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Ring Signatures: Logarithmic-Size, No Setup—from Standard Assumptions

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Advances in Cryptology – EUROCRYPT 2019 (EUROCRYPT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11478))

Abstract

Ring signatures allow for creating signatures on behalf of an ad hoc group of signers, hiding the true identity of the signer among the group. A natural goal is to construct a ring signature scheme for which the signature size is short in the number of ring members. Moreover, such a construction should not rely on a trusted setup and be proven secure under falsifiable standard assumptions. Despite many years of research this question is still open.

In this paper, we present the first construction of size-optimal ring signatures which do not rely on a trusted setup or the random oracle heuristic. Specifically, our scheme can be instantiated from standard assumptions and the size of signatures grows only logarithmically in the number of ring members.

We also extend our techniques to the setting of linkable ring signatures, where signatures created using the same signing key can be linked.

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Notes

  1. 1.

    Bender et al. [6] actually use 2-message public-coin witness-indistinguishable proofs (ZAPs) rather than NIWI proofs, which is a slightly weaker primitive than NIWI proofs.

  2. 2.

    E.g. in the construction of IND-CCA secure encryption schemes.

  3. 3.

    The expression can be unrolled into a disjunction of \(6 \cdot \left( {5 \atopwithdelims ()2} + {5 \atopwithdelims ()3} \right) = 480\) clauses, where each clause is a conjunction of 5 statements.

References

  1. Abe, M., Ohkubo, M., Suzuki, K.: 1-out-of-n signatures from a variety of keys. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 415–432. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36178-2_26

    Chapter  Google Scholar 

  2. Backes, M., Döttling, N., Hanzlik, L., Kluczniak, K., Schneider, J.: Ring signatures: logarithmic-size, no setup – from standard assumptions. Cryptology ePrint Archive, Report 2019/196 (2019). http://eprint.iacr.org/2019/196

  3. Backes, M., Hanzlik, L., Kluczniak, K., Schneider, J.: Signatures with flexible public key: introducing equivalence classes for public keys. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018. LNCS, vol. 11273, pp. 405–434. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03329-3_14

    Chapter  Google Scholar 

  4. Barak, B., Ong, S.J., Vadhan, S.P.: Derandomization in cryptography. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 299–315. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45146-4_18

    Chapter  MATH  Google Scholar 

  5. Baum, C., Lin, H., Oechsner, S.: Towards practical lattice-based one-time linkable ring signatures. Cryptology ePrint Archive, Report 2018/107 (2018). https://eprint.iacr.org/2018/107

  6. Bender, A., Katz, J., Morselli, R.: Ring signatures: stronger definitions, and constructions without random oracles. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 60–79. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_4

    Chapter  Google Scholar 

  7. Bitansky, N.: Verifiable random functions from non-interactive witness-indistinguishable proofs. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 567–594. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70503-3_19

    Chapter  Google Scholar 

  8. Bitansky, N., Paneth, O.: ZAPs and non-interactive witness indistinguishability from indistinguishability obfuscation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 401–427. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_16

    Chapter  MATH  Google Scholar 

  9. Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 416–432. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-39200-9_26

    Chapter  Google Scholar 

  10. Boyen, X.: Mesh signatures. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 210–227. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72540-4_12

    Chapter  Google Scholar 

  11. Boyen, X., Haines, T.: Forward-secure linkable ring signatures. In: Susilo, W., Yang, G. (eds.) ACISP 2018. LNCS, vol. 10946, pp. 245–264. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93638-3_15

    Chapter  Google Scholar 

  12. Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: Ostrovsky, R. (ed.) 52nd Annual Symposium on Foundations of Computer Science, Palm Springs, CA, USA, 22–25 October 2011, pp. 97–106. IEEE Computer Society Press (2011)

    Google Scholar 

  13. Chandran, N., Groth, J., Sahai, A.: Ring signatures of sub-linear size without random oracles. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 423–434. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73420-8_38

    Chapter  Google Scholar 

  14. Chow, S.S.M., Wei, V.K.-W., Liu, J.K., Yuen, T.H.: Ring signatures without random oracles. In: Lin, F.-C., Lee, D.-T., Lin, B.-S., Shieh, S., Jajodia, S. (eds.) 1st ACM Symposium on Information, Computer and Communications Security, ASIACCS 2006, 21–24 March 2006, Taipei, Taiwan, pp. 297–302. ACM Press (2006)

    Google Scholar 

  15. Dodis, Y., Kiayias, A., Nicolosi, A., Shoup, V.: Anonymous identification in ad hoc groups. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 609–626. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_36

    Chapter  MATH  Google Scholar 

  16. Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography (extended abstract). In: 23rd Annual ACM Symposium on Theory of Computing, 6–8 May 1991, New Orleans, LA, USA, pp. 542–552. ACM Press (1991)

    Google Scholar 

  17. Dwork, C., Naor, M.: Zaps and their applications. In: 41st Annual Symposium on Foundations of Computer Science, 12–14 November 2000, Redondo Beach, CA, USA, pp. 283–293. IEEE Computer Society Press (2000)

    Google Scholar 

  18. ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_2

    Chapter  Google Scholar 

  19. Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) 41st Annual ACM Symposium on Theory of Computing, 31 May–2 June 2009, Bethesda, MD, USA, pp. 169–178. ACM Press (2009)

    Google Scholar 

  20. Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 75–92. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_5

    Chapter  Google Scholar 

  21. Ghadafi, E.M.: Sub-linear blind ring signatures without random oracles. In: Stam, M. (ed.) IMACC 2013. LNCS, vol. 8308, pp. 304–323. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-45239-0_18

    Chapter  Google Scholar 

  22. Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: 21st Annual ACM Symposium on Theory of Computing, 15–17 May 1989, Seattle, WA, USA, pp. 25–32. ACM Press (1989)

    Google Scholar 

  23. González, A.: A ring signature of size \({O}(\root 3 \of {n})\) without random oracles. Cryptology ePrint Archive, Report 2017/905 (2017). http://eprint.iacr.org/2017/905

  24. Goyal, R., Hohenberger, S., Koppula, V., Waters, B.: A generic approach to constructing and proving verifiable random functions. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 537–566. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70503-3_18

    Chapter  Google Scholar 

  25. Groth, J., Ostrovsky, R., Sahai, A.: Non-interactive zaps and new techniques for NIZK. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 97–111. Springer, Heidelberg (2006). https://doi.org/10.1007/11818175_6

    Chapter  Google Scholar 

  26. Herranz, J., Sáez, G.: Forking lemmas for ring signature schemes. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 266–279. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-24582-7_20

    Chapter  Google Scholar 

  27. Hubacek, P., Wichs, D.: On the communication complexity of secure function evaluation with long output. In: Roughgarden, T. (ed.) 6th Conference on Innovations in Theoretical Computer Science, ITCS 2015, 11–13 January 2015, Rehovot, Israel, pp. 163–172. Association for Computing Machinery (2015)

    Google Scholar 

  28. Libert, B., Peters, T., Qian, C.: Logarithmic-size ring signatures with tight security from the DDH assumption. In: Lopez, J., Zhou, J., Soriano, M. (eds.) ESORICS 2018. LNCS, vol. 11099, pp. 288–308. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98989-1_15

    Chapter  Google Scholar 

  29. Liu, J.K., Wei, V.K., Wong, D.S.: Linkable spontaneous anonymous group signature for ad hoc groups. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol. 3108, pp. 325–335. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27800-9_28

    Chapter  Google Scholar 

  30. Lu, X., Au, M.H., Zhang, Z.: Raptor: a practical lattice-based (linkable) ring signature. Cryptology ePrint Archive, Report 2018/857 (2018). https://eprint.iacr.org/2018/857

  31. Malavolta, G., Schröder, D.: Efficient ring signatures in the standard model. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10625, pp. 128–157. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70697-9_5

    Chapter  MATH  Google Scholar 

  32. Noether, S.: Ring signature confidential transactions for monero. Cryptology ePrint Archive, Report 2015/1098 (2015). http://eprint.iacr.org/2015/1098

  33. Okamoto, T., Pietrzak, K., Waters, B., Wichs, D.: New realizations of somewhere statistically binding hashing and positional accumulators. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 121–145. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48797-6_6

    Chapter  Google Scholar 

  34. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H.N., Fagin, R. (eds.) 37th Annual ACM Symposium on Theory of Computing, 22–24 May 2005, Baltimore, MA, USA, pp. 84–93. ACM Press (2005)

    Google Scholar 

  35. Rivest, R.L., Shamir, A., Tauman, Y.: How to leak a secret. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 552–565. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_32

    Chapter  Google Scholar 

  36. Schäge, S., Schwenk, J.: A CDH-based ring signature scheme with short signatures and public keys. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 129–142. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14577-3_12

    Chapter  MATH  Google Scholar 

  37. 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

    Chapter  Google Scholar 

  38. Shacham, H., Waters, B.: Efficient ring signatures without random oracles. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 166–180. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71677-8_12

    Chapter  Google Scholar 

  39. Torres, W.A.A., et al.: Post-quantum one-time linkable ring signature and application to ring confidential transactions in blockchain (lattice RingCT v1.0). In: Susilo, W., Yang, G. (eds.) ACISP 2018. LNCS, vol. 10946, pp. 558–576. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93638-3_32

    Chapter  Google Scholar 

  40. Tsang, P.P., Wei, V.K.: Short linkable ring signatures for e-voting, e-cash and attestation. In: Deng, R.H., Bao, F., Pang, H.H., Zhou, J. (eds.) ISPEC 2005. LNCS, vol. 3439, pp. 48–60. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-31979-5_5

    Chapter  Google Scholar 

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Acknowledgments

This work has been partially funded/supported by the German Ministry for Education and Research through funding for the project CISPA-Stanford Center for Cybersecurity (Funding numbers: 16KIS0762 and 16KIS0927).

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Authors and Affiliations

  1. CISPA Helmholtz Center for Information Security, Saarland Informatics Campus, Saarbrücken, Germany

    Michael Backes, Nico Döttling, Lucjan Hanzlik, Kamil Kluczniak & Jonas Schneider

  2. Stanford University, Stanford, USA

    Lucjan Hanzlik

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  1. Michael Backes
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Correspondence to Michael Backes .

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  1. Technion, Haifa, Israel

    Yuval Ishai

  2. COSIC Group, KU Leuven, Heverlee, Belgium

    Vincent Rijmen

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Backes, M., Döttling, N., Hanzlik, L., Kluczniak, K., Schneider, J. (2019). Ring Signatures: Logarithmic-Size, No Setup—from Standard Assumptions. In: Ishai, Y., Rijmen, V. (eds) Advances in Cryptology – EUROCRYPT 2019. EUROCRYPT 2019. Lecture Notes in Computer Science(), vol 11478. Springer, Cham. https://doi.org/10.1007/978-3-030-17659-4_10

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