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Homomorphic Authenticated Encryption Secure against Chosen-Ciphertext Attack

  • Chihong Joo
  • Aaram Yun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8874)

Abstract

We study homomorphic authenticated encryption, where privacy and authenticity of data are protected simultaneously. We define homomorphic versions of various security notions for privacy and authenticity, and investigate relations between them. In particular, we show that it is possible to give a natural definition of IND-CCA for homomorphic authenticated encryption, unlike the case of homomorphic encryption. Also, we construct a simple homomorphic authenticated encryption scheme supporting arithmetic circuits, which is chosen-ciphertext secure both for privacy and authenticity. Our scheme is based on the error-free approximate GCD assumption.

Keywords

homomorphic authenticated encryption homomorphic MAC homomorphic encryption 

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References

  1. 1.
    Bellare, M., Desai, A., Jokipii, E., Rogaway, P.: A concrete security treatment of symmetric encryption. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science, pp. 394–403 (1997)Google Scholar
  2. 2.
    Bellare, M., Goldreich, O., Mityagin, A.: The power of verification queries in message authentication and authenticated encryption. Cryptology ePrint Archive, Report 2004/309 (2004)Google Scholar
  3. 3.
    Bellare, M., Hofheinz, D., Kiltz, E.: Subtleties in the definition of IND-CCA: When and how should challenge decryption be disallowed? J. Cryptol (2013)Google Scholar
  4. 4.
    Bellare, M., Namprempre, C.: Authenticated encryption: Relations among notions and analysis of the generic composition paradigm. J. Cryptol. 21(4), 469–491 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Boneh, D., Freeman, D.M.: Homomorphic signatures for polynomial functions. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 149–168. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Brakerski, Z., Gentry, C., Halevi, S.: Packed ciphertexts in LWE-based homomorphic encryption. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 1–13. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  8. 8.
    Brakerski, Z., Gentry, C., Vaikuntanathan, V. (Leveled) fully homomorphic encryption without bootstrapping. In: Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, ITCS 2012, pp. 309–325. ACM (2012)Google Scholar
  9. 9.
    Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science (FOCS), pp. 97–106. IEEE Computer Society CPS (2011)Google Scholar
  10. 10.
    Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505–524. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  11. 11.
    Catalano, D., Fiore, D.: Practical homomorphic MACs for arithmetic circuits. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 336–352. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  12. 12.
    Catalano, D., Fiore, D., Warinschi, B.: Homomorphic signatures with efficient verification for polynomial functions. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 371–389. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  13. 13.
    Cheon, J.H., Coron, J.S., Kim, J., Lee, M.S., Lepoint, T., Tibouchi, M., Yun, A.: Batch fully homomorphic encryption over the integers. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 315–335. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  14. 14.
    Coron, J.S., Lepoint, T., Tibouchi, M.: Scale-invariant fully homomorphic encryption over the integers. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 311–328. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  15. 15.
    Coron, J.S., Mandal, A., Naccache, D., Tibouchi, M.: Fully homomorphic encryption over the integers with shorter public keys. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 487–504. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  16. 16.
    Coron, J.S., Naccache, D., Tibouchi, M.: Public key compression and modulus switching for fully homomorphic encryption over the integers. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 446–464. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  17. 17.
    van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 24–43. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Dworkin, M.: Recommendation for block cipher modes of operation: Galois/Counter Mode (GCM) for confidentiality and authentication. Special Publication 800-38D, NIST, pp. 800–838 (2007)Google Scholar
  19. 19.
    Gennaro, R., Wichs, D.: Fully homomorphic message authenticators. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 301–320. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. 20.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, pp. 169–178. ACM (2009)Google Scholar
  21. 21.
    Gentry, C., Halevi, S.: Implementing gentry’s fully-homomorphic encryption scheme. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 129–148. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  22. 22.
    Gentry, C., Halevi, S., Smart, N.P.: Fully homomorphic encryption with polylog overhead. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 465–482. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  23. 23.
    Gentry, C., Halevi, S., Smart, N.P.: Homomorphic evaluation of the AES circuit. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 850–867. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  24. 24.
    Gorbunov, S., Vaikuntanathan, V.: (Leveled) fully homomorphic signatures from lattices. Cryptology ePrint Archive, Report 2014/463 (2014)Google Scholar
  25. 25.
    Krovetz, T., Rogaway, P.: The software performance of authenticated-encryption modes. In: Joux, A. (ed.) FSE 2011. LNCS, vol. 6733, pp. 306–327. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  26. 26.
    Rogaway, P., Bellare, M., Black, J.: OCB: A block-cipher mode of operation for efficient authenticated encryption. ACM Trans. Inf. Syst. Secur. 6(3), 365–403 (2003)CrossRefGoogle Scholar
  27. 27.
    Smart, N.P., Vercauteren, F.: Fully homomorphic encryption with relatively small key and ciphertext sizes. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 420–443. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  28. 28.
    Wichs, D.: Leveled fully homomorphic signatures from standard lattices. Cryptology ePrint Archive, Report 2014/451 (2014)Google Scholar

Copyright information

© International Association for Cryptologic Research 2014

Authors and Affiliations

  • Chihong Joo
    • 1
  • Aaram Yun
    • 1
  1. 1.Ulsan National Institute of Science and Technology (UNIST)Republic of Korea

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