Abstract
Zero-knowledge identification schemes solve the problem of authenticating one party to another via an insecure channel without disclosing any additional information that might be used by an impersonator. In this paper we propose a scheme whose security relies on the existence of a commitment scheme and on the hardness of worst-case lattice problems. We adapt a code-based identification scheme devised by Cayrel and Véron, which constitutes an improvement of Stern’s construction. Our solution sports analogous improvements over the lattice adaption of Stern’s scheme which Kawachi et al. presented at ASIACRYPT 2008. Specifically, due to a smaller cheating probability close to 1/2 and a similar communication cost, any desired level of security will be achieved in fewer rounds. Compared to Lyubashevsky’s scheme presented at ASIACRYPT 2009, our proposal, like Kawachi’s, offers a much milder security assumption: namely, the hardness of SIS for trinary solutions. The same assumption was used for the SWIFFT hash function, which is secure for much smaller parameters than those proposed by Lyubashevsky.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ajtai, M.: Generating hard instances of lattice problems. Electronic Colloquium on Computational Complexity (ECCC) 3(7) (1996)
Ajtai, M., Dwork, C.: A public-key cryptosystem with worst-case/average-case equivalence. Electronic Colloquium on Computational Complexity (ECCC) 3(65) (1996)
Bellare, M., Palacio, A.: GQ and Schnorr identification schemes: Proofs of security against impersonation under active and concurrent attacks. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 162–162. Springer, Heidelberg (2002)
Cayrel, P.-L., Véron, P.: Improved code-based identification scheme (2010), http://arxiv.org/abs/1001.3017v1
Feige, U., Fiat, A., Shamir, A.: Zero knowledge proofs of identity. In: STOC 1987, pp. 210–217. ACM, New York (1987)
Feige, U., Shamir, A.: Witness indistinguishable and witness hiding protocols. In: STOC 1990, pp. 416–426. ACM, New York (1990)
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)
Gaborit, P., Girault, M.: Lightweight code-based identification and signature. IEEE Transactions on Information Theory (ISIT), 186–194 (2007)
Gama, N., Nguyen, P.Q.: Predicting lattice reduction. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 31–51. Springer, Heidelberg (2008)
Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems. In: Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing, p. 304. ACM, New York (1985)
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)
Kilian, J., Petrank, E.: Concurrent and resettable zero-knowledge in polyloalgorithm rounds. In: STOC 2001: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, pp. 560–569. ACM, New York (2001)
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.: Fiat-shamir with aborts: Applications to lattice and factoring-based signatures. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 598–616. Springer, Heidelberg (2009)
Lyubashevsky, V., Micciancio, D.: Generalized compact knapsacks are collision resistant. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 144–155. Springer, Heidelberg (2006)
Lyubashevsky, V., Micciancio, D.: Asymptotically efficient lattice-based digital signatures. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 37–54. Springer, Heidelberg (2008)
Lyubashevsky, V., Micciancio, D., Peikert, C., Rosen, A.: Swifft: A modest proposal for fft hashing. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 54–72. Springer, Heidelberg (2008)
Micciancio, D.: Generalized compact knapsacks, cyclic lattices, and efficient one-way functions. In: Computational Complexity. Springer, Heidelberg (2007)
Micciancio, D., Goldwasser, S.: Complexity of Lattice Problems: a cryptographic perspective. The Kluwer International Series in Engineering and Computer Science, vol. 671. Kluwer Academic Publishers, Boston (March 2002)
Micciancio, D., Regev, O.: Worst-case to average-case reductions based on gaussian measures. SIAM J. Comput. 37(1), 267–302 (2007)
Ohta, K., Okamoto, T.: On concrete security treatment of signatures derived from identification. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 354–369. Springer, Heidelberg (1998)
Shor, P.W.: Polynominal time algorithms for discrete logarithms and factoring on a quantum computer. In: Huang, M.-D.A., Adleman, L.M. (eds.) ANTS 1994. LNCS, vol. 877, p. 289. Springer, Heidelberg (1994)
Stern, J.: A new identification scheme based on syndrome decoding. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 13–21. Springer, Heidelberg (1994)
Véron, P.: Improved identification schemes based on error-correcting codes. Appl. Algebra Eng. Commun. Comput. 8(1), 57–69 (1996)
Wagner, D.: A generalized birthday problem. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 288–303. Springer, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cayrel, PL., Lindner, R., Rückert, M., Silva, R. (2010). Improved Zero-Knowledge Identification with Lattices. In: Heng, SH., Kurosawa, K. (eds) Provable Security. ProvSec 2010. Lecture Notes in Computer Science, vol 6402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16280-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-16280-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16279-4
Online ISBN: 978-3-642-16280-0
eBook Packages: Computer ScienceComputer Science (R0)