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Tightly CCA-secure encryption scheme in a multi-user setting with corruptions

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Abstract

The security of public-key encryption (PKE) schemes in a multi-user setting is aimed at capturing real-world scenarios in which an adversary could attack multiple users and multiple ciphertexts of its choice. However, the fact that a real-world adversary can also mount key-exposure attacks for a set of multiple public keys requires us to consider a more realistic notion of security in multi-user settings. In this study, we establish the security notion of PKE in a multi-user setting with corruptions, where an adversary is able to issue (adaptive) encryption, decryption, and corruption (i.e., private key) queries. We then propose the first practical PKE scheme whose security is proven in a multi-user setting with corruptions. The security of our scheme is based on the computational Diffie–Hellman (CDH) assumption and is proven to be tightly chosen-ciphertext secure in a random oracle model. Our scheme essentially follows the recently proposed modular approach of combining KEM and augmented DEM in a multi-user setting, but we show that this modular approach works well in a multi-user setting with corruptions.

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Notes

  1. “Almost” tightness means that the security loss L is determined by \(O(\lambda )\) for a security parameter \(\lambda \).

  2. “Multi-instance” means that there exist multiple key generation centers, which correspond to multiple users in the process of converting from IBE to PKE.

  3. Roughly speaking, our variant works as follows: for a public key \((g,X_{1}=g^{x_1}, X_{2}=g^{x_2})\) with a corresponding secret key \((x_1, x_2)\), encryption is done by computing \((g^{s}, X_{1}^{s}, X_{2}^{s})\) for a random s and outputting a ciphertext \((g^{s}, H(g^{s}, X_{1}^{s}, X_{2}^{s})\oplus m)\) for a message m.

References

  1. Attrapadung N., Furukawa J., Gomi T., Hanaoka G., Imai H., Zhang R.: Efficient identity-based encryption with tight security reduction. In: Pointcheval D., Mu Y., Chen K. (eds.) CANS, vol. 4301, pp. 19–36. Lecture Notes in Computer ScienceSpringer, Berlin (2006).

    Google Scholar 

  2. Attrapadung N., Hanaoka G., Yamada S.: A framework for identity-based encryption with almost tight security. In: Iwata T., Cheon J.H. (eds.) ASIACRYPT, vol. 9452, pp. 521–549. Lecture Notes in Computer ScienceSpringer, Berlin (2015).

    Google Scholar 

  3. Bader, C., Hofheinz, D., Jager, T., Kiltz, E., Li, Y.: Tightly-secure authenticated key exchange. In: TCC’15, Springer, Lecture Notes in Computer Science, vol. 9014, pp. 629–658 (2015)

  4. Bellare M., Rogaway P.: Introduction to Modern Cryptography. University of California at San Diego, San Diego (2005).

    MATH  Google Scholar 

  5. Bellare, M., Desai, A., Pointcheval, D., Rogaway, P.: Relations among notions of security for public-key encryption schemes. In: CRYPTO’98, vol. 1462, pp. 26–45. Springer (1998)

  6. Bellare M., Boldyreva A., Micali S.: Public-key encryption in a multi-user setting: security proofs and improvements. In: Preneel B. (ed.) EUROCRYPT’00, vol. 1807, pp. 259–274. Lecture Notes in Computer ScienceSpringer, Berlin (2000).

    Google Scholar 

  7. Boneh D., Franklin M.K.: Identity-based encryption from the weil pairing. In: Kilian J. (ed.) CRYPTO‘01, vol. 2139, pp. 213–229. Lecture Notes in Computer ScienceSpringer, Berlin (2001).

    Google Scholar 

  8. Boneh D., Canetti R., Halevi S., Katz J.: Chosen-ciphertext security from identity-based encryption. SIAM J. Comput. 36(5), 1301–1328 (2007).

    Article  MathSciNet  Google Scholar 

  9. Cash D., Kiltz E., Shoup V.: The twin Diffie–Hellman problem and applications. In: Smart N. (ed.) EUROCRYPT, vol. 4965, pp. 127–145. Lecture Notes in Computer ScienceSpringer, Berlin (2008).

    Google Scholar 

  10. Cramer R., Shoup V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. CRYPTO’98, Lecture Notes in Computer Science, vol. 1462, pp. 13–25. Springer, Berlin (1998).

    Google Scholar 

  11. Diffie W., Hellman M.E.: New directions in cryptography. IEEE Trans. Inf. Theory 22(6), 644–654 (2006).

    Article  MathSciNet  Google Scholar 

  12. Dolev D., Dwork C., Naor M.: Nonmalleable cryptography. SIAM J. Comput. 30(2), 391–437 (2000).

    Article  MathSciNet  Google Scholar 

  13. Fujisaki E., Okamoto T.: How to enhance the security of public-key encryption at minimum cost. In: Imai H., Zheng Y. (eds.) PKC, Lecture Notes in Computer Science, vol. 1560, pp. 53–68. Springer, Berlin (1999).

    Google Scholar 

  14. Gay R., Hofheinz D., Kiltz E., Wee H.: Tightly cca-secure encryption without pairings. In: Fischlin M., Coron J.S. (eds.) EUROCRYPT, Part I, Lecture Notes in Computer Science, vol. 9665, pp. 1–27. Springer, New York (2016).

    Google Scholar 

  15. Gay, R., Hofheinz, D., Kohl, L.: Kurosawa-desmedt meets tight security. In: CRYPTO’17, vol. 10403, pp. 133–160. Springer, Berlin (2017)

  16. Giacon F., Kiltz E., Poettering B.: Hybrid encryption in a multi-user setting, revisited. In: Abdalla M., Dahab R. (eds.) PKC’18, Lecture Notes in Computer Science, vol. 10769, pp. 159–189. Springer, Berlin (2018).

    MATH  Google Scholar 

  17. Gjøsteen, K., Jager, T.: Practical and tightly-secure digital signatures and authenticated key exchange. In: CRYPTO’18, Lecture Notes in Computer Science, vol. 10992, pp. 95–125. Springer (2018)

  18. Gong J., Chen J., Dong X., Cao Z., Tang S.: Extended nested dual system groups, revisited. In: Cheng C.M., Chung K.M., Persiano G., Yang B.Y. (eds.) PKC’16, Lecture Notes in Computer Science, vol. 9614, pp. 133–163. Springer, Berlin (2016).

    Google Scholar 

  19. Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: EUROCRYPT’08, Lecture Notes in Computer Science, vol. 4965, pp. 415–432. Springer (2008)

  20. Hofheinz, D.: Adaptive partitioning. In: EUROCRYPT’17, Lecture Notes in Computer Science, vol. 10212, pp. 489–518. Springer (2017)

  21. Hofheinz D., Jager T.: Tightly secure signatures and public-key encryption. In: Safavi-Naini R., Canetti R. (eds.) CRYPTO, Lecture Notes in Computer Science, vol. 7417, pp. 590–607. Springer, Cham (2012).

    Google Scholar 

  22. Hofheinz D., Koch J., Striecks C.: Identity-based encryption with (almost) tight security in the multi-instance, multi-ciphertext setting. In: Katz J. (ed.) PKC, Lecture Notes in Computer Science, vol. 9020, pp. 799–822. Springer, Cham (2015).

    MATH  Google Scholar 

  23. Hofheinz, D., Hövelmanns, K., Kiltz, E.: A modular analysis of the fujisaki-okamoto transformation. In: TCC’17, Lecture Notes in Computer Science, vol. 10677, pp. 341–371. Springer (2017)

  24. Libert, B., Joye, M., Yung, M., Peters, T.: Concise multi-challenge cca-secure encryption and signatures with almost tight security. In: ASIACRYPT’14, Lecture Notes in Computer Science, vol. 8874, pp. 1–21. Springer (2014)

  25. Libert B., Peters T., Joye M., Yung M.: Compactly hiding linear spans. In: Iwata T., Cheon J.H. (eds.) ASIACRYPT, Part I, Lecture Notes in Computer Science, vol. 9452, pp. 681–707. Springer, Cham (2015).

    Google Scholar 

  26. Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: H. Ortiz (ed.) STOC’90, pp. 427–437. ACM (1990)

  27. Rackoff, C., Simon, D.R.: Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. In: CRYPTO’91, vol. 576, pp. 433–444. Springer (1991)

  28. Shamir A.: Identity-based cryptosystems and signature schemes. In: Blakley G.R., Chaum D. (eds.) CRYPTO‘84, Lecture Notes in Computer Science, vol. 196, pp. 47–53. Springer, Berlin (1984).

    Google Scholar 

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Acknowledgements

The study was funded by Institute for Information and communications Technology Promotion (Grant No. 2016-6-00600, A Study on Functional Encryption: Construction, Security Analysis, and Implementation).

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Authors and Affiliations

  1. Korea University, Seoul, Korea

    Youngkyung Lee & Dong Hoon Lee

  2. Sangmyung University, Seoul, Korea

    Jong Hwan Park

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  1. Youngkyung Lee
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Correspondence to Jong Hwan Park.

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Communicated by R. Steinfeld.

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Lee, Y., Lee, D.H. & Park, J.H. Tightly CCA-secure encryption scheme in a multi-user setting with corruptions. Des. Codes Cryptogr. 88, 2433–2452 (2020). https://doi.org/10.1007/s10623-020-00794-z

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