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Compact IBBE and Fuzzy IBE from Simple Assumptions

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Security and Cryptography for Networks (SCN 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11035))

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Abstract

We propose new constructions for identity-based broadcast encryption (IBBE) and fuzzy identity-based encryption (FIBE) in bilinear groups of composite order. Our starting point is the IBBE scheme of Delerablée (Asiacrypt 2007) and the FIBE scheme of Herranz et al. (PKC 2010) proven secure under parameterised assumptions called generalised decisional bilinear Diffie-Hellman (GDDHE) and augmented multi-sequence of exponents Diffie-Hellman (aMSE-DDH) respectively. The two schemes are described in the prime-order pairing group. We transform the schemes into the setting of (symmetric) composite-order groups and prove security from two static assumptions (subgroup decision).

The Déjà Q framework of Chase et al. (Asiacrypt 2016) is known to cover a large class of parameterised assumptions (dubbed über assumption), that is, these assumptions, when defined in asymmetric composite-order groups, are implied by subgroup decision assumptions in the underlying composite-order groups. We argue that the GDDHE and aMSE-DDH assumptions are not covered by the Déjà Q über assumption framework. We therefore work out direct security reductions for the two schemes based on subgroup decision assumptions. Furthermore, our proofs involve novel extensions of Déjà Q techniques of Wee (TCC 2016-A) and Chase et al.

Our constructions have constant-size ciphertexts. The IBBE has constant-size keys as well and guarantees stronger security as compared to Delerablée’s IBBE, thus making it the first compact IBBE known to be selectively secure without random oracles under simple assumptions. The fuzzy IBE scheme is the first to simultaneously feature constant-size ciphertexts and security under standard assumptions.

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Notes

  1. 1.

    We believe our arguments showing that the assumptions under question are not covered by the Déjà Q framework are sufficient. Also, we do not know if there exist other parameterised assumptions in this class that could possibly be used to prove security of the IBBE and FIBE schemes.

  2. 2.

    Alternatively, the scheme of [26] can be proved secure in the standard model if the adversary also announces all its private keys queries (in addition to the target set of identities) before seeing the public parameters.

  3. 3.

    The proof of Wee’s broadcast encryption [62, Sect. 4] has a similar correlation between the \(\mathbb {G}_{p_2}\) components of private keys and public parameters but, in the final step, the statistical argument involved simpler-to-analyse Vandermonde matrices.

  4. 4.

    The assumption is originally given in symmetric groups. In order to work with the Déjà Q framework, one must transform it into asymmetric groups (using Abe et al.’s method [3] as suggested in [23]) which depends on the scheme and the reduction.

References

  1. Abdalla, M., et al.: Searchable encryption revisited: consistency properties, relation to anonymous IBE, and extensions. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 205–222. Springer, Heidelberg (2005). https://doi.org/10.1007/11535218_13

    Chapter  Google Scholar 

  2. Abdalla, M., Kiltz, E., Neven, G.: Generalized key delegation for hierarchical identity-based encryption. In: Biskup, J., López, J. (eds.) ESORICS 2007. LNCS, vol. 4734, pp. 139–154. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74835-9_10

    Chapter  Google Scholar 

  3. Abe, M., Groth, J., Ohkubo, M., Tango, T.: Converting cryptographic schemes from symmetric to asymmetric bilinear groups. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 241–260. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_14

    Chapter  Google Scholar 

  4. Attrapadung, N., Herranz, J., Laguillaumie, F., Libert, B., de Panafieu, E., Ràfols, C.: Attribute-based encryption schemes with constant-size ciphertexts. Theor. Comput. Sci. 422, 15–38 (2012)

    Article  MathSciNet  Google Scholar 

  5. Attrapadung, N., Libert, B.: Functional encryption for inner product: achieving constant-size ciphertexts with adaptive security or support for negation. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 384–402. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13013-7_23

    Chapter  Google Scholar 

  6. Attrapadung, N., Libert, B., de Panafieu, E.: Expressive key-policy attribute-based encryption with constant-size ciphertexts. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 90–108. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19379-8_6

    Chapter  MATH  Google Scholar 

  7. Attrapadung, N.: Dual system encryption via doubly selective security: framework, fully secure functional encryption for regular languages, and more. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 557–577. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_31

    Chapter  Google Scholar 

  8. Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: 1st ACM Conference on Computer and Communications Security (1993)

    Google Scholar 

  9. Boneh, D., Boyen, X., Goh, E.-J.: Hierarchical identity based encryption with constant size ciphertext. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 440–456. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_26

    Chapter  Google Scholar 

  10. Boneh, D., Di Crescenzo, G., Ostrovsky, R., Persiano, G.: Public key encryption with keyword search. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 506–522. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_30

    Chapter  Google Scholar 

  11. Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. SIAM J. Comput. 32(3), 586–615 (2003). Earlier version in CRYPTO 2001. LNCS, vol. 2139, pp. 213–229 (2001)

    Article  MathSciNet  Google Scholar 

  12. Boneh, D., et al.: Fully key-homomorphic encryption, arithmetic circuit ABE and compact garbled circuits. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 533–556. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_30

    Chapter  Google Scholar 

  13. Boneh, D., Gentry, C., Waters, B.: Collusion resistant broadcast encryption with short ciphertexts and private keys. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 258–275. Springer, Heidelberg (2005). https://doi.org/10.1007/11535218_16

    Chapter  Google Scholar 

  14. Boneh, D., Hamburg, M.: Generalized identity based and broadcast encryption schemes. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 455–470. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89255-7_28

    Chapter  Google Scholar 

  15. Boneh, D., Sahai, A., Waters, B.: Functional encryption: definitions and challenges. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 253–273. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19571-6_16

    Chapter  Google Scholar 

  16. Boneh, D., Waters, B., Zhandry, M.: Low overhead broadcast encryption from multilinear maps. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 206–223. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_12

    Chapter  Google Scholar 

  17. Boyen, X., Waters, B.: Anonymous hierarchical identity-based encryption (without random oracles). In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 290–307. Springer, Heidelberg (2006). https://doi.org/10.1007/11818175_17

    Chapter  Google Scholar 

  18. Canetti, R., Halevi, S., Katz, J.: A forward-secure public-key encryption scheme. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 255–271. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-39200-9_16

    Chapter  Google Scholar 

  19. Chen, J., Gong, J., Weng, J.: Tightly secure IBE under constant-size master public key. In: Fehr, S. (ed.) PKC 2017. LNCS, vol. 10174, pp. 207–231. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54365-8_9

    Chapter  Google Scholar 

  20. Chen, J., Libert, B., Ramanna, S.C.: Non-zero inner product encryption with short ciphertexts and private keys. In: Zikas, V., De Prisco, R. (eds.) SCN 2016. LNCS, vol. 9841, pp. 23–41. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-44618-9_2

    Chapter  MATH  Google Scholar 

  21. Chen, J., Wee, H.: Semi-adaptive attribute-based encryption and improved delegation for boolean formula. In: Abdalla, M., De Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 277–297. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10879-7_16

    Chapter  Google Scholar 

  22. Chase, M., Meiklejohn, S.: Déjà Q: using dual systems to revisit q-type assumptions. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 622–639. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-55220-5_34

    Chapter  Google Scholar 

  23. Chase, M., Maller, M., Meiklejohn, S.: Déjà Q all over again: tighter and broader reductions of q-type assumptions. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10032, pp. 655–681. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53890-6_22

    Chapter  Google Scholar 

  24. Cheon, J.H.: Security analysis of the strong diffie-hellman problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 1–11. Springer, Heidelberg (2006). https://doi.org/10.1007/11761679_1

    Chapter  Google Scholar 

  25. Cheon, J.H., Han, K., Lee, C., Ryu, H., Stehlé, D.: Cryptanalysis of the multilinear map over the integers. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 3–12. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_1

    Chapter  Google Scholar 

  26. Delerablée, C.: Identity-based broadcast encryption with constant size ciphertexts and private keys. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 200–215. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76900-2_12

    Chapter  Google Scholar 

  27. Delerablée, C., Pointcheval, D.: Dynamic threshold public-key encryption. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 317–334. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85174-5_18

    Chapter  Google Scholar 

  28. Derler, D., Jager, T., Slamanig, D., Striecks, C.: Bloom filter encryption and applications to efficient forward-secret 0-RTT key exchange. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 425–455. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_14

    Chapter  Google Scholar 

  29. Fiat, A., Naor, M.: Broadcast encryption. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 480–491. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48329-2_40

    Chapter  Google Scholar 

  30. Freeman, D.M.: Converting pairing-based cryptosystems from composite-order groups to prime-order groups. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 44–61. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_3

    Chapter  Google Scholar 

  31. Gay, R., Kerenidis, I., Wee, H.: Communication complexity of conditional disclosure of secrets and attribute-based encryption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 485–502. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48000-7_24

    Chapter  Google Scholar 

  32. Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS 2013 (2013)

    Google Scholar 

  33. Gong, J., Libert, B., Ramanna, S.C.: Compact IBBE and Fuzzy IBE from Simple Assumptions. https://hal.inria.fr/hal-01686690/

  34. Gentry, C., Waters, B.: Adaptive security in broadcast encryption systems (with short ciphertexts). In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 171–188. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01001-9_10

    Chapter  MATH  Google Scholar 

  35. Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute-based encryption for circuits from LWE. In: STOC 2013 (2013)

    Google Scholar 

  36. Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: ACM CCS 2006 (2006)

    Google Scholar 

  37. Herranz, J., Laguillaumie, F., Ràfols, C.: Constant size ciphertexts in threshold attribute-based encryption. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 19–34. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13013-7_2

    Chapter  Google Scholar 

  38. Hohenberger, S., Waters, B.: Attribute-based encryption with fast decryption. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 162–179. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_11

    Chapter  Google Scholar 

  39. Katz, J., Sahai, A., Waters, B.: Predicate encryption supporting disjunctions, polynomial equations, and inner products. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 146–162. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78967-3_9

    Chapter  Google Scholar 

  40. Lewko, A., Sahai, A., Waters, B.: Revocation systems with very small private keys. In: 2010 IEEE Symposium on Security and Privacy (2010)

    Google Scholar 

  41. Lewko, A., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully secure functional encryption: attribute-based encryption and (hierarchical) inner product encryption. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 62–91. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_4

    Chapter  Google Scholar 

  42. Lewko, A., Waters, B.: New techniques for dual system encryption and fully secure HIBE with short ciphertexts. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 455–479. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11799-2_27

    Chapter  Google Scholar 

  43. Naor, M., Naor, D., Lotspiech, J.: Revocation and tracing schemes for stateless receivers. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 41–62. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_3

    Chapter  Google Scholar 

  44. Naor, M., Pinkas, B.: Efficient trace and revoke schemes. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 1–20. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45472-1_1

    Chapter  Google Scholar 

  45. Nguyen, L.: Accumulators from bilinear pairings and applications. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 275–292. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-30574-3_19

    Chapter  Google Scholar 

  46. Okamoto, T., Takashima, K.: Fully secure functional encryption with general relations from the decisional linear assumption. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 191–208. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_11

    Chapter  Google Scholar 

  47. Okamoto, T., Takashima, K.: Achieving short ciphertexts or short secret-keys for adaptively secure general inner-product encryption. In: Lin, D., Tsudik, G., Wang, X. (eds.) CANS 2011. LNCS, vol. 7092, pp. 138–159. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25513-7_11

    Chapter  Google Scholar 

  48. Okamoto, T., Takashima, K.: Fully secure unbounded inner-product and attribute-based encryption. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 349–366. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34961-4_22

    Chapter  Google Scholar 

  49. Okamoto, T., Takashima, K.: Achieving short ciphertexts or short secret-keys for adaptively secure general inner-product encryption. Des. Codes Crypt. 77(2–3), 725–771 (2015)

    Article  MathSciNet  Google Scholar 

  50. Ostrovsky, R., Sahai, A., Waters, B.: Attribute-based encryption with non-monotonic access structures. In: ACM CCS 2007 (2007)

    Google Scholar 

  51. Rouselakis, Y., Waters, B.: Practical constructions and new proof methods for large universe attribute-based encryption. In: ACM CCCS 2013 (2013)

    Google Scholar 

  52. Sakai, R., Furukawa, J.: Identity-based broadcast encryption. In: Cryptology ePrint Archive: Report 2007/217 (2007). http://eprint.iacr.org/2007/217

  53. Sakai, R., Kasahara, M.: ID-based cryptosystems with pairing on elliptic curve. In: Cryptology ePrint Archive: Report 2003/054 (2003). http://eprint.iacr.org/2003/054

  54. 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

    Chapter  Google Scholar 

  55. 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

    Chapter  Google Scholar 

  56. Takashima, K.: Expressive attribute-based encryption with constant-size ciphertexts from the decisional linear assumption. In: Abdalla, M., De Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 298–317. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10879-7_17

    Chapter  Google Scholar 

  57. Takashima, K.: New proof techniques for DLIN-based adaptively secure attribute-based encryption. In: Pieprzyk, J., Suriadi, S. (eds.) ACISP 2017. LNCS, vol. 10342, pp. 85–105. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60055-0_5

    Chapter  Google Scholar 

  58. Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005). https://doi.org/10.1007/11426639_7

    Chapter  Google Scholar 

  59. Waters, B.: Dual system encryption: realizing fully secure IBE and HIBE under simple assumptions. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 619–636. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_36

    Chapter  Google Scholar 

  60. Waters, B.: Ciphertext-policy attribute-based encryption: an expressive, efficient, and provably secure realization. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 53–70. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19379-8_4

    Chapter  Google Scholar 

  61. Waters, B.: Functional encryption for regular languages. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 218–235. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_14

    Chapter  Google Scholar 

  62. Wee, H.: Déjà Q: encore! un petit IBE. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9563, pp. 237–258. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49099-0_9

    Chapter  Google Scholar 

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Acknowledgements

We want to thank all anonymous reviewers for invaluable comments. This work was funded in part by the “Programme Avenir Lyon Saint-Etienne de l’Université de Lyon” in the framework of the programme “Investissements d’Avenir” (ANR-11-IDEX-0007) and by the French ANR ALAMBIC project (ANR-16-CE39-0006). Part of this work was done when the last author was at Laboratoire LIP, ENS de Lyon, France and Indian Institute of Technology Bhubaneswar, India.

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  1. ENS de Lyon, Laboratoire LIP (U. Lyon, CNRS, ENSL, INRIA, UCBL), Lyon, France

    Junqing Gong & Benoît Libert

  2. CNRS, Laboratoire LIP, Lyon, France

    Benoît Libert

  3. Indian Institute of Technology, Kharagpur, India

    Somindu C. Ramanna

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  1. Junqing Gong
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  2. Benoît Libert
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Correspondence to Junqing Gong , Benoît Libert or Somindu C. Ramanna .

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  1. University of Catania, Catania, Italy

    Dario Catalano

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

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Gong, J., Libert, B., Ramanna, S.C. (2018). Compact IBBE and Fuzzy IBE from Simple Assumptions. In: Catalano, D., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science(), vol 11035. Springer, Cham. https://doi.org/10.1007/978-3-319-98113-0_30

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