Abstract
Support of membership revocation is a desirable functionality for any group signature scheme. Among the known revocation approaches, verifier-local revocation (VLR) seems to be the most flexible one, because it only requires the verifiers to possess some up-to-date revocation information, but not the signers. All of the contemporary VLR group signatures operate in the bilinear map setting, and all of them will be insecure once quantum computers become a reality. In this work, we introduce the first lattice-based VLR group signature, and thus, the first such scheme that is believed to be quantum-resistant. In comparison with existing lattice-based group signatures, our scheme has several noticeable advantages: support of membership revocation, logarithmic-size signatures, and weaker security assumption. In the random oracle model, our scheme is proved to be secure based on the hardness of the \(\mathsf{SIVP}_{\widetilde{\mathcal{O}}(n^{1.5})}\) problem in general lattices - an assumption that is as weak as those of state-of-the-art lattice-based standard signatures. Moreover, our construction works without relying on encryption schemes, which is an intriguing feature for group signatures.
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References
Ajtai, M.: Generating Hard Instances of Lattice Problems (Extended Abstract). In: STOC, pp. 99–108. ACM (1996)
Ajtai, M.: Generating Hard Instances of the Short Basis Problem. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 1–9. Springer, Heidelberg (1999)
Alwen, J., Peikert, C.: Generating Shorter Bases for Hard Random Lattices. Theory Comput. Syst. 48(3), 535–553 (2011)
Ateniese, G., Camenisch, J., Joye, M., Tsudik, G.: A Practical and Provably Secure Coalition-Resistant Group Signature Scheme. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 255–270. Springer, Heidelberg (2000)
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)
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)
Bichsel, P., Camenisch, J., Neven, G., Smart, N.P., Warinschi, B.: Get Shorty via Group Signatures without Encryption. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 381–398. Springer, Heidelberg (2010)
Boneh, D., Boyen, X., Shacham, H.: Short Group Signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)
Boneh, D., Shacham, H.: Group Signatures with Verifier-local Revocation. In: ACM-CCS, pp. 168–177. ACM (2004)
Brickell, E.: An Efficient Protocol for Anonymously Providing Assurance of the Container of the Private Key. Submitted to the Trusted Comp. Group (April 2003)
Camenisch, J., Groth, J.: Group Signatures: Better Efficiency and New Theoretical Aspects. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 120–133. Springer, Heidelberg (2005)
Camenisch, J., Lysyanskaya, A.: Dynamic Accumulators and Application to Efficient Revocation of Anonymous Credentials. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 61–76. Springer, Heidelberg (2002)
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)
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)
Chaum, D., van Heyst, E.: Group Signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991)
Chen, L., Pedersen, T.P.: New Group Signature Schemes (Extended Abstract). In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 171–181. Springer, Heidelberg (1995)
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)
Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for Hard Lattices and New Cryptographic Constructions. In: STOC, pp. 197–206. ACM (2008)
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)
Groth, J.: Fully Anonymous Group Signatures Without Random Oracles. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 164–180. Springer, Heidelberg (2007)
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)
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)
Laguillaumie, F., Langlois, A., Libert, B., Stehlé, D.: Lattice-Based Group Signatures with Logarithmic Signature Size. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 41–61. Springer, Heidelberg (2013)
Langlois, A., Ling, S., Nguyen, K., Wang, H.: Lattice-based Group Signature Scheme with Verifier-local Revocation. Cryptology ePrint Archive, Report 2014/033 (2014), http://eprint.iacr.org/2014/033
Libert, B., Peters, T., Yung, M.: Group Signatures with Almost-for-Free Revocation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 571–589. Springer, Heidelberg (2012)
Libert, B., Vergnaud, D.: Group Signatures with Verifier-Local Revocation and Backward Unlinkability in the Standard Model. In: Garay, J.A., Miyaji, A., Otsuka, A. (eds.) CANS 2009. LNCS, vol. 5888, pp. 498–517. Springer, Heidelberg (2009)
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)
Lyubashevsky, V.: Lattice-Based Identification Schemes Secure Under Active Attacks. In: Cramer, R. (ed.) PKC 2008. LNCS, vol. 4939, pp. 162–179. Springer, Heidelberg (2008)
Lyubashevsky, V.: Lattice Signatures without Trapdoors. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 738–755. Springer, Heidelberg (2012)
Micciancio, D., Peikert, C.: Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012)
Micciancio, D., Regev, O.: Lattice-based Cryptography. In: Post-Quantum Cryptography, pp. 147–191. Springer (2009)
Micciancio, D., Vadhan, S.P.: Statistical Zero-Knowledge Proofs with Efficient Provers: Lattice Problems and More. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 282–298. Springer, Heidelberg (2003)
Nakanishi, T., Funabiki, N.: Verifier-Local Revocation Group Signature Schemes with Backward Unlinkability from Bilinear Maps. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 533–548. Springer, Heidelberg (2005)
Nakanishi, T., Funabiki, N.: A Short Verifier-Local Revocation Group Signature Scheme with Backward Unlinkability. In: Yoshiura, H., Sakurai, K., Rannenberg, K., Murayama, Y., Kawamura, S.-I. (eds.) IWSEC 2006. LNCS, vol. 4266, pp. 17–32. Springer, Heidelberg (2006)
Peikert, C.: An Efficient and Parallel Gaussian Sampler for Lattices. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 80–97. Springer, Heidelberg (2010)
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)
Regev, O.: On Lattices, Learning with Errors, Random Linear Codes, and Cryptography. In: STOC, pp. 84–93. ACM (2005)
Rückert, M.: Adaptively Secure Identity-Based Identification from Lattices without Random Oracles. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 345–362. Springer, Heidelberg (2010)
Shor, P.W.: Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. SIAM Journal on Computing 26(5), 1484–1509 (1997)
Stern, J.: A New Paradigm for Public Key Identification. IEEE Transactions on Information Theory 42(6), 1757–1768 (1996)
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Langlois, A., Ling, S., Nguyen, K., Wang, H. (2014). Lattice-Based Group Signature Scheme with Verifier-Local Revocation. In: Krawczyk, H. (eds) Public-Key Cryptography – PKC 2014. PKC 2014. Lecture Notes in Computer Science, vol 8383. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54631-0_20
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