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Improved Threshold Signatures, Proactive Secret Sharing, and Input Certification from LSS Isomorphisms

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Progress in Cryptology – LATINCRYPT 2021 (LATINCRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12912))

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Abstract

In this paper we present a series of applications steming from a formal treatment of linear secret-sharing isomorphisms, which are linear transformations between different secret-sharing schemes defined over vector spaces over a field \(\mathbb {F}\) and allow for efficient multiparty conversion from one secret-sharing scheme to the other. This concept generalizes the folklore idea that moving from a secret-sharing scheme over \(\mathbb {F}_{p}\) to a secret sharing “in the exponent” can be done non-interactively by multiplying the share unto a generator of e.g., an elliptic curve group. We generalize this idea and show that it can also be used to compute arbitrary bilinear maps and in particular pairings over elliptic curves.

We include the following practical applications originating from our framework: First we show how to securely realize the Pointcheval-Sanders signature scheme (CT-RSA 2016) in MPC. Second we present a construction for dynamic proactive secret-sharing which outperforms the current state of the art from CCS 2019. Third we present a construction for MPC input certification using digital signatures that we show experimentally to outperform the previous best solution in this area.

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Notes

  1. 1.

    A verifiable secret-sharing scheme is one in which parties can verify that the dealer shared the secret correctly.

  2. 2.

    Note that the use of the vector \(\boldsymbol{r}_v\) here where all but one entries are random is similar to e.g., the choice of a random polynomial with a fixed 0-coefficient in Shamir’s secret sharing.

  3. 3.

    A downside of e.g., ECDSA signatures is that messages have to be hashed first, which creates a significant problem when messages are secret-shared, as hashing secret-shared data is quite expensive.

  4. 4.

    One caveat is that the shares on their own may not define the secret if the adversary is allowed to change the corrupt parties’ shares, which is the case for an active adversary. This is an issue for example with additive secret sharing and an dishonest majority (which can be fixed by adding homomorphic MACs), but not for Shamir secret sharing with an honest majority. We discuss this in detail in the full version.

  5. 5.

    For a more detailed derivation of this complexity, see the full version.

  6. 6.

    Notice that in the case the protocol does not succeed, nothing can be said about what caused it to abort. If this property is desired, then the protocol underlying \(\varPi _{\mathsf {CertInput}}\) have to support identifiable abort.

References

  1. Aranha, D., Dalskov, A., Escudero, D., Orlandi, D.: Improved threshold signatures, proactive secret sharing and input certification from LSS isomorphisms. Cryptology ePrint Archieves Report 2020/691 (2020). https://eprint.iacr.org/2020/691

  2. Aranha, D.F., Gouvêa, C.P.L., Markmann, T., Wahby, R.S., Liao, K.: RELIC is an Efficient LIbrary for Cryptography. https://github.com/relic-toolkit/relic

  3. Au, M.H., Susilo, W., Mu, Y.: Constant-size dynamic k-TAA. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 111–125. Springer, Heidelberg (2006). https://doi.org/10.1007/11832072_8

    Chapter  Google Scholar 

  4. Boneh, D., Boyen, X.: Short Signatures Without Random Oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_4

    Chapter  Google Scholar 

  5. Blanton, M., Bayatbabolghani, F.: Efficient server-aided secure two-party function evaluation with applications to genomic computation. PoPETs 2016(4), 144–164 (2016)

    Google Scholar 

  6. Bamiloshin, M., Ben-Efraim, A., Farràs, O., Padró, C.: Common information, matroid representation, and secret sharing for matroid ports. Des. Codes Cryptogr. 89(1), 143–166 (2020). https://doi.org/10.1007/s10623-020-00811-1

    Article  MathSciNet  MATH  Google Scholar 

  7. Beimel, A., Ben-Efraim, A., Padró, C., Tyomkin, I.: Multi-linear secret-sharing schemes. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 394–418. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54242-8_17

    Chapter  Google Scholar 

  8. Ben-Sasson, E., et al.: Decentralized anonymous payments from bitcoin. In: 2014 IEEE Symposium on Security and Privacy, pp. 459–474. IEEE Computer Society Press, May 2014

    Google Scholar 

  9. Beaver, D.: Efficient multiparty protocols using circuit randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420–432. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-46766-1_34

    Chapter  Google Scholar 

  10. Baron, J., El Defrawy, K., Lampkins, J., Ostrovsky, R.: How to withstand mobile virus attacks, revisited. In: Halldórsson, M.M., Dolev, S. (eds.) 33rd ACM PODC, pp. 293–302. ACM, July 2014

    Google Scholar 

  11. Baron, J., Defrawy, K.E., Lampkins, J., Ostrovsky, R.: Communication-optimal proactive secret sharing for dynamic groups. In: Malkin, T., Kolesnikov, V., Lewko, A.B., Polychronakis, M. (eds.) ACNS 2015. LNCS, vol. 9092, pp. 23–41. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-28166-7_2

    Chapter  Google Scholar 

  12. Blanton, M., Jeong, M.: Improved Signature schemes for secure multi-party computation with certified inputs. In: Lopez, J., Zhou, J., Soriano, M. (eds.) ESORICS 2018. LNCS, vol. 11099, pp. 438–460. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-98989-1_22

  13. Cascudo, I., Cramer, R., Xing, C., Yuan, C.: Amortized complexity of information-theoretically secure MPC revisited. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 395–426. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96878-0_14

  14. Cramer, R., Damgård, I., Ishai, Y.: Share conversion, pseudorandom secret-sharing and applications to secure computation. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 342–362. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30576-7_19

    Chapter  Google Scholar 

  15. Cramer, R., Damgård, I., Maurer, U.: General secure multi-party computation from any linear secret-sharing scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 316–334. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45539-6_22

    Chapter  Google Scholar 

  16. Cramer, R., Bjerre Damgård, I., Nielsen, J.B.: Secure Multiparty Computation, Cambridge University Press, Cambridge (2015)

    Google Scholar 

  17. Canetti, R., Gennaro, R., Goldfeder, S., Makriyannis, N.: Udi Peled. Uc non-interactive, proactive, threshold ecdsa with identifiable aborts. In: Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security (CCS 2020), pp. 1769–1787, New York, NY, USA, Association for Computing Machinery (2020)

    Google Scholar 

  18. Chen, H., Kim, M., Razenshteyn, I., Rotaru, D., Song, Y., Wagh, S.: Maliciously secure matrix multiplication with applications to private deep learning. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12493, pp. 31–59. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64840-4_2

  19. Camenisch, J., Lysyanskaya, A.: Signature schemes and anonymous credentials from bilinear maps. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 56–72. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_4

    Chapter  Google Scholar 

  20. Chase, M., Meiklejohn, S., Zaverucha. G.: Algebraic MACs and keyed-verification anonymous credentials. In: Ahn, G.-J., Yung, M., Li, N. (eds.) ACM CCS 2014, pp. 1205–1216. ACM Press, November 2014

    Google Scholar 

  21. Chase, M., Perrin, T., Zaverucha, G.: The signal private group system and anonymous credentials supporting efficient verifiable encryption. In: Ligatti, J., Ou, X., Katz, J., Vigna, G. (eds.) ACM CCS 2020, pp. 1445–1459. ACM Press, November 2020

    Google Scholar 

  22. Döttling, N., Hartmann, D., Hofheinz, D., Kiltz, E., Schäge, S., Ursu, B.: On the impossibility of short algebraic signatures. Cryptology ePrint Archive, Report 2021/738 (2021). https://eprint.iacr.org/2021/738

  23. Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority - or: breaking the SPDZ limits. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1–18. Springer, Heidelberg (2013)

    Google Scholar 

  24. Dalskov, A., Orlandi, C., Keller, M., Shrishak, K., Shulman, H.: Securing DNSSEC Keys via Threshold ECDSA from Generic MPC. In: Chen, L., Li, N., Liang, K., Schneider, S. (eds.) ESORICS 2020. LNCS, vol. 12309, pp. 654–673. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59013-0_32

  25. Damgård, I., Nielsen, J.B.: Scalable and unconditionally secure multiparty computation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 572–590. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74143-5_32

    Chapter  Google Scholar 

  26. Feldman, P.: A practical scheme for non-interactive verifiable secret sharing. In: 28th FOCS, pp. 427–437. IEEE Computer Society Press, Washington, October 1987

    Google Scholar 

  27. Fiore, D., Gennaro. R.: Publicly verifiable delegation of large polynomials and matrix computations, with applications. In: Yu, T., Danezis, G., Gligor, V.D. (eds.) ACM CCS 2012, pp. 501–512. ACM Press, October 2012

    Google Scholar 

  28. Falk, B.H., Noble, D.: Secure computation over lattices and elliptic curves. Cryptology ePrint Archive, Report 2020/926 (2020). https://eprint.iacr.org/2020/926

  29. Garay, J.A., Gennaro, R., Jutla, C., Rabin, T.: Secure distributed storage and retrieval. Theor. Comput. Sci. 243(1–2), 363–389 (2000)

    Google Scholar 

  30. Goldwasser, S., Micali, S., Rivest, R.L.: A digital signature scheme secure against adaptive chosen-message attacks. SIAM J. Comput. 17(2), 281–308 (1988)

    Article  MathSciNet  Google Scholar 

  31. Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: Juels, A., Wright, R.N., De Capitani di Vimercati, S. (eds.) ACM CCS 2006, pp. 89–98. ACM Press, October/November (2006). Cryptology ePrint Archive Report 2006/309

    Google Scholar 

  32. Herzberg, A., Jakobsson, M., Jarecki, S., Krawczyk, H., Yung, M.: Proactive public key and signature systems. In: Graveman, R., Janson, P.A., Neuman, C., Gong, L. (eds.) ACM CCS 97, pp. 100–110. ACM Press, April 1997

    Google Scholar 

  33. Herzberg, A., Jarecki, S., Krawczyk, H., Yung, M.: Proactive secret sharing Or: how to cope with perpetual leakage. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 339–352. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-44750-4_27

    Chapter  Google Scholar 

  34. Kim, T., Barbulescu, R.: Extended tower number field sieve: a new complexity for the medium prime case. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 543–571. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_20

  35. Katz, J., Malozemoff, A.J., Wang, X.: Efficiently enforcing input validity in secure two-party computation. Cryptology ePrint Archive, Report 2016/184 (2016). https://eprint.iacr.org/2016/184

  36. Kate, A., Zaverucha, G.M., Goldberg, I.: Constant-size commitments to polynomials and their applications. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 177–194. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_11

    Chapter  Google Scholar 

  37. Menezes, A., Sarkar, P., Singh, S.: Challenges with assessing the impact of NFS advances on the security of pairing-based cryptography. In: Mycrypt, vol.10311 LNCS, pp. 83–108. Springer (2016)

    Google Scholar 

  38. Deepak Maram, S.K., et al.: CHURP: dynamic-committee proactive secret sharing. In: Cavallaro, L., Kinder, J., Wang, K., Katz, J. (eds.) ACM CCS 2019, pp. 2369–2386. ACM Press, November 2019

    Google Scholar 

  39. Ostrovsky, R., Yung, M.: How to withstand mobile virus attacks (extended abstract). In: Logrippo, L. (ed) 10th ACM PODC, pp. 51–59. ACM, August 1991

    Google Scholar 

  40. 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

    Chapter  Google Scholar 

  41. Shamir, A.: How to share a secret. Commun. Assoc. Comput. Mach. 22(11), 612–613 (1979)

    MathSciNet  MATH  Google Scholar 

  42. Shoup, V.: Practical threshold signatures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 207–220. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45539-6_15

    Chapter  Google Scholar 

  43. Schultz, D.A., Liskov, B., Liskov, M.: Mobile proactive secret sharing. In: Bazzi, R.A., Patt-Shamir, B. (eds.) 27th ACM PODC, p. 458. ACM, August 2008

    Google Scholar 

  44. Smart, N.P., Talibi Alaoui, Y.: Distributing any elliptic curve based protocol. In: Albrecht, M. (ed.) IMACC 2019. LNCS, vol. 11929, pp. 342–366. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-35199-1_17

    Chapter  Google Scholar 

  45. Chi-Chih Yao, A.: Protocols for secure computations (extended abstract). In: 23rd FOCS, pp. 160–164. IEEE Computer Society Press, November 1982

    Google Scholar 

  46. Zhang, Y., Blanton, M., Bayatbabolghani, F.: Enforcing input correctness via certification in garbled circuit evaluation. In: Foley, S.N., Gollmann, D., Snekkenes, E. (eds.) ESORICS 2017. LNCS, vol. 10493, pp. 552–569. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66399-9_30

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Acknowledgments

The authors would like to thank Greg Zaverucha and the anonymous reviewers for useful feedback on earlier versions of this paper.

This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreements No 669255 (MPCPRO) and No 803096 (SPEC), the Concordium Blockhain Research Center at Aarhus University (COBRA), the Carlsberg Foundation under the Semper Ardens Research Project CF18-112 (BCM), and the Danish Independent Research Council under Grant-ID DFF-6108-00169 (FoCC). The first and last authors are affiliated to the DIGIT Centre for Digitalisation, Big Data and Data Analytics at Aarhus University.

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Authors and Affiliations

  1. Aarhus University, Aarhus, Denmark

    Diego F. Aranha, Daniel Escudero & Claudio Orlandi

  2. Partisia, Aarhus, Denmark

    Anders Dalskov

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  1. Diego F. Aranha
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Correspondence to Diego F. Aranha .

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  1. Microsoft Research, Redmond, WA, USA

    Patrick Longa

  2. Universitat Pompeu Fabra, Barcelona, Spain

    Carla Ràfols

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Aranha, D.F., Dalskov, A., Escudero, D., Orlandi, C. (2021). Improved Threshold Signatures, Proactive Secret Sharing, and Input Certification from LSS Isomorphisms. In: Longa, P., Ràfols, C. (eds) Progress in Cryptology – LATINCRYPT 2021. LATINCRYPT 2021. Lecture Notes in Computer Science(), vol 12912. Springer, Cham. https://doi.org/10.1007/978-3-030-88238-9_19

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