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Chosen Ciphertext Security via Point Obfuscation

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNSC,volume 8349)

Abstract

In this paper, we show two new constructions of chosen ciphertext secure (CCA secure) public key encryption (PKE) from general assumptions. The key ingredient in our constructions is an obfuscator for point functions with multi-bit output (MBPF obfuscators, for short), that satisfies some (average-case) indistinguishability-based security, which we call AIND security, in the presence of hard-to-invert auxiliary input. Specifically, our first construction is based on a chosen plaintext secure PKE scheme and an MBPF obfuscator satisfying the AIND security in the presence of computationally hard-to-invert auxiliary input. Our second construction is based on a lossy encryption scheme and an MBPF obfuscator satisfying the AIND security in the presence of statistically hard-to-invert auxiliary input. To clarify the relative strength of AIND security, we show the relations among security notions for MBPF obfuscators, and show that AIND security with computationally (resp. statistically) hard-to-invert auxiliary input is implied by the average-case virtual black-box (resp. virtual grey-box) property with the same type of auxiliary input. Finally, we show that a lossy encryption scheme can be constructed from an obfuscator for point functions (point obfuscator) that satisfies re-randomizability and a weak form of composability in the worst-case virtual grey-box sense. This result, combined with our second generic construction and several previous results on point obfuscators and MBPF obfuscators, yields a CCA secure PKE scheme that is constructed solely from a re-randomizable and composable point obfuscator. We believe that our results make an interesting bridge that connects CCA secure PKE and program obfuscators, two seemingly isolated but important cryptographic primitives in the area of cryptography.

Keywords

  • public key encryption
  • lossy encryption
  • key encapsulation mechanism
  • chosen ciphertext security
  • point obfuscation

References

  1. Ananth, P., Boneh, D., Garg, S., Sahai, A., Zhandry, M.: Differing-inputs obfuscation and Applications (2013), http://eprint.iacr.org/2013/689

  2. Barak, B., Bitansky, N., Canetti, R., Kalai, Y.T., Paneth, O., Sahai, A.: Obfuscation for evasive functions. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 26–51. Springer, Heidelberg (2014), http://eprint.iacr.org/2013/668

    Google Scholar 

  3. Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S., Yang, K.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001)

    CrossRef  Google Scholar 

  4. Bellare, M., Brakerski, Z., Naor, M., Ristenpart, T., Segev, G., Shacham, H., Yilek, S.: Hedged public-key encryption: How to protect against bad randomness. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 232–249. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  5. Bellare, M., Hoang, V.T., Keelveedhi, S.: Instantiating random oracles via UCEs. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 398–415. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  6. Bellare, M., Hofheinz, D., Yilek, S.: Possibility and impossibility results for encryption and commitment secure under selective opening. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 1–35. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  7. Bitansky, N., Canetti, R.: On strong simulation and composable point obfuscation (2010); Full version of [8], http://eprint.iacr.org/2010/414

  8. Bitansky, N., Canetti, R.: On strong simulation and composable point obfuscation. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 520–537. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  9. Bitansky, N., Paneth, O.: Point obfuscation and 3-round zero-knowledge. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 189–207. Springer, Heidelberg (2012)

    Google Scholar 

  10. Bleichenbacher, D.: Chosen ciphertext attacks against protocols based on the RSA encryption standard PKCS #1. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 1–12. Springer, Heidelberg (1998)

    CrossRef  Google Scholar 

  11. Boneh, D., Papakonstantinou, P.A., Rackoff, C., Vahlis, Y., Waters, B.: On the impossibility of basing identity based encryption on trapdoor permutations. In: FOCS 2008, pp. 283–292 (2008)

    Google Scholar 

  12. Boyle, E., Chung, K.-M., Pass, R.: On extractability obfuscation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 52–73. Springer, Heidelberg (2014), http://eprint.iacr.org/2013/650

    Google Scholar 

  13. Brakerski, Z., Rothblum, G.N.: Black-box obfuscation for d-CNFs. To appear in ITCS 2014 (2013), http://eprint.iacr.org/2013/557

  14. Brakerski, Z., Rothblum, G.N.: Obfuscating conjunctions. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 416–434. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  15. Brakerski, Z., Rothblum, G.N.: Virtual black-box obfuscation for all circuits via generic graded encoding. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 1–25. Springer, Heidelberg (2014), http://eprint.iacr.org/2013/563

    Google Scholar 

  16. Brakerski, Z., Segev, G.: Better security for deterministic public-key encryption: The auxiliary-input setting. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 543–560. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  17. Canetti, R.: Towards realizing random oracles: Hash functions that hide all partial information. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 455–469. Springer, Heidelberg (1997)

    CrossRef  Google Scholar 

  18. Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: FOCS 2001, pp. 136–145 (2001)

    Google Scholar 

  19. Canetti, R., Dakdouk, R.R.: Obfuscating point functions with multibit output. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 489–508. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  20. Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 207–222. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  21. Canetti, R., Tauman Kalai, Y., Varia, M., Wichs, D.: On symmetric encryption and point obfuscation. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 52–71. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  22. Canetti, R., Rothblum, G.N., Varia, M.: Obfuscation of hyperplane membership. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 72–89. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  23. Coron, J.-S., Lepoint, T., Tibouchi, M.: Practical multilinear maps over the integers. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 476–493. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

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

    CrossRef  MATH  MathSciNet  Google Scholar 

  25. Dachman-Soled, D.: A black-box construction of a CCA2 encryption scheme from a plaintext aware encryption scheme (2013), http://eprint.iacr.org/2013/680

  26. Dodis, Y., Goldwasser, S., Tauman Kalai, Y., Peikert, C., Vaikuntanathan, V.: Public-key encryption with auxiliary inputs. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 361–381. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  27. Dodis, Y., Kalai, Y.T., Lovett, S.: On cryptography with auxiliary input. In: STOC 2009, pp. 621–630 (2009)

    Google Scholar 

  28. Dodis, Y., Smith, A.: Correcting errors without leaking partial information. In: STOC 2005, pp. 654–663 (2005)

    Google Scholar 

  29. Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. In: STOC 1991, pp. 542–552 (1991)

    Google Scholar 

  30. Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1–17. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  31. Garg, S., Gentry, C., Halevi, S., Raykova, M.: Two-round secure MPC from indistinguishability obfuscation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 74–94. Springer, Heidelberg (2014), http://eprint.iacr.org/2013/601

    Google Scholar 

  32. Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all curcuits. To appear in FOCS (2013), http://eprint.iacr.org/2013/451

  33. Gertner, Y., Malkin, T., Myers, S.: Towards a separation of semantic and CCA security for public key encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 434–455. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  34. Gertner, Y., Malkin, T., Reingold, O.: On the impossibility of basing trapdoor functions on trapdoor predicates. In: FOCS 2001, pp. 126–135 (2001)

    Google Scholar 

  35. Goldreich, O., Rothblum, R.D.: Enhancements of trapdoor permutations. J. of Cryptology 26(3), 484–512 (2013)

    CrossRef  MATH  MathSciNet  Google Scholar 

  36. Goldwasser, S., Kalai, Y.T.: On the impossibility of obfuscation with auxiliary input. In: FOCS 2005, pp. 553–562 (2005)

    Google Scholar 

  37. Goldwasser, S., Kalai, Y.T., Peikart, C., Vaikuntanathan, V.: Robustness of the learning with errors assumption. In: ICS 2010, pp. 230–240 (2010)

    Google Scholar 

  38. Goldwasser, S., Rothblum, G.N.: On best-possible obfuscation. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 194–213. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  39. Hemenway, B., Libert, B., Ostrovsky, R., Vergnaud, D.: Lossy encryption: Constructions from general assumptions and efficient selective opening chosen ciphertext security. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 70–88. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  40. Hemenway, B., Ostrovsky, R.: On homomorphic encryption and chosen-ciphertext security. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 52–65. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  41. Hemenway, B., Ostrovsky, R.: Building lossy trapdoor functions from lossy encryption. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 241–260. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  42. Hohenberger, S., Lewko, A., Waters, B.: Detecting dangerous queries: A new approach for chosen ciphertext security. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 663–681. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  43. Hohenberger, S., Rothblum, G.N., Shelat, A., Vaikuntanathan, V.: Securely obfuscating re-encryption. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 233–252. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  44. Hohenberger, S., Sahai, A., Waters, B.: Replacing a random oracle: Full domain hash from indistinguishability obfuscation (2013), http://eprint.iacr.org/2013/509

  45. Kiltz, E.: Chosen-ciphertext security from tag-based encryption. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 581–600. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  46. Kiltz, E., Mohassel, P., O’Neill, A.: Adaptive trapdoor functions and chosen-ciphertext security. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 673–692. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  47. Lin, H., Tessaro, S.: Amplification of chosen-ciphertext security. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 503–519. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  48. Lynn, B.Y.S., Prabhakaran, M., Sahai, A.: Positive results and techniques for obfuscation. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 20–39. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  49. Mol, P., Yilek, S.: Chosen-ciphertext security from slightly lossy trapdoor functions. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 296–311. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  50. Myers, S., Shelat, A.: Bit encryption is complete. In: FOCS 2009, pp. 607–616 (2009)

    Google Scholar 

  51. Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: STOC 1989, pp. 33–43 (1989)

    Google Scholar 

  52. Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: STOC 1990, pp. 427–437 (1990)

    Google Scholar 

  53. Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: STOC 2008, pp. 187–196 (2008)

    Google Scholar 

  54. Rackoff, C., Simon, D.R.: Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 433–444. Springer, Heidelberg (1992)

    Google Scholar 

  55. Rosen, A., Segev, G.: Chosen-ciphertext security via correlated products. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 419–436. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  56. Sahai, A.: Non-malleable non-interactive zero knowledge and adaptive chosen-ciphertext security. In: FOCS 1999, pp. 543–553 (1999)

    Google Scholar 

  57. Sahai, A., Waters, B.: How to use indistinguishability obfuscation: Deniable encryption, and more (2013), http://eprint.iacr.org/2013/454

  58. Wee, H.: On obfuscating point functions. In: STOC 2005, pp. 523–532 (2005)

    Google Scholar 

  59. Wee, H.: Efficient chosen-ciphertext security via extractable hash proofs. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 314–332. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

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Matsuda, T., Hanaoka, G. (2014). Chosen Ciphertext Security via Point Obfuscation. In: Lindell, Y. (eds) Theory of Cryptography. TCC 2014. Lecture Notes in Computer Science, vol 8349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54242-8_5

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