Abstract
Both threshold and blind signatures have, individually, received a considerable amount of attention. However little is known about their combination, i.e., a threshold signature which is also blind, in that no coalition of signers learns anything about the message being signed or the signature being produced. Several applications of blind signatures (e.g., anonymous tokens) would benefit from distributed signing as a means to increase trust in the service and hence reduce the risks of key compromise. This paper builds the first blind threshold signatures in pairing-free groups. Our main contribution is a construction that transforms an underlying blind non-threshold signature scheme with a suitable structure into a threshold scheme, preserving its blindness. The resulting signing protocol proceeds in three rounds, and produces signatures consisting of one group element and two scalars. The underlying non-threshold blind signature schemes are of independent interest, and improve upon the current state of the art (Tessaro and Zhu, EUROCRYPT ’22) with shorter signatures (three elements, instead of four) and simpler proofs of security. All of our schemes are proved secure in the Random Oracle and Algebraic Group Models, assuming the hardness of the discrete logarithm problem.
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Notes
- 1.
One motivation for statistical and/or perfect blindness is the looming threat of quantum attacks, which would affect the blindness of current schemes more than they would affect one-more unforgeability, for which the use of quantum-safe assumptions, while important, still remains less critical.
- 2.
For each \(\mathcal {O}^{\textsf{ISign}_2}\) query at most n entries are added, and for each \(\mathsf {H_{cm}}\) query at most one entry is added.
References
Abe, M.: A secure three-move blind signature scheme for polynomially many signatures. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 136–151. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44987-6_9
Abe, M., Okamoto, T.: Provably secure partially blind signatures. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 271–286. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44598-6_17
Baldimtsi, F., Lysyanskaya, A.: On the security of one-witness blind signature schemes. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 82–99. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-42045-0_5
Barreto, P.L., Zanon, G.H.M.: Blind signatures from zero-knowledge arguments. Cryptology ePrint Archive, Paper 2023/067 (2023). https://eprint.iacr.org/2023/067
Bellare, M., Crites, E.C., Komlo, C., Maller, M., Tessaro, S., Zhu, C.: Better than advertised security for non-interactive threshold signatures. In: Dodis, Y., Shrimpton, T. (eds.) CRYPTO 2022. LNCS, vol. 13510, pp. 517–550. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-15985-5_18
Bellare, M., Namprempre, C., Pointcheval, D., Semanko, M.: The one-more-RSA-inversion problems and the security of Chaum’s blind signature scheme. J. Cryptol. 16(3), 185–215 (2003). https://doi.org/10.1007/s00145-002-0120-1
Bellare, M., Rogaway, P.: The security of triple encryption and a framework for code-based game-playing proofs. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 409–426. Springer, Heidelberg (2006). https://doi.org/10.1007/11761679_25
Benhamouda, F., Lepoint, T., Loss, J., Orrù, M., Raykova, M.: On the (in)security of ROS. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021. LNCS, vol. 12696, pp. 33–53. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77870-5_2
Boldyreva, A.: Threshold signatures, multisignatures and blind signatures based on the gap-Diffie-Hellman-group signature scheme. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 31–46. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36288-6_3
Boneh, D., Lynn, B., Shacham, H.: Short signatures from the weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_30
Chaum, D.: Blind signatures for untraceable payments. In: Chaum, D., Rivest, R.L., Sherman, A.T. (eds.) CRYPTO 1982, Santa Barbara, California, USA, 23–25 August 1982, pp. 199–203. Plenum Press, New York (1982). https://doi.org/10.1007/978-1-4757-0602-4_18
Chaum, D., Fiat, A., Naor, M.: Untraceable electronic cash. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 319–327. Springer, New York (1990). https://doi.org/10.1007/0-387-34799-2_25
Denis, F., Jacobs, F., Wood, C.A.: RSA Blind Signatures. Internet-Draft draft-IRTF-CFRG-RSA-blind-signatures-02. Work in Progress. Internet Engineering Task Force (2021). https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-rsa-blind-signatures-02
Desmedt, Y.: Society and group oriented cryptography: a new concept. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 120–127. Springer, Heidelberg (1988). https://doi.org/10.1007/3-540-48184-2_8
Desmedt, Y., Frankel, Y.: Threshold cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0_28
Fuchsbauer, G., Kiltz, E., Loss, J.: The algebraic group model and its applications. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 33–62. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_2
Fuchsbauer, G., Plouviez, A., Seurin, Y.: Blind Schnorr signatures and signed ELGamal encryption in the algebraic group model. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 63–95. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_3
Fuchsbauer, G., Wolf, M.: (concurrently secure) blind schnorr from schnorr. Cryptology ePrint Archive, Paper 2022/1676 (2022). https://eprint.iacr.org/2022/1676
Hauck, E., Kiltz, E., Loss, J.: A modular treatment of blind signatures from identification schemes. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11478, pp. 345–375. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17659-4_12
Hendrickson, S., Iyengar, J., Pauly, T., Valdez, S., Wood, C.A.: Private Access Tokens. Internet-Draft draft-private-access-tokens-01. Work in Progress. Internet Engineering Task Force (2021). https://datatracker.ietf.org/doc/html/draft-private-access-tokens-01
icloud private relay overview. https://www.apple.com/privacy/docs/iCloud_Private_Relay_Overview_Dec2021.PDF. Accessed 03 Feb 2023
Kastner, J., Loss, J., Xu, J.: The Abe-Okamoto partially blind signature scheme revisited. In: Agrawal, S., Lin, D. (eds.) ASIACRYPT 2022, Part IV. LNCS, vol. 13794, pp. 279–309. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-22972-5_10
Komlo, C., Goldberg, I.: FROST: flexible round-optimized schnorr threshold signatures. In: Dunkelman, O., Jacobson, Jr., M.J., O’Flynn, C. (eds.) SAC 2020. LNCS, vol. 12804, pp. 34–65. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-81652-0_2
Kuchta, V., Manulis, M.: Rerandomizable threshold blind signatures. In: Yung, M., Zhu, L., Yang, Y. (eds.) INTRUST 2014. LNCS, vol. 9473, pp. 70–89. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-27998-5_5
Lindell, Y.: Simple three-round multiparty schnorr signing with full simulatability. IACR Cryptology ePrint Archive, p. 374 (2022). https://eprint.iacr.org/2022/374
Lysyanskaya, A.: Security analysis of RSA-BSSA. Cryptology ePrint Archive, Paper 2022/895, PKC 2023 (2022). https://doi.org/10.1007/978-3-031-31368-4_10
Maurer, U.: Abstract models of computation in cryptography. In: Smart, N.P. (ed.) Cryptography and Coding 2005. LNCS, vol. 3796, pp. 1–12. Springer, Heidelberg (2005). https://doi.org/10.1007/11586821_1
Okamoto, T.: Provably secure and practical identification schemes and corresponding signature schemes. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 31–53. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-48071-4_3
PCM: Click fraud prevention and attribution sent to advertiser. https://webkit.org/blog/11940/pcm-click-fraud-prevention-and-attribution-sent-to-advertiser/. Accessed 03 Feb 2023
Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_9
Pointcheval, D., Sanders, O.: Short randomizable signatures. In: Sako, K. (ed.) CT-RSA 2016. LNCS, vol. 9610, pp. 111–126. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29485-8_7
Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. Cryptol. 13(3), 361–396 (2000). https://doi.org/10.1007/s001450010003
Rial, A., Piotrowska, A.M.: Security analysis of coconut, an attribute-based credential scheme with threshold issuance. IACR Cryptology ePrint Archive, p. 11 (2022). https://eprint.iacr.org/2022/011
Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978). https://doi.org/10.1145/359340.359342
Schnorr, C.P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0_22
Schnorr, C.P.: Security of blind discrete log signatures against interactive attacks. In: Qing, S., Okamoto, T., Zhou, J. (eds.) ICICS 2001. LNCS, vol. 2229, pp. 1–12. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45600-7_1
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979). https://doi.org/10.1145/359168.359176
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_18
Sonnino, A., Al-Bassam, M., Bano, S., Meiklejohn, S., Danezis, G.: Coconut: threshold issuance selective disclosure credentials with applications to distributed ledgers. In: 26th Annual Network and Distributed System Security Symposium, NDSS 2019, San Diego, California, USA, 24–27 February 2019. The Internet Society (2019). https://www.ndss-symposium.org/ndss-paper/coconut-threshold-issuance-selective-disclosure-credentials-with-applications-to-distributed-ledgers/
Stinson, D.R., Strobl, R.: Provably secure distributed schnorr signatures and a (t, n) threshold scheme for implicit certificates. In: Varadharajan, V., Mu, Y. (eds.) ACISP 2001. LNCS, vol. 2119, pp. 417–434. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-47719-5_33
Tessaro, S., Zhu, C.: Short pairing-free blind signatures with exponential security. In: Dunkelman, O., Dziembowski, S. (eds.) EUROCRYPT 2022. LNCS, vol. 13276, pp. 782–811. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-07085-3_27
Trust tokens. https://developer.chrome.com/docs/privacy-sandbox/trust-tokens/. Accessed 03 Feb 2023
Vo, D.-L., Zhang, F., Kim, K.: A new threshold blind signature scheme from pairings. In: Proceedings of the 2003 Symposium on Cryptography and Information Security (SCIS 2003) (2003)
VPN by google one, explained. https://one.google.com/about/vpn/howitworks. Accessed 02 Feb 2023
Acknowledgements
Elizabeth Crites is supported by Input Output through their funding of the Blockchain Technology Lab at the University of Edinburgh. Tessaro and Zhu are supported in part by NSF grants CNS-2026774, CNS-2154174, a JP Morgan Faculty Award, a CISCO Faculty Award, and a gift from Microsoft.
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Crites, E., Komlo, C., Maller, M., Tessaro, S., Zhu, C. (2023). Snowblind: A Threshold Blind Signature in Pairing-Free Groups. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14081. Springer, Cham. https://doi.org/10.1007/978-3-031-38557-5_23
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