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Forward-Secure Group Signatures from Lattices

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Post-Quantum Cryptography (PQCrypto 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11505))

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Abstract

Group signature is a fundamental cryptographic primitive, aiming to protect anonymity and ensure accountability of users. It allows group members to anonymously sign messages on behalf of the whole group, while incorporating a tracing mechanism to identify the signer of any suspected signature. Most of the existing group signature schemes, however, do not guarantee security once secret keys are exposed. To reduce potential damages caused by key exposure attacks, Song (ACMCCS 2001) put forward the concept of forward-secure group signature (FSGS), which prevents attackers from forging group signatures pertaining to past time periods even if a secret group signing key is revealed at the current time period. For the time being, however, all known secure FSGS schemes are based on number-theoretic assumptions, and are vulnerable against quantum computers.

In this work, we construct the first lattice-based FSGS scheme. Our scheme is proven secure under the Short Integer Solution and Learning With Errors assumptions. At the heart of our construction is a scalable lattice-based key evolving mechanism, allowing users to periodically update their secret keys and to efficiently prove in zero-knowledge that key evolution process is done correctly. To realize this essential building block, we first employ the Bonsai tree structure by Cash et al. (EUROCRYPT 2010) to handle the key evolution process, and then develop Langlois et al.’s construction (PKC 2014) to design its supporting zero-knowledge protocol.

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Notes

  1. 1.

    This set can be determined by the Nodeselect algorithm presented by Libert and Yung [42].

References

  1. Abdalla, M., Reyzin, L.: A new forward-secure digital signature scheme. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 116–129. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44448-3_10

    Chapter  Google Scholar 

  2. Ajtai, M.: Generating Hard Instances of Lattice Problems (Extended Abstract). In: STOC 1996, pp. 99–108. ACM (1996)

    Google Scholar 

  3. Alwen, J., Peikert, C.: Generating shorter bases for hard random lattices. In: STACS 2009, pp. 75–86 (2009)

    Google Scholar 

  4. Anderson, R.: Two remarks on public key cryptology. Technical report, University of Cambridge, Computer Laboratory (2002)

    Google Scholar 

  5. Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast cryptographic primitives and circular-secure encryption based on hard learning problems. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 595–618. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_35

    Chapter  Google Scholar 

  6. Bellare, M., Micciancio, D., Warinschi, B.: Foundations of group signatures: formal definitions, simplified requirements, and a construction based on general assumptions. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 614–629. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-39200-9_38

    Chapter  Google Scholar 

  7. Bellare, M., Miner, S.K.: A forward-secure digital signature scheme. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 431–448. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48405-1_28

    Chapter  Google Scholar 

  8. Bellare, M., Shi, H., Zhang, C.: Foundations of group signatures: the case of dynamic groups. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 136–153. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30574-3_11

    Chapter  Google Scholar 

  9. 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_26

    Chapter  Google Scholar 

  10. Boneh, D., Shacham, H.: Group signatures with verifier-local revocation. In: ACM-CCS 2004, pp. 168–177. ACM (2004)

    Google Scholar 

  11. Boschini, C., Camenisch, J., Neven, G.: Floppy-sized group signatures from lattices. In: Preneel, B., Vercauteren, F. (eds.) ACNS 2018. LNCS, vol. 10892, pp. 163–182. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93387-0_9

    Chapter  Google Scholar 

  12. Boyen, X.: Lattice mixing and vanishing trapdoors: a framework for fully secure short signatures and more. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 499–517. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13013-7_29

    Chapter  Google Scholar 

  13. Boyen, X., Shacham, H., Shen, E., Waters, B.: Forward-secure signatures with untrusted update. In: ACM-CCS 2006, pp. 191–200. ACM (2006)

    Google Scholar 

  14. Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: ITCS 2012, pp. 309–325. ACM (2012)

    Google Scholar 

  15. Camenisch, J., Neven, G., Rückert, M.: Fully anonymous attribute tokens from lattices. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 57–75. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32928-9_4

    Chapter  Google Scholar 

  16. Canetti, R., Halevi, S., Katz, J.: A forward-secure public-key encryption scheme. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 255–271. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-39200-9_16

    Chapter  Google Scholar 

  17. Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 207–222. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_13

    Chapter  Google Scholar 

  18. Cash, D., Hofheinz, D., Kiltz, E., Peikert, C.: Bonsai trees, or how to delegate a lattice basis. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 523–552. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_27

    Chapter  Google Scholar 

  19. Chaum, D., van Heyst, E.: Group signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_22

    Chapter  Google Scholar 

  20. Cheng, S., Nguyen, K., Wang, H.: Policy-based signature scheme from lattices. Des. Codes Cryptography 81(1), 43–74 (2016)

    Article  MathSciNet  Google Scholar 

  21. del Pino, R., Lyubashevsky, V., Seiler, G.: Lattice-based group signatures and zero-knowledge proofs of automorphism stability. In: ACM-CCS 2018, pp. 574–591. ACM (2018)

    Google Scholar 

  22. Dodis, Y., Katz, J., Xu, S., Yung, M.: Key-insulated public key cryptosystems. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 65–82. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_5

    Chapter  Google Scholar 

  23. 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_12

    Chapter  Google Scholar 

  24. Gentry, C., Peikert, C., Vaikuntanathan, V.: How to use a short basis: trapdoors for hard lattices and new cryptographic constructions. In: STOC 2008, pp. 197–206. ACM (2008)

    Google Scholar 

  25. Gordon, S.D., Katz, J., Vaikuntanathan, V.: A group signature scheme from lattice assumptions. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 395–412. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_23

    Chapter  Google Scholar 

  26. Itkis, G., Reyzin, L.: Forward-secure signatures with optimal signing and verifying. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 332–354. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_20

    Chapter  Google Scholar 

  27. Kansal, M., Dutta, R., Mukhopadhyay, S.: Forward Secure Efficient Group Signature in Dynamic Setting using Lattices. IACR Cryptology ePrint Archive, 2017:1128. https://eprint.iacr.org/2017/1128

  28. Kawachi, A., Tanaka, K., Xagawa, K.: Concurrently secure identification schemes based on the worst-case hardness of lattice problems. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 372–389. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89255-7_23

    Chapter  Google Scholar 

  29. Kiayias, A., Tsiounis, Y., Yung, M.: Traceable signatures. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 571–589. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_34

    Chapter  Google Scholar 

  30. Kiayias, A., Yung, M.: Secure scalable group signature with dynamic joins and separable authorities. IJSN 1(1), 24–45 (2006)

    Article  Google Scholar 

  31. Laguillaumie, F., Langlois, A., Libert, B., Stehlé, D.: Lattice-based group signatures with logarithmic signature size. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013. LNCS, vol. 8270, pp. 41–61. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-42045-0_3

    Chapter  Google Scholar 

  32. Langlois, A., Ling, S., Nguyen, K., Wang, H.: Lattice-based group signature scheme with verifier-local revocation. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 345–361. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54631-0_20. http://eprint.iacr.org/2014/033

    Chapter  Google Scholar 

  33. Libert, B., Ling, S., Mouhartem, F., Nguyen, K., Wang, H.: Signature schemes with efficient protocols and dynamic group signatures from lattice assumptions. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 373–403. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_13

    Chapter  Google Scholar 

  34. Libert, B., Ling, S., Mouhartem, F., Nguyen, K., Wang, H.: Zero-knowledge arguments for matrix-vector relations and lattice-based group encryption. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 101–131. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_4

    Chapter  Google Scholar 

  35. Libert, B., Ling, S., Mouhartem, F., Nguyen, K., Wang, H.: Adaptive oblivious transfer with access control from lattice assumptions. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 533–563. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_19

    Chapter  Google Scholar 

  36. Libert, B., Ling, S., Nguyen, K., Wang, H.: Zero-knowledge arguments for lattice-based accumulators: logarithmic-size ring signatures and group signatures without trapdoors. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 1–31. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49896-5_1

    Chapter  Google Scholar 

  37. Libert, B., Ling, S., Nguyen, K., Wang, H.: Zero-knowledge arguments for lattice-based PRFs and applications to e-cash. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10626, pp. 304–335. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70700-6_11

    Chapter  Google Scholar 

  38. Libert, B., Ling, S., Nguyen, K., Wang, H.: Lattice-based zero-knowledge arguments for integer relations. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 700–732. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_24

    Chapter  Google Scholar 

  39. Libert, B., Mouhartem, F., Nguyen, K.: A lattice-based group signature scheme with message-dependent opening. In: Manulis, M., Sadeghi, A.-R., Schneider, S. (eds.) ACNS 2016. LNCS, vol. 9696, pp. 137–155. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39555-5_8

    Chapter  Google Scholar 

  40. Libert, B., Quisquater, J.-J., Yung, M.: Forward-secure signatures in untrusted update environments: efficient and generic constructions. In: ACM-CCS 2007, pp. 266–275. ACM (2007)

    Google Scholar 

  41. Libert, B., Quisquater, J.-J., Yung, M.: Key evolution systems in untrusted update environments. ACM Trans. Inf. Syst. Secur. (TISSEC) 13(4), 37 (2010)

    Article  Google Scholar 

  42. Libert, B., Yung, M.: Dynamic fully forward-secure group signatures. In: Asia-CCS 2010, pp. 70–81. ACM (2010)

    Google Scholar 

  43. Ling, S., Nguyen, K., Stehlé, D., Wang, H.: Improved zero-knowledge proofs of knowledge for the ISIS problem, and applications. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 107–124. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_8

    Chapter  Google Scholar 

  44. Ling, S., Nguyen, K., Wang, H.: Group signatures from lattices: simpler, tighter, shorter, ring-based. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 427–449. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46447-2_19

    Chapter  Google Scholar 

  45. Ling, S., Nguyen, K., Wang, H., Xu, Y.: Lattice-based group signatures: achieving full dynamicity with ease. In: Gollmann, D., Miyaji, A., Kikuchi, H. (eds.) ACNS 2017. LNCS, vol. 10355, pp. 293–312. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-61204-1_15

    Chapter  Google Scholar 

  46. Ling, S., Nguyen, K., Wang, H., Xu, Y.: Accountable tracing signatures from lattices. In: Matsui, M. (ed.) CT-RSA 2019. LNCS, vol. 11405, pp. 556–576. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-12612-4_28

    Chapter  Google Scholar 

  47. Ling, S., Nguyen, K., Wang, H., Xu, Y.: Constant-size group signatures from lattices. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10770, pp. 58–88. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76581-5_3

    Chapter  Google Scholar 

  48. Micciancio, D., Peikert, C.: Hardness of SIS and LWE with small parameters. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 21–39. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_2

    Chapter  Google Scholar 

  49. Micciancio, D., Regev, O.: Worst-case to average-case reductions based on Gaussian measures. SIAM J. Comput. 37(1), 267–302 (2007)

    Article  MathSciNet  Google Scholar 

  50. Nakanishi, T., Hira, Y., Funabiki, N.: Forward-secure group signatures from pairings. In: Shacham, H., Waters, B. (eds.) Pairing 2009. LNCS, vol. 5671, pp. 171–186. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03298-1_12

    Chapter  Google Scholar 

  51. Nguyen, K., Tan, B.H.M., Wang, H.: Zero-knowledge password policy check from lattices. In: Nguyen, P., Zhou, J. (eds.) ISC 2017. LNCS, vol. 10599, pp. 92–113. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-319-69659-1_6

    Google Scholar 

  52. Nguyen, P.Q., Zhang, J., Zhang, Z.: Simpler efficient group signatures from lattices. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 401–426. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46447-2_18

    Chapter  Google Scholar 

  53. Peikert, C., Rosen, A.: Efficient collision-resistant hashing from worst-case assumptions on cyclic lattices. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 145–166. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_8

    Chapter  Google Scholar 

  54. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC 2005, pp. 84–93. ACM (2005)

    Google Scholar 

  55. Sakai, Y., Emura, K., Hanaoka, G., Kawai, Y., Matsuda, T., Omote, K.: Group signatures with message-dependent opening. In: Abdalla, M., Lange, T. (eds.) Pairing 2012. LNCS, vol. 7708, pp. 270–294. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36334-4_18

    Chapter  Google Scholar 

  56. Song, D.X.: Practical forward secure group signature schemes. In: ACM-CCS 2001, pp. 225–234. ACM (2001)

    Google Scholar 

  57. Stern, J.: A new paradigm for public key identification. IEEE Trans. Inf. Theory 42(6), 1757–1768 (1996)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The research is supported by Singapore Ministry of Education under Research Grant MOE2016-T2-2-014(S). Khoa Nguyen is also supported by the Gopalakrishnan – NTU Presidential Postdoctoral Fellowship 2018.

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Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    San Ling, Khoa Nguyen, Huaxiong Wang & Yanhong Xu

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  1. San Ling
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Correspondence to Yanhong Xu .

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Editors and Affiliations

  1. University of Cincinnati, Cincinnati, OH, USA

    Jintai Ding

  2. Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA

    Rainer Steinwandt

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Ling, S., Nguyen, K., Wang, H., Xu, Y. (2019). Forward-Secure Group Signatures from Lattices. In: Ding, J., Steinwandt, R. (eds) Post-Quantum Cryptography. PQCrypto 2019. Lecture Notes in Computer Science(), vol 11505. Springer, Cham. https://doi.org/10.1007/978-3-030-25510-7_3

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