Advertisement

Chosen Ciphertext Security from Injective Trapdoor Functions

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12170)

Abstract

We provide a construction of chosen ciphertext secure public-key encryption from (injective) trapdoor functions. Our construction is black box and assumes no special properties (e.g. “lossy”, “correlated product secure”) of the trapdoor function.

References

  1. 1.
    Bellare, M., Halevi, S., Sahai, A., Vadhan, S.: Many-to-one trapdoor functions and their relation to public-key cryptosystems. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 283–298. Springer, Heidelberg (1998).  https://doi.org/10.1007/BFb0055735CrossRefGoogle Scholar
  2. 2.
    Brakerski, Z., Lombardi, A., Segev, G., Vaikuntanathan, V.: Anonymous IBE, leakage resilience and circular security from new assumptions. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10820, pp. 535–564. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-78381-9_20CrossRefGoogle Scholar
  3. 3.
    Cash, D., Kiltz, E., Shoup, V.: The twin Diffie–Hellman problem and applications. J. Cryptol. 22(4), 470–504 (2009).  https://doi.org/10.1007/s00145-009-9041-6MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cho, C., Döttling, N., Garg, S., Gupta, D., Miao, P., Polychroniadou, A.: Laconic oblivious transfer and its applications. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10402, pp. 33–65. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63715-0_2CrossRefGoogle Scholar
  5. 5.
    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/BFb0055717CrossRefGoogle Scholar
  6. 6.
    Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-46035-7_4CrossRefGoogle Scholar
  7. 7.
    Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM J. Comput. 30(2), 391–437 (2000)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Döttling, N., Garg, S.: From selective IBE to full IBE and selective HIBE. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10677, pp. 372–408. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-70500-2_13CrossRefGoogle Scholar
  9. 9.
    Döttling, N., Garg, S.: Identity-based encryption from the Diffie-Hellman assumption. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 537–569. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-63688-7_18CrossRefGoogle Scholar
  10. 10.
    Döttling, N., Garg, S., Hajiabadi, M., Masny, D.: New constructions of identity-based and key-dependent message secure encryption schemes. In: Abdalla, M., Dahab, R. (eds.) PKC 2018. LNCS, vol. 10769, pp. 3–31. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-76578-5_1CrossRefzbMATHGoogle Scholar
  11. 11.
    Döttling, N., Müller-Quade, J., Nascimento, A.C.A.: IND-CCA secure cryptography based on a variant of the LPN problem. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 485–503. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-34961-4_30CrossRefGoogle Scholar
  12. 12.
    Dwork, C., Naor, M., Reingold, O.: Immunizing encryption schemes from decryption errors. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 342–360. Springer, Heidelberg (2004).  https://doi.org/10.1007/978-3-540-24676-3_21CrossRefGoogle Scholar
  13. 13.
    Fujisaki, E., Okamoto, T.: How to enhance the security of public-key encryption at minimum cost. In: Imai, H., Zheng, Y. (eds.) PKC 1999. LNCS, vol. 1560, pp. 53–68. Springer, Heidelberg (1999).  https://doi.org/10.1007/3-540-49162-7_5CrossRefzbMATHGoogle Scholar
  14. 14.
    Garg, S., Gay, R., Hajiabadi, M.: New techniques for efficient trapdoor functions and applications. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019, Part III. LNCS, vol. 11478, pp. 33–63. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-17659-4_2CrossRefGoogle Scholar
  15. 15.
    Garg, S., Hajiabadi, M.: Trapdoor functions from the computational Diffie-Hellman assumption. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part II. LNCS, vol. 10992, pp. 362–391. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-96881-0_13CrossRefGoogle Scholar
  16. 16.
    Gertner, Y., Malkin, T., Reingold, O.: On the impossibility of basing trapdoor functions on trapdoor predicates. In: 42nd Annual Symposium on Foundations of Computer Science, FOCS 2001, Las Vegas, Nevada, USA, 14–17 October 2001, pp. 126–135. IEEE Computer Society (2001)Google Scholar
  17. 17.
    Goldreich, O.: Basing non-interactive zero-knowledge on (enhanced) trapdoor permutations: the state of the art. In: Goldreich, O. (ed.) Studies in Complexity and Cryptography. Miscellanea on the Interplay Between Randomness and Computation. LNCS, vol. 6650, pp. 406–421. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22670-0_28CrossRefGoogle Scholar
  18. 18.
    Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: Proceedings of the 21st Annual ACM Symposium on Theory of Computing, pp. 25–32 (1989)Google Scholar
  19. 19.
    Goldwasser, S., Micali, S.: Probabilistic encryption. J. Comput. Syst. Sci. 28(2), 270–299 (1984)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Hanaoka, G., Kurosawa, K.: Efficient chosen ciphertext secure public key encryption under the computational Diffie-Hellman assumption. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 308–325. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-89255-7_19CrossRefGoogle Scholar
  21. 21.
    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)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Hemenway, B., Ostrovsky, R.: Lossy trapdoor functions from smooth homomorphic hash proof systems. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 16, p. 127 (2009)Google Scholar
  23. 23.
    Hofheinz, D., Kiltz, E.: Practical chosen ciphertext secure encryption from factoring. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 313–332. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-01001-9_18CrossRefGoogle Scholar
  24. 24.
    Katz, J., Lindell, Y.: Introduction to Modern Cryptography. Chapman & Hall/CRC, Boca Raton (2008)zbMATHGoogle Scholar
  25. 25.
    Kiltz, E., Masny, D., Pietrzak, K.: Simple chosen-ciphertext security from low-noise LPN. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 1–18. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54631-0_1CrossRefGoogle Scholar
  26. 26.
    Kitagawa, F., Matsuda, T.: CPA-to-CCA transformation for KDM security. In: Hofheinz, D., Rosen, A. (eds.) TCC 2019. LNCS, vol. 11892, pp. 118–148. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-36033-7_5CrossRefGoogle Scholar
  27. 27.
    Koppula, V., Waters, B.: Realizing chosen ciphertext security generically in attribute-based encryption and predicate encryption. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 671–700. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-26951-7_23CrossRefzbMATHGoogle Scholar
  28. 28.
    Lamport, L.: Constructing digital signatures from a one-way function. Technical report, SRI International Computer Science Laboratory (1979)Google Scholar
  29. 29.
    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).  https://doi.org/10.1007/978-3-642-13013-7_18CrossRefGoogle Scholar
  30. 30.
    Naor, M.: Bit commitment using pseudo-randomness. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 128–136. Springer, New York (1990).  https://doi.org/10.1007/0-387-34805-0_13 CrossRefGoogle Scholar
  31. 31.
    Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, Baltimore, Maryland, USA, 13–17 May 1990, pp. 427–437 (1990)Google Scholar
  32. 32.
    Pandey, O.: Personal communication (2013)Google Scholar
  33. 33.
    Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, Victoria, British Columbia, Canada, 7–20 May 2008, pp. 187–196 (2008)Google Scholar
  34. 34.
    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).  https://doi.org/10.1007/3-540-46766-1_35CrossRefGoogle Scholar
  35. 35.
    Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Rosen, A., Segev, G.: Chosen-ciphertext security via correlated products. SIAM J. Comput. 39(7), 3058–3088 (2010)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Shoup, V.: Why chosen ciphertext security matters. IBM TJ Watson Research Center (1998)Google Scholar
  38. 38.
    Yao, A.C.: Theory and applications of trapdoor functions (extended abstract). In: 23rd Annual Symposium on Foundations of Computer Science, pp. 80–91 (1982)Google Scholar

Copyright information

© International Association for Cryptologic Research 2020

Authors and Affiliations

  1. 1.Johns Hopkins UniversityBaltimoreUSA
  2. 2.Weizmann Institute of ScienceRehovotIsrael
  3. 3.University of TexasAustinUSA
  4. 4.NTT ResearchPalo AltoUSA

Personalised recommendations