Revocable Identity-Based Encryption from Codes with Rank Metric

  • Donghoon Chang
  • Amit Kumar Chauhan
  • Sandeep Kumar
  • Somitra Kumar Sanadhya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10808)

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.

Keywords

Code-based cryptography Identity-based encryption Key revocation Rank metric LRPC codes RSD problem 

References

  1. 1.
    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 CrossRefGoogle Scholar
  2. 2.
    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 Google Scholar
  3. 3.
    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 CrossRefGoogle Scholar
  4. 4.
    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 2006Google Scholar
  5. 5.
    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 2007Google Scholar
  6. 6.
    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 CrossRefGoogle Scholar
  7. 7.
    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)CrossRefMATHGoogle Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    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 CrossRefGoogle Scholar
  10. 10.
    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 CrossRefGoogle Scholar
  11. 11.
    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)Google Scholar
  12. 12.
    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 CrossRefGoogle Scholar
  13. 13.
    Gabidulin, E.M.: Theory of codes with maximum rank distance. Probl. Peredachi Informatsii 21, 3–16 (1985)MathSciNetMATHGoogle Scholar
  14. 14.
    Gaborit, P.: Shorter keys for code based cryptography. In: Internatinal Workshop on Coding and Cryptography-WCC’2205, pp. 81–91 (2004)Google Scholar
  15. 15.
    Gaborit, P., Hauteville, A., Phan, D.H., Tillich, J.: Identity-based encryption from codes with rank metric. IACR Cryptology ePrint Archive 2017/514 (2017)Google Scholar
  16. 16.
    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)Google Scholar
  17. 17.
    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 Google Scholar
  18. 18.
    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)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Gallager, R.G.: Low-density parity -check codes. Ph.D. thesis. MIT Press (1963)Google Scholar
  20. 20.
    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 2015Google Scholar
  21. 21.
    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 CrossRefGoogle Scholar
  22. 22.
    Loidreau, P.: Asymptotic behaviour of codes in rank metric over finite fields. Des. Codes Crypt. 71(1), 105–118 (2014)MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    McEliece, R.J.: A public-key cryptosystem based on algebraic coding theory. Deep Space Netw. Prog. Rep. 44, 114–116 (1978)Google Scholar
  24. 24.
    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 CrossRefGoogle Scholar
  25. 25.
    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 2013Google Scholar
  26. 26.
    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)Google Scholar
  27. 27.
    Naor, M., Nissim, K.: Certificate revocation and certificate update. IEEE J. Sel. Areas Commun. 18(4), 561–570 (2000)CrossRefGoogle Scholar
  28. 28.
    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 CrossRefGoogle Scholar
  29. 29.
    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)Google Scholar
  30. 30.
    Wang, J., Bi, J.: Lattice-based identity-based broadcast encryption scheme. IACR Cryptology ePrint Archive 2010/288 (2010)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Indraprastha Institute of Information Technology (IIIT-D), DelhiDelhiIndia
  2. 2.Indian Institute of Technology RoparRupnagarIndia
  3. 3.Department of Mathematics, Shaheed Bhagat Singh CollegeUniversity of DelhiDelhiIndia

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