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2020 | OriginalPaper | Chapter

Linearly-Homomorphic Signatures and Scalable Mix-Nets

Authors : Chloé Hébant, Duong Hieu Phan, David Pointcheval

Published in: Public-Key Cryptography – PKC 2020

Publisher: Springer International Publishing

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Abstract

Anonymity is a primary ingredient for our digital life. Several tools have been designed to address it such as, for authentication, blind signatures, group signatures or anonymous credentials and, for confidentiality, randomizable encryption or mix-nets. When it comes to complex electronic voting schemes, random shuffling of authenticated ciphertexts with mix-nets is the only known tool. However, it requires huge and complex zero-knowledge proofs to guarantee the actual permutation of the initial ciphertexts in a privacy-preserving way.

In this paper, we propose a new approach for proving correct shuffling of signed ElGamal ciphertexts: the mix-servers can simply randomize individual ballots, which means the ciphertexts, the signatures, and the verification keys, with an additional global proof of constant size, and the output will be publicly verifiable. The security proof is in the generic bilinear group model. The computational complexity for the each mix-server is linear in the number of ballots. Verification is also linear in the number of ballots, but independent of the number of rounds of mixing. This leads to a new highly scalable technique. Our construction makes use of linearly-homomorphic signatures, with new features, that are of independent interest.

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Abe, M., Fuchsbauer, G., Groth, J., Haralambiev, K., Ohkubo, M.: Structure-preserving signatures and commitments to group elements. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 209–236. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_12CrossRef

Ahn, J.H., Boneh, D., Camenisch, J., Hohenberger, S., shelat, a., Waters, B., et al.: Computing on authenticated data. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 1–20. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28914-9_1

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

Blazy, O., Fuchsbauer, G., Izabachène, M., Jambert, A., Sibert, H., Vergnaud, D.: Batch Groth–Sahai. In: Zhou, J., Yung, M. (eds.) ACNS 2010. LNCS, vol. 6123, pp. 218–235. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13708-2_14CrossRef

Blazy, O., Fuchsbauer, G., Pointcheval, D., Vergnaud, D.: Signatures on randomizable ciphertexts. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 403–422. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19379-8_25CrossRef

Boneh, D., Boyen, X., Goh, E.-J.: Hierarchical identity based encryption with constant size ciphertext. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_26CrossRef

Boneh, D., Drijvers, M., Neven, G.: Compact multi-signatures for smaller blockchains. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018, Part II. LNCS, vol. 11273, pp. 435–464. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03329-3_15CrossRef

Boneh, D., Freeman, D., Katz, J., Waters, B.: Signing a linear subspace: signature schemes for network coding. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 68–87. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00468-1_5CrossRef

Boneh, D., Freeman, D.M.: Homomorphic signatures for polynomial functions. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 149–168. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20465-4_10CrossRef

10.

Boneh, D., Freeman, D.M.: Linearly homomorphic signatures over binary fields and new tools for lattice-based signatures. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 1–16. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19379-8_1CrossRef

11.

Boyen, X.: The uber-assumption family. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 39–56. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85538-5_3CrossRef

12.

Camenisch, J., Hohenberger, S., Pedersen, M.Ø.: Batch verification of short signatures. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 246–263. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72540-4_14CrossRef

13.

Chase, M., Kohlweiss, M., Lysyanskaya, A., Meiklejohn, S.: Malleable proof systems and applications. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 281–300. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_18CrossRef

14.

Chaum, D.L.: Untraceable electronic mail, return addresses, and digital pseudonyms. Commun. ACM 24(2), 84–90 (1981). https://doi.org/10.1145/358549.358563CrossRef

15.

Cortier, V., Smyth, B.: Attacking and fixing Helios: an analysis of ballot secrecy. J. Comput. Secur. 21(1), 89–148 (2013). http://dl.acm.org/citation.cfm?id=2595846.2595849CrossRef

16.

Damgård, I.: Towards practical public key systems secure against chosen ciphertext attacks. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 445–456. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_36CrossRef

17.

Fauzi, P., Lipmaa, H., Siim, J., Zając, M.: An efficient pairing-based shuffle argument. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017, Part II. LNCS, vol. 10625, pp. 97–127. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70697-9_4CrossRef

18.

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_12CrossRef

19.

Freeman, D.M.: Improved security for linearly homomorphic signatures: a generic framework. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 697–714. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-30057-8_41CrossRef

20.

Fuchsbauer, G., Hanser, C., Slamanig, D.: Structure-preserving signatures on equivalence classes and constant-size anonymous credentials. J. Cryptol. 32(2), 498–546 (2019)MathSciNetCrossRef

21.

Furukawa, J., Sako, K.: An efficient scheme for proving a shuffle. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 368–387. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_22CrossRef

22.

Groth, J.: Short pairing-based non-interactive zero-knowledge arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321–340. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_19CrossRef

23.

Groth, J., Ishai, Y.: Sub-linear zero-knowledge argument for correctness of a shuffle. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 379–396. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_22CrossRef

24.

Groth, J., Lu, S.: A non-interactive shuffle with pairing based verifiability. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 51–67. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76900-2_4CrossRef

25.

Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 415–432. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_24CrossRef

26.

Hada, S., Tanaka, T.: On the existence of 3-round zero-knowledge protocols. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 408–423. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055744CrossRef

27.

Hébant, C., Phan, D.H., Pointcheval, D.: Linearly-homomorphic signatures and scalable mix-nets. Cryptology ePrint Archive, Report 2019/547 (2019). https://eprint.iacr.org/2019/547

28.

Herold, G., Hoffmann, M., Klooß, M., Ràfols, C., Rupp, A.: New techniques for structural batch verification in bilinear groups with applications to Groth-Sahai proofs. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 2017, pp. 1547–1564. ACM Press , October/November 2017

29.

Johnson, R., Molnar, D., Song, D., Wagner, D.: Homomorphic signature schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 244–262. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45760-7_17CrossRef

30.

Libert, B., Peters, T., Joye, M., Yung, M.: Linearly homomorphic structure-preserving signatures and their applications. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, part II. LNCS, vol. 8043, pp. 289–307. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_17CrossRef

31.

Neff, C.A.: A verifiable secret shuffle and its application to e-voting. In: Reiter, M.K., Samarati, P. (eds.) ACM CCS 2001, pp. 116–125. ACM Press, November 2001

32.

Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-69053-0_18CrossRef

Title: Linearly-Homomorphic Signatures and Scalable Mix-Nets
Authors: Chloé Hébant
Duong Hieu Phan
David Pointcheval
Publisher: Springer International Publishing
Book: Public-Key Cryptography – PKC 2020
Print ISBN: 978-3-030-45387-9

Electronic ISBN: 978-3-030-45388-6

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-45388-6_21

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