Abstract
Fuzzy identity-based signature (FIBS) is exactly like a traditional identity-based signature except that the signature issued under an identity \(\textsf {id}\) can be verified under any identity \(\textsf {id}'\) that is “close enough” to \(\textsf {id}\). This property allows FIBS having an efficient application in biometric authentication and only three schemes over lattices exist, among which two constructions are existentially unforgetable against adaptively chosen identity and message attacks (EU-aID-CMA) in the random model, the only exception proved to be strongly unforgetable against selectively chosen identity and message attacks (SU-sID-CMA) is constructed in the standard model. In this work, we propose a new FIBS from the hardness of lattice problems for identities living in a small universe, i.e., \(\{0,1\}^{\ell }\), the new construction is proved to be SU-sID-CMA in the standard model. In particular, compared with the existing lattice FIBS schemes, the new construction enjoys a smaller communication cost, and the faster signing and verifying operations, thus, it is more practical.
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References
Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_28
Agrawal, S., Boyen, X., Vaikuntanathan, V., Voulgaris, P., Wee, H.: Functional encryption for threshold functions (or fuzzy IBE) from lattices. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 280–297. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-30057-8_17
Ajtai, M.: Generating hard instances of lattice problems (extended abstract). In: STOC, pp. 99–108 (1996)
Alwen, J., Peikert, C.: Generating shorter bases for hard random lattices. In: STACS, pp. 75–86 (2009)
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
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
Gentry, C., Peikert, C., Vaikuntanathan, V.: How to use a short basis: trapdoors for hard lattices and new cryptographic constructions. In: STOC, pp. 197–206 (2008)
Krawczyk, H., Rabin, T.: Chameleon signatures. In: NDSS, pp. 143–154 (2000)
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). https://doi.org/10.1007/978-3-642-29011-4_41
Micciancio, D., Regev, O.: Worst-case to average-case reductions based on gaussian measures. SIAM J. Comput. 37(1), 267–302 (2007)
Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457–473. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_27
Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakley, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47–53. Springer, Heidelberg (1985). https://doi.org/10.1007/3-540-39568-7_5
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)
Wang, C.J.: A provable secure fuzzy identity based signature scheme. Sci. China Inf. Sci. 55(9), 2139–2148 (2012)
Wang, C.J., Kim, J.H.: Two constructions of fuzzy identity based signature. In: BMEI, pp. 1–5. IEEE Press, New York (2009)
Yang, P.Y., Cao, Z.F., Dong, X.L.: Fuzzy identity based signature. IACR Cryptology ePrint Archive 2008/002 (2008)
Yang, P.Y., Cao, Z.F., Dong, X.L.: Fuzzy identity based signature with applications to biometric authentication. Comput. Electr. Eng. 37(4), 532–540 (2011)
Yang, C.L., Zheng, S.H., Wang, L.C., Tian, M.M., Gu, L.Z., Yang, Y.X.: A fuzzy identity-based signature scheme from lattices in the standard model. Math. Prob. Eng. 2014(8), 1–10 (2014)
Yao, Y.Q., Li, Z.J.: A novel fuzzy identity based signature scheme based on the short integer solution problem. Comput. Electr. Eng. 40(6), 1930–1939 (2014)
Zhang, L.Y., Wu, Q., Hu, Y.P.: Fuzzy biometric identity-based signature in the standard model. App. Mech. Mater. 44(4), 3350–3354 (2011)
Zhang, X.J., Xu, C.X., Zhang, Y.: Fuzzy identity-based signature scheme from lattice and its application in biometric authentication. TIIS 11(5), 2762–2777 (2017)
Acknowledgments
We thank the anonymous referees for their helpful comments and the research of authors is supported by the National Natural Science Foundation of China (No. 61572445) and the Anhui Provincial Natural Science Foundation of China (No. 1708085QF154).
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Zhang, Y., Gan, Y., Yin, Y., Jia, H., Jiang, M. (2018). Efficient Lattice FIBS for Identities in a Small Universe. In: Li, F., Takagi, T., Xu, C., Zhang, X. (eds) Frontiers in Cyber Security. FCS 2018. Communications in Computer and Information Science, vol 879. Springer, Singapore. https://doi.org/10.1007/978-981-13-3095-7_7
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