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Rate-1 Incompressible Encryption from Standard Assumptions

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Theory of Cryptography (TCC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13748))

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Abstract

Incompressible encryption, recently proposed by Guan, Wichs and Zhandry (EUROCRYPT’22), is a novel encryption paradigm geared towards providing strong long-term security guarantees against adversaries with bounded long-term memory. Given that the adversary forgets just a small fraction of a ciphertext, this notion provides strong security for the message encrypted therein, even if, at some point in the future, the entire secret key is exposed. This comes at the price of having potentially very large ciphertexts. Thus, an important efficiency measure for incompressible encryption is the message-to-ciphertext ratio (also called the rate). Guan et al. provided a low-rate instantiation of this notion from standard assumptions and a rate-1 instantiation from indistinguishability obfuscation (iO). In this work, we propose a simple framework to build rate-1 incompressible encryption from standard assumptions. Our construction can be realized from, e.g. the DDH and additionally the DCR or the LWE assumptions.

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Notes

  1. 1.

    Dziembowski [26] introduced this concept under the name forward-secure storage in the symmetric key setting.

  2. 2.

    In our case the leakage function L is described by the adversary’s second stage \({\mathcal {A}}_2\).

  3. 3.

    HPS have been instrumental in many prior works on leakage resilience cryptography e.g. [3, 36].

  4. 4.

    Note that such a pair is not in \(\mathcal {L}\), except with negligible probability 1/p.

  5. 5.

    There is a technical subtlety in the security definition of incompressible SKE which we omitted before: We allow the first stage \({\mathcal {A}}'_1\) of a symmetric-key adversary \({\mathcal {A}}'\) to produce a large state (i.e. scaling with the message size), which is provided to both \({\mathcal {A}}'_2\) and \({\mathcal {A}}'_3\). This is to communicate a potentially large public key \(\textsf{PK}\) from \({\mathcal {A}}_1\) to \({\mathcal {A}}_3\) without putting a burden on the leakage-budget of the leaker-stage \({\mathcal {A}}'_2\). One could consider an alternative definition where this communication from \({\mathcal {A}}'_1\) to \({\mathcal {A}}'_3\) is not allowed. In such a setting we could still prove our construction secure by compressing the auxiliary information \(\textsf{aux}\) from which \(\textsf{PK}\) and \(c_0\) are generated using a PRG.

References

  1. Abdalla, M., Benhamouda, F., Pointcheval, D.: Disjunctions for hash proof systems: new constructions and applications. In: Oswald, E., Fischlin, M. (eds.) Advances in Cryptology - EUROCRYPT 2015, Part II. LNCS, vol. 9057, pp. 69–100. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_3

  2. Alamati, N., De Feo, L., Montgomery, H., Patranabis, S.: Cryptographic group actions and applications. In: Moriai, S., Wang, H. (eds.) Advances in Cryptology - ASIACRYPT 2020, Part II. LNCS, vol. 12492, pp. 411–439. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-64834-3_14

  3. Alwen, J., Dodis, Y., Naor, M., Segev, G., Walfish, S., Wichs, D.: Public-key encryption in the bounded-retrieval model. In: Gilbert, H. (ed.) Advances in Cryptology - EUROCRYPT 2010. LNCS, vol. 6110, pp. 113–134. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_6

  4. Alwen, J., Dodis, Y., Wichs, D.: Leakage-resilient public-key cryptography in the bounded-retrieval model. In: Halevi, S. (ed.) Advances in Cryptology - CRYPTO 2009. LNCS, vol. 5677, pp. 36–54. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03356-8_3

  5. Aumann, Y., Rabin, M.O.: Information theoretically secure communication in the limited storage space model. In: Wiener, M.J. (ed.) Advances in Cryptology - CRYPTO 2099. LNCS, vol. 1666, pp. 65–79. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48405-1_5

  6. Barak, B., et al.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) Advances in Cryptology - CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_1

  7. Bellare, M., Boldyreva, A., Palacio, A.: An uninstantiable random-oracle-model scheme for a hybrid-encryption problem. In: Cachin, C., Camenisch, J. (eds.) Advances in Cryptology - EUROCRYPT 2004. LNCS, vol. 3027, pp. 171–188. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24676-3_11

  8. Bellare, M., Dai, W.: Defending against key exfiltration: efficiency improvements for big-key cryptography via large-alphabet subkey prediction. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 2017: 24th Conference on Computer and Communications Security, pp. 923–940. ACM Press, Dallas, TX, USA (2017). https://doi.org/10.1145/3133956.3133965

  9. Bellare, M., Kane, D., Rogaway, P.: Big-key symmetric encryption: resisting key exfiltration. In: Robshaw, M., Katz, J. (eds.) Advances in Cryptology - CRYPTO 2016, Part I. LNCS, vol. 9814, pp. 373–402. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53018-4_14

  10. Black, J.: The ideal-cipher model, revisited: an uninstantiable blockcipher-based hash function. In: Robshaw, M.J.B. (ed.) Fast Software Encryption - FSE 2006. LNCS, vol. 4047, pp. 328–340. Springer, Heidelberg (2006). https://doi.org/10.1007/11799313_21

  11. Branco, P., Döttling, N., Dujmovic, J.: Rate-1 incompressible encryption from standard assumptions. IACR Cryptol. ePrint Arch. 697 (2022). https://eprint.iacr.org/2022/697

  12. Brzuska, C., Farshim, P., Mittelbach, A.: Random-oracle uninstantiability from indistinguishability obfuscation. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015: 12th Theory of Cryptography Conference, Part II. LNCS, vol. 9015, pp. 428–455. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46497-7_17

  13. Cachin, C., Maurer, U.: Unconditional security against memory-bounded adversaries. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 292–306. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052243

    Chapter  Google Scholar 

  14. Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited. J. ACM 51(4), 557–594 (2004). https://doi.org/10.1145/1008731.1008734

  15. Chevalier, C., Fouque, P.A., Pointcheval, D., Zimmer, S.: Optimal randomness extraction from a Diffie-Hellman element. In: Joux, A. (ed.) Advances in Cryptology - EUROCRYPT 2009. LNCS, vol. 5479, pp. 572–589. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01001-9_33

  16. Cramer, R., Shoup, V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055717

    Chapter  Google Scholar 

  17. Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) Advances in Cryptology - EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_4

  18. Cramer, R., Shoup, V.: Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack. SIAM J. Comput. 33(1), 167–226 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  19. Damgård, I., Ganesh, C., Orlandi, C.: Proofs of replicated storage without timing assumptions. In: Boldyreva, A., Micciancio, D. (eds.) Advances in Cryptology - CRYPTO 2019, Part I. LNCS, vol. 11692, pp. 355–380. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-030-26948-7_13

  20. Damgård, I., Jurik, M.: A generalisation, a simplification and some applications of Paillier’s probabilistic public-key system. In: Kim, K. (ed.) PKC 2001: 4th International Workshop on Theory and Practice in Public Key Cryptography. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44586-2_9

  21. Dent, A.W.: Adapting the weaknesses of the random oracle model to the generic group model. In: Zheng, Y. (ed.) Advances in Cryptology - ASIACRYPT 2002. LNCS, vol. 2501, pp. 100–109. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36178-2_6

  22. Di Crescenzo, G., Lipton, R.J., Walfish, S.: Perfectly secure password protocols in the bounded retrieval model. In: Halevi, S., Rabin, T. (eds.) TCC 2006: 3rd Theory of Cryptography Conference. LNCS, vol. 3876, pp. 225–244. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_12

  23. Dodis, Y., Ostrovsky, R., Reyzin, L., Smith, A.: Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. SIAM J. Comput. 38(1), 97–139 (2008). https://doi.org/10.1137/060651380, https://doi.org/10.1137/060651380

  24. Dodis, Y., Quach, W., Wichs, D.: Speak much, remember little: cryptography in the bounded storage model, revisited. Cryptology ePrint Archive, Report 2021/1270 (2021). https://eprint.iacr.org/2021/1270

  25. Dziembowski, S.: Intrusion-resilience via the bounded-storage model. In: Halevi, S., Rabin, T. (eds.) TCC 2006: 3rd Theory of Cryptography Conference. LNCS, vol. 3876, pp. 207–224. Springer, Heidelberg (2006). https://doi.org/10.1007/11681878_11

  26. Dziembowski, S.: On forward-secure storage (extended abstract). In: Dwork, C. (ed.) Advances in Cryptology - CRYPTO 2006. LNCS, vol. 4117, pp. 251–270. Springer, Heidelberg (2006). https://doi.org/10.1007/11818175_15

  27. Garg, R., Lu, G., Waters, B.: New techniques in replica encodings with client setup. In: Pass, R., Pietrzak, K. (eds.) TCC 2020: 18th Theory of Cryptography Conference, Part III. LNCS, vol. 12552, pp. 550–583. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-64381-2_20

  28. Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th Annual Symposium on Foundations of Computer Science, pp. 40–49. IEEE Computer Society Press, Berkeley, CA, USA (2013). https://doi.org/10.1109/FOCS.2013.13

  29. Goldwasser, S., Kalai, Y.T.: On the (in)security of the Fiat-Shamir paradigm. In: 44th Annual Symposium on Foundations of Computer Science, pp. 102–115. IEEE Computer Society Press, Cambridge, MA, USA (2003). https://doi.org/10.1109/SFCS.2003.1238185

  30. Gorbunov, S., Vaikuntanathan, V., Wee, H.: Functional encryption with bounded collusions via multi-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) Advances in Cryptology - CRYPTO 2012. LNCS, vol. 7417, pp. 162–179. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_11

  31. Goyal, R., Koppula, V., Waters, B.: Lockable obfuscation. In: Umans, C. (ed.) 58th Annual Symposium on Foundations of Computer Science, pp. 612–621. IEEE Computer Society Press, Berkeley, CA, USA (2017). https://doi.org/10.1109/FOCS.2017.62

  32. Guan, J., Wichs, D., Zhandry, M.: Incompressible cryptography. In: Dunkelman, O., Dziembowski, S. (eds.) Advances in Cryptology - EUROCRYPT 2022, Part I. LNCS, vol. 13275, pp. 700–730. Springer, Heidelberg (2022). https://doi.org/10.1007/978-3-031-06944-4_24

  33. Guan, J., Zhandry, M.: Simple schemes in the bounded storage model. In: Ishai, Y., Rijmen, V. (eds.) Advances in Cryptology - EUROCRYPT 2019, Part III. LNCS, vol. 11478, pp. 500–524. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-030-17659-4_17

  34. Guan, J., Zhandry, M.: Disappearing cryptography in the bounded storage model. In: Nissim, K., Waters, B. (eds.) TCC 2021: 19th Theory of Cryptography Conference, Part II. LNCS, vol. 13043, pp. 365–396. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-030-90453-1_13

  35. Håstad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364–1396 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  36. Hazay, C., López-Alt, A., Wee, H., Wichs, D.: Leakage-resilient cryptography from minimal assumptions. In: Johansson, T., Nguyen, P.Q. (eds.) Advances in Cryptology - EUROCRYPT 2013. LNCS, vol. 7881, pp. 160–176. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38348-9_10

  37. Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from well-founded assumptions. In: STOC, pp. 60–73. ACM (2021)

    Google Scholar 

  38. Kalai, Y.T.: Smooth projective hashing and two-message oblivious transfer. In: Cramer, R. (ed.) Advances in Cryptology - EUROCRYPT 2005. LNCS, vol. 3494, pp. 78–95. Springer, Heidelberg(2005). https://doi.org/10.1007/11426639_5

  39. Maurer, U.: Conditionally-perfect secrecy and a provably-secure randomized cipher. J. Cryptol. 5(1), 53–66 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  40. Maurer, U.M.: Protocols for secret key agreement by public discussion based on common information. In: Brickell, E.F. (ed.) Advances in Cryptology - CRYPTO 1992. LNCS, vol. 740, pp. 461–470. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-48071-4_32

  41. Maurer, U.M., Renner, R., Holenstein, C.: Indifferentiability, impossibility results on reductions, and applications to the random oracle methodology. In: Naor, M. (ed.) TCC 2004: 1st Theory of Cryptography Conference. LNCS, vol. 2951, pp. 21–39. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24638-1_2

  42. Moran, T., Wichs, D.: Incompressible encodings. In: Micciancio, D., Ristenpart, T. (eds.) Advances in Cryptology - CRYPTO 2020, Part I. LNCS, vol. 12170, pp. 494–523. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-030-56784-2_17

  43. Naor, M.: On cryptographic assumptions and challenges (invited talk). In: Boneh, D. (ed.) Advances in Cryptology - CRYPTO 2003. LNCS, vol. 2729, pp. 96–109. Springer, Heidelberg 2003). https://doi.org/10.1007/978-3-540-45146-4_6

  44. Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) Advances in Cryptology - EUROCRYPT 19 LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg 1999). https://doi.org/10.1007/3-540-48910-X_16

  45. Raz, R.: A time-space lower bound for a large class of learning problems. In: Umans, C. (ed.) 58th Annual Symposium on Foundations of Computer Science,pp. 732–742. IEEE Computer Society Press, Berkeley, CA, USA (2017). https://doi.org/10.1109/FOCS.2017.73

  46. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H.N., Fagin, R. (eds.) 37th Annual ACM Symposium on Theory of Computing, pp. 84–93. ACM Press, Baltimore, MA, USA (2005). https://doi.org/10.1145/1060590.1060603

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Acknowledgement

We would like to thank Stefan Dziembowski, Daniel Wichs, and the anonymous reviewers of TCC for discussions and comments.

Nico Döttling is funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. (ERC-2021-STG 101041207 LACONIC).

Part of the work of Pedro Branco was done while at IST University of Lisbon.

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Authors and Affiliations

  1. Johns Hopkins University, Baltimore, MD, 21218, USA

    Pedro Branco

  2. Helmholtz Center for Information Security (CISPA), 66123, Saarbrücken, Germany

    Nico Döttling & Jesko Dujmović

  3. Saarland University, 66123, Saarbrücken, Germany

    Jesko Dujmović

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  1. Pedro Branco
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  2. Nico Döttling
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Correspondence to Pedro Branco .

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  1. Ruhr University Bochum, Bochum, Germany

    Eike Kiltz

  2. Massachusetts Institute of Technology, Cambridge, MA, USA

    Vinod Vaikuntanathan

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Branco, P., Döttling, N., Dujmović, J. (2022). Rate-1 Incompressible Encryption from Standard Assumptions. In: Kiltz, E., Vaikuntanathan, V. (eds) Theory of Cryptography. TCC 2022. Lecture Notes in Computer Science, vol 13748. Springer, Cham. https://doi.org/10.1007/978-3-031-22365-5_2

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