Abstract
In this paper, we present an identity-based encryption scheme from codes with efficient key revocation. Recently, in Crypto 2017, Gaborit et al. proposed a first identity-based encryption scheme from codes with rank metric, called RankIBE. To extract the decryption key from any public identity, they constructed a trapdoor function which relies on RankSign, a signature scheme proposed by Gaborit et al. in PQCrypto 2014. We adopt the same trapdoor function to add efficient key revocation functionality in the RankIBE scheme. Our revocable IBE scheme from codes with rank metric makes use of a binary tree data structure to reduce the amount of work in terms of key updates for the key authority. The total size of key updates requires logarithmic complexity in the maximum number of users and linear in the number of revoked users. We prove that our revocable IBE scheme is selective-ID secure in the random oracle model, under the hardness of three problems: the Rank Syndrome Decoding (RSD) problem, the Augmented Low Rank Parity Check Code (\(\textsf {LRPC}^+\)) problem, and the Rank Support Learning (RSL) problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
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
Aiello, W., Lodha, S., Ostrovsky, R.: Fast digital identity revocation. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 137–152. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055725
Baldi, M., Bodrato, M., Chiaraluce, F.: A new analysis of the McEliece cryptosystem based on QC-LDPC codes. In: Ostrovsky, R., De Prisco, R., Visconti, I. (eds.) SCN 2008. LNCS, vol. 5229, pp. 246–262. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85855-3_17
Baldi, M., Chiaraluce, F., Garello, R.: On the usage of quasi-cyclic low-density parity-check codes in the McEliece cryptosystem. In: 2006 First International Conference on Communications and Electronics, pp. 305–310, October 2006
Baldi, M., Chiaraluce, F., Garello, R., Mininni, F.: Quasi-cyclic low-density parity-check codes in the McEliece cryptosystem. In: 2007 IEEE International Conference on Communications, pp. 951–956, June 2007
Berger, T.P., Cayrel, P.-L., Gaborit, P., Otmani, A.: Reducing key length of the McEliece cryptosystem. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 77–97. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02384-2_6
Berlekamp, E., McEliece, R., van Tilborg, H.: On the inherent intractability of certain coding problems (corresp.). IEEE Trans. Inf. Theory 24(3), 384–386 (1978)
Boldyreva, A., Goyal, V., Kumar, V.: Identity-based encryption with efficient revocation. In: Proceedings of the 2008 ACM Conference on Computer and Communications Security, CCS 2008, Alexandria, Virginia, USA, 27–31 October 2008, pp. 417–426 (2008)
Boneh, D., Franklin, M.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_13
Chen, J., Lim, H.W., Ling, S., Wang, H., Nguyen, K.: Revocable identity-based encryption from lattices. In: Susilo, W., Mu, Y., Seberry, J. (eds.) ACISP 2012. LNCS, vol. 7372, pp. 390–403. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31448-3_29
Chen, L., Jordan, S., Liu, Y.K., Moody, D., Peralta, R., Perlner, R., Smith-Tone, D.: Report on post-quantum cryptography. National Institute of Standards and Technology Internal Report 8105 (2016)
Faugère, J.-C., Otmani, A., Perret, L., Tillich, J.-P.: Algebraic cryptanalysis of McEliece variants with compact keys. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 279–298. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_14
Gabidulin, E.M.: Theory of codes with maximum rank distance. Probl. Peredachi Informatsii 21, 3–16 (1985)
Gaborit, P.: Shorter keys for code based cryptography. In: Internatinal Workshop on Coding and Cryptography-WCC’2205, pp. 81–91 (2004)
Gaborit, P., Hauteville, A., Phan, D.H., Tillich, J.: Identity-based encryption from codes with rank metric. IACR Cryptology ePrint Archive 2017/514 (2017)
Gaborit, P., Murat, G., Ruatta, O., Zémor, G.: Low rank parity check codes and their application to cryptography. In: Proceedings of the Workshop on Coding and Cryptography WCC’2013 (2013)
Gaborit, P., Ruatta, O., Schrek, J., Zémor, G.: RankSign: an efficient signature algorithm based on the rank metric. In: Mosca, M. (ed.) PQCrypto 2014. LNCS, vol. 8772, pp. 88–107. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11659-4_6
Gaborit, P., Zémor, G.: On the hardness of the decoding and the minimum distance problems for rank codes. IEEE Trans. Inf. Theory 62(12), 7245–7252 (2016)
Gallager, R.G.: Low-density parity -check codes. Ph.D. thesis. MIT Press (1963)
Hauteville, A., Tillich, J.P.: New algorithms for decoding in the rank metric and an attack on the LRPC cryptosystem. In: 2015 IEEE International Symposium on Information Theory (ISIT), pp. 2747–2751, June 2015
Libert, B., Vergnaud, D.: Adaptive-ID secure revocable identity-based encryption. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 1–15. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00862-7_1
Loidreau, P.: Asymptotic behaviour of codes in rank metric over finite fields. Des. Codes Crypt. 71(1), 105–118 (2014)
McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. Deep Space Netw. Prog. Rep. 44, 114–116 (1978)
Misoczki, R., Barreto, P.S.L.M.: Compact McEliece keys from Goppa codes. In: Jacobson, M.J., Rijmen, V., Safavi-Naini, R. (eds.) SAC 2009. LNCS, vol. 5867, pp. 376–392. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-05445-7_24
Misoczki, R., Tillich, J.P., Sendrier, N., Barreto, P.S.L.M.: MDPC-McEliece: new McEliece variants from moderate density parity-check codes. In: 2013 IEEE International Symposium on Information Theory, pp. 2069–2073, July 2013
Monico, C., Rosenthal, J., Shokrollahi, A.: Using low density parity check codes in the McEliece cryptosystem. In: 2000 IEEE International Symposium on Information Theory, p. 215 (2000)
Naor, M., Nissim, K.: Certificate revocation and certificate update. IEEE J. Sel. Areas Commun. 18(4), 561–570 (2000)
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.: Polynominal time algorithms for discrete logarithms and factoring on a quantum computer. In: Adleman, L.M., Huang, M.-D. (eds.) ANTS-I. Springer, Heidelberg (1994)
Wang, J., Bi, J.: Lattice-based identity-based broadcast encryption scheme. IACR Cryptology ePrint Archive 2010/288 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Chang, D., Chauhan, A.K., Kumar, S., Sanadhya, S.K. (2018). Revocable Identity-Based Encryption from Codes with Rank Metric. In: Smart, N. (eds) Topics in Cryptology – CT-RSA 2018. CT-RSA 2018. Lecture Notes in Computer Science(), vol 10808. Springer, Cham. https://doi.org/10.1007/978-3-319-76953-0_23
Download citation
DOI: https://doi.org/10.1007/978-3-319-76953-0_23
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76952-3
Online ISBN: 978-3-319-76953-0
eBook Packages: Computer ScienceComputer Science (R0)