-RSA 2015, The Cryptographer’s Track at the RSA Conference 2015, San Francisco, CA, USA, April 20-24, 2015. Proceedings, vol. 9048, LNCS, pp. 487–505. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16715-2_26

17.

Castagnos, G., Laguillaumie, F., Tucker, I.: Practical fully secure unrestricted inner product functional encryption modulo \(p\). In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11273, pp. 733–764. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-030-03329-3_25CrossRef

18.

Choudhuri, A.R., Goel, A., Green, M., Jain, A., Kaptchuk, G.: Fluid MPC: secure multiparty computation with dynamic participants. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12826, pp. 94–123. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84245-1_4CrossRef

19.

Cramer, R., Damgård, I., Nielsen, J.B.: Multiparty computation from threshold homomorphic encryption. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 280–299. Springer, Heidelberg (2001)CrossRef

20.

David, B., et al.: Perfect MPC over layered graphs. In: Handschuh, H., Lysyanskaya, A., (eds.), Advances in Cryptology - CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Santa Barbara, CA, USA, August 20-24, 2023, Proceedings, Part I, vol. 14081, LNCS, pp. 360–392. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-38557-5_12

21.

Dobson, S., Galbraith, S.D., Smith, B.: Trustless unknown-order groups. Math. Cryptol. 1(2), 25–39 (2022)

22.

Faust, S., Kohlweiss, M., Marson, G.A., Venturi, D.: On the non-malleability of the Fiat-Shamir transform. In: Galbraith, S.D., Nandi, M. (eds.) INDOCRYPT 2012. LNCS, vol. 7668, pp. 60–79. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34931-7_5

23.

Fouque, P.-A., Stern, J.: One round threshold discrete-log key generation without private channels. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 300–316. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44586-2_22CrossRef

24.

Fujisaki, E., Okamoto, T.: A practical and provably secure scheme for publicly verifiable secret sharing and its applications. In: Nyberg, K. (ed.), EUROCRYPT 1998, vol. 1403, LNCS, pp. 32–46. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0054115

25.

Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure distributed key generation for discrete-log based cryptosystems. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 295–310. Springer, Heidelberg (1999)

26.

Gentry, C., et al.: YOSO: you only speak once - secure MPC with stateless ephemeral roles. In: Malkin, T., Peikert, C., (eds.) CRYPTO 2021, Part II, vol. 12826, LNCS, pp. 64–93. Springer, Heidelberg (2021)

27.

Gentry, C., Halevi, S., Lyubashevsky, V.: Practical non-interactive publicly verifiable secret sharing with thousands of parties. In: Dunkelman, O., Dziembowski, S. (eds.) EUROCRYPT 2022, Part I, vol. 13275, LNCS, pp. 458–487. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-06944-4_16

28.

Gentry, C., Halevi, S., Magri, B., Nielsen, J.B., Yakoubov, S.: Random-index PIR and applications. In: Nissim, K., Waters, B. (eds.) TCC 2021. LNCS, vol. 13044, pp. 32–61. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-030-90456-2_2CrossRef

29.

Groth, J.: Non-interactive distributed key generation and key resharing. Cryptology ePrint Archive, Paper 2021/339 (2021). https://eprint.iacr.org/2021/339

30.

Gurkan, K., Jovanovic, P., Maller, M., Meiklejohn, S., Stern, G., Tomescu, A.: Aggregatable distributed key generation. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12696, pp. 147–176. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-030-77870-5_6CrossRef

31.

Heidarvand, S., Villar, J.L.: Public verifiability from pairings in secret sharing schemes. In: Avanzi, R.M., Keliher, L., Sica, F., (eds.) SAC 2008, vol. 5381, LNCS, pp. 294–308. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04159-4_19

32.

Kate, A., Mangipudi, E.V., Mukherjee, P., Saleem, H., Aravinda, S., Thyagarajan, K.: Non-interactive VSS using class groups and application to DKG. Cryptology ePrint Archive, Paper 2023/451 (2023). https://eprint.iacr.org/2023/451

33.

Katz, J.: Round optimal robust distributed key generation. Cryptology ePrint Archive, Paper 2023/1094 (2023). https://eprint.iacr.org/2023/1094

34.

Pedersen, P.T.: A threshold cryptosystem without a trusted party (extended abstract) (rump session). In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 522–526. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_47CrossRef

35.

Rachuri, R., Scholl, P.: Le Mans: dynamic and fluid MPC for dishonest majority. In: Dodis, Y., Shrimpton, T. (eds.) CRYPTO 2022. LNCS, vol. 13507, pp. 719–749. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-15802-5_25CrossRef

36.

Ruiz, A., Villar, J.L.: Publicly verifiable secret sharing from Paillier’s cryptosystem. In: WEWoRC 2005–Western European Workshop on Research in Cryptology (2005)

37.

Schoenmakers, B.: A simple publicly verifiable secret sharing scheme and its application to electronic. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 148–164. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48405-1_10CrossRef

38.

Stadler, M.: Publicly verifiable secret sharing. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 190–199. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-68339-9_17CrossRef

39.

Tucker, I.: Functional encryption and distributed signatures based on projective hash functions, the benefit of class groups. (Chiffrement fonctionnel et signatures distribuées fondés sur des fonctions de hachage à projection, l’apport des groupes de classe). Ph.D. thesis, University of Lyon, France (2020)

Titel: Publicly Verifiable Secret Sharing Over Class Groups and Applications to DKG and YOSO
verfasst von: Ignacio Cascudo
Bernardo David
Verlag: Springer Nature Switzerland
Buch: Advances in Cryptology – EUROCRYPT 2024
Print ISBN: 978-3-031-58739-9

Electronic ISBN: 978-3-031-58740-5

Copyright-Jahr: 2024
DOI: https://doi.org/10.1007/978-3-031-58740-5_8

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