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Distributed Broadcast Encryption from Bilinear Groups

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Advances in Cryptology – ASIACRYPT 2023 (ASIACRYPT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14442))

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Abstract

Distributed broadcast encryption (DBE) improves on the traditional notion of broadcast encryption by eliminating the key-escrow problem: In a DBE system, users generate their own secret keys non-interactively without the help of a trusted party. Then anyone can broadcast a message for a subset S of the users, in such a way that the resulting ciphertext size is sublinear in (and, ideally, independent of) |S|. Unfortunately, the only known constructions of DBE requires heavy cryptographic machinery, such as general-purpose indistinguishability obfuscation, or come without a security proof.

In this work, we formally show that obfuscation is not necessary for DBE, and we present two practical DBE schemes from standard assumptions in prime-order bilinear groups. Our constructions are conceptually simple, satisfy the strong notion of adaptive security, and are concretely efficient. In fact, their performance, in terms of number of group elements and efficiency of the algorithms, is comparable with that of traditional (non distributed) broadcast encryption schemes from bilinear groups.

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Notes

  1. 1.

    In [38] under the name’Ad Hoc Broadcast Encryption’.

  2. 2.

    k-Lin tells us that

    $$ [\textbf{B}]_2,[\textbf{r}_i]_2,[\textbf{t}^\top \textbf{B}]_2,[\textbf{t}^\top \textbf{r}_i] \approx _c [\textbf{B}]_2,[\textbf{r}_i]_2,[\textbf{t}^\top \textbf{B}]_2,[\textbf{t}^\top \textbf{r}_i + \delta _i] $$

    Now, the reduction samples a random \(\tilde{\textbf{W}}_i\) and programs \(\textbf{W}_i = \tilde{\textbf{W}}_i + \textbf{a}^\perp \textbf{t}\).

References

  1. Agrawal, S., Wichs, D., Yamada, S.: Optimal broadcast encryption from LWE and pairings in the standard model. In: Pass, R., Pietrzak, K. (eds.) TCC 2020, Part I. LNCS, vol. 12550, pp. 149–178. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-64375-1_6

  2. Agrawal, S., Yamada, S.: Optimal broadcast encryption from pairings and LWE. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part I. LNCS, vol. 12105, pp. 13–43. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-45721-1_2

  3. Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_3

  4. 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

  5. Boneh, D., Waters, B.: A fully collusion resistant broadcast, trace, and revoke system. In: Juels, A., Wright, R.N., De Capitani di Vimercati, S. (eds.) ACM CCS 2006, pp. 211–220. ACM Press (2006). https://doi.org/10.1145/1180405.1180432

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

  7. Boneh, D., Zhandry, M.: Multiparty key exchange, efficient traitor tracing, and more from indistinguishability obfuscation. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 480–499. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44371-2_27

  8. Brakerski, Z., Döttling, N., Garg, S., Malavolta, G.: Candidate iO from homomorphic encryption schemes. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part I. LNCS, vol. 12105, pp. 79–109. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-45721-1_4

  9. Brakerski, Z., Döttling, N., Garg, S., Malavolta, G.: Factoring and pairings are not necessary for IO: circular-secure LWE suffices. In: Bojanczyk, M., Merelli, E., Woodruff, D.P. (eds.) 49th International Colloquium on Automata, Languages, and Programming, ICALP 2022, July 4–8, 2022, Paris, France. LIPIcs, vol. 229, pp. 28:1–28:20. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022). https://doi.org/10.4230/LIPIcs.ICALP.2022.28

  10. Brakerski, Z., Vaikuntanathan, V.: Lattice-inspired broadcast encryption and succinct ciphertext-policy abe. In: 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Schloss Dagstuhl-Leibniz-Zentrum für Informatik (2022)

    Google Scholar 

  11. Chen, J., Gay, R., Wee, H.: Improved dual system ABE in prime-order groups via predicate encodings. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 595–624. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_20

  12. Döttling, N., Kolonelos, D., Lai, R.W.F., Lin, C., Malavolta, G., Rahimi, A.: Efficient laconic cryptography from learning with errors. In: EUROCRYPT 2023, Part III, pp. 417–446. LNCS, Springer, Heidelberg (2023). https://doi.org/10.1007/978-3-031-30620-4_14

  13. Escala, A., Herold, G., Kiltz, E., Ràfols, C., Villar, J.: An algebraic framework for Diffie-Hellman assumptions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 129–147. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40084-1_8

  14. Fiat, A., Naor, M.: Broadcast encryption. In: Stinson, D.R. (ed.) CRYPTO’93. LNCS, vol. 773, pp. 480–491. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48329-2_40

  15. Francati, D., Friolo, D., Maitra, M., Malavolta, G., Rahimi, A., Venturi, D.: Registered (inner-product) functional encryption. IACR Cryptol. ePrint Arch. p. 395 (2023), https://eprint.iacr.org/2023/395

  16. Garg, S., Hajiabadi, M., Mahmoody, M., Rahimi, A.: Registration-based encryption: removing private-key generator from IBE. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018, Part I. LNCS, vol. 11239, pp. 689–718. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-030-03807-6_25

  17. Garg, S., Hajiabadi, M., Mahmoody, M., Rahimi, A., Sekar, S.: Registration-based encryption from standard assumptions. In: Lin, D., Sako, K. (eds.) PKC 2019, Part II. LNCS, vol. 11443, pp. 63–93. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-030-17259-6_3

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

  19. Gay, R., Kowalczyk, L., Wee, H.: Tight adaptively secure broadcast encryption with short ciphertexts and keys. In: Catalano, D., De Prisco, R. (eds.) SCN 18. LNCS, vol. 11035, pp. 123–139. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-319-98113-0_7

  20. Gay, R., Pass, R.: Indistinguishability obfuscation from circular security. In: STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pp. 736–749. ACM Press (2021). https://doi.org/10.1145/3406325.3451070

  21. 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

  22. Glaeser, N., Kolonelos, D., Malavolta, G., Rahimi, A.: Efficient registration-based encryption. In: Meng, W., Jensen, C.D., Cremers, C., Kirda, E. (eds.) ACM CCS 2023. ACM Press (2023). https://doi.org/10.1145/3576915.3616596

  23. Groth, J., Kohlweiss, M., Maller, M., Meiklejohn, S., Miers, I.: Updatable and universal common reference strings with applications to zk-SNARKs. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part III. LNCS, vol. 10993, pp. 698–728. Springer, Heidelberg (2018). https://doi.org/10.1007/978-3-319-96878-0_24

  24. Hofheinz, D., Kiltz, E.: Secure hybrid encryption from weakened key encapsulation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 553–571. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74143-5_31

  25. Hohenberger, S., Lu, G., Waters, B., Wu, D.J.: Registered attribute-based encryption. In: EUROCRYPT 2023, Part III, pp. 511–542. LNCS, Springer, Heidelberg (2023). https://doi.org/10.1007/978-3-031-30620-4_17

  26. Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from well-founded assumptions. In: STOC 2021: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pp. 60–73. ACM Press (2021). https://doi.org/10.1145/3406325.3451093

  27. Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from LPN over \(\mathbb{F} _p\), DLIN, and PRGs in \({NC}^0\). In: Dunkelman, O., Dziembowski, S. (eds.) EUROCRYPT 2022, Part I. LNCS, vol. 13275, pp. 670–699. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-06944-4_23

  28. Kolonelos, D., Malavolta, G., Wee, H.: Distributed broadcast encryption from bilinear groups. Cryptology ePrint Archive (2023)

    Google Scholar 

  29. Lewko, A.B., 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

  30. Maller, M., Bowe, S., Kohlweiss, M., Meiklejohn, S.: Sonic: zero-knowledge SNARKs from linear-size universal and updatable structured reference strings. In: Cavallaro, L., Kinder, J., Wang, X., Katz, J. (eds.) ACM CCS 2019, pp. 2111–2128. ACM Press (2019). https://doi.org/10.1145/3319535.3339817

  31. Phan, D.H., Pointcheval, D., Strefler, M.: Decentralized dynamic broadcast encryption. In: Visconti, I., Prisco, R.D. (eds.) SCN 12. LNCS, vol. 7485, pp. 166–183. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32928-9_10

  32. Shacham, H.: A cramer-shoup encryption scheme from the linear assumption and from progressively weaker linear variants. Cryptology ePrint Archive, Report 2007/074 (2007). https://eprint.iacr.org/2007/074

  33. 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

  34. Wee, H.: Broadcast encryption with size \({N}^{1/3}\) and more from \(k\)-lin. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021, Part IV. LNCS, vol. 12828, pp. 155–178. Springer, Heidelberg, Virtual Event (2021). https://doi.org/10.1007/978-3-030-84259-8_6

  35. Wee, H.: Optimal broadcast encryption and CP-ABE from evasive lattice assumptions. In: Dunkelman, O., Dziembowski, S. (eds.) EUROCRYPT 2022, Part II. LNCS, vol. 13276, pp. 217–241. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-07085-3_8

  36. Wee, H., Wichs, D.: Candidate obfuscation via oblivious LWE sampling. In: Canteaut, A., Standaert, F.X. (eds.) EUROCRYPT 2021, Part III. LNCS, vol. 12698, pp. 127–156. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-030-77883-5_5

  37. Wu, Q., Qin, B., Zhang, L., Domingo-Ferrer, J.: Ad hoc broadcast encryption. In: Proceedings of the 17th ACM Conference on Computer and Communications Securit, pp. 741–743 (2010). https://crises-deim.urv.cat/web/docs/publications/conferences/318.pdf

  38. Wu, Q., Qin, B., Zhang, L., Domingo-Ferrer, J.: Ad hoc broadcast encryption (poster presentation). In: Al-Shaer, E., Keromytis, A.D., Shmatikov, V. (eds.) ACM CCS 2010, pp. 741–743. ACM Press (2010). https://doi.org/10.1145/1866307.1866416

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Acknowledgments

We would like to thank Brent Waters and David Wu for helpful discussions on [25]. We would, also, like to thank Duong Hieu Phan and Ji Luo for helpful discussions on prior works. G.M. was partially funded by the German Federal Ministry of Education and Research (BMBF) in the course of the 6GEM research hub under grant number 16KISK038 and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC 2092 CASA - 390781972. D.K. received funding from projects from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under project PICOCRYPT (grant agreement No. 101001283) and from the Spanish Government under projects PRODIGY (TED2021-132464B-I00) and ESPADA (PID2022-142290OB-I00). The last two projects are co-funded by European Union EIE, and NextGenerationEU/PRTR funds.

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Authors and Affiliations

  1. IMDEA Software Institute, Madrid, Spain

    Dimitris Kolonelos

  2. Universidad Politécnica de Madrid, Madrid, Spain

    Dimitris Kolonelos

  3. Bocconi University, Milan, Italy

    Giulio Malavolta

  4. Max Planck Institute for Security and Privacy, Bochum, Germany

    Giulio Malavolta

  5. NTT Research, Palo Alto, CA, USA

    Hoeteck Wee

  6. École Normale Supérieure - PSL, Paris, France

    Hoeteck Wee

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  1. Dimitris Kolonelos
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Correspondence to Dimitris Kolonelos .

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Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Jian Guo

  2. Monash University, Melbourne, VIC, Australia

    Ron Steinfeld

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Kolonelos, D., Malavolta, G., Wee, H. (2023). Distributed Broadcast Encryption from Bilinear Groups. In: Guo, J., Steinfeld, R. (eds) Advances in Cryptology – ASIACRYPT 2023. ASIACRYPT 2023. Lecture Notes in Computer Science, vol 14442. Springer, Singapore. https://doi.org/10.1007/978-981-99-8733-7_13

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