Public Key Encryption against Related Key Attacks

  • Hoeteck Wee
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7293)

Abstract

In this work, we present efficient public-key encryption schemes resilient against linear related key attacks (RKA) under standard assumptions and in the standard model. Specifically, we obtain encryption schemes based on hardness of factoring, BDDH and LWE that remain secure even against an adversary that may query the decryption oracle on linear shifts of the actual secret key. Moreover, the ciphertext overhead is only an additive constant number of group elements.

Keywords

Encryption Scheme Cryptology ePrint Archive Challenge Ciphertext Decryption Oracle Hash Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Agrawal, S., Boneh, D., Boyen, X.: Efficient Lattice (H)IBE in the Standard Model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast Cryptographic Primitives and Circular-Secure Encryption Based on Hard Learning Problems. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 595–618. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Applebaum, B., Ishai, Y., Kushilevitz, E.: Semantic security under related-key attacks and applications. In: ICS, pp. 45–55 (2011)Google Scholar
  4. 4.
    Bellare, M., Cash, D.: Pseudorandom Functions and Permutations Provably Secure against Related-Key Attacks. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 666–684. Springer, Heidelberg (2010)Google Scholar
  5. 5.
    Bellare, M., Kohno, T.: A Theoretical Treatment of Related-key Attacks: RKA-PRPs, RKA-PRFs, and Applications. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 491–506. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Bellare, M., Shoup, S.: Two-Tier Signatures, Strongly Unforgeable Signatures, and Fiat-Shamir Without Random Oracles. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 201–216. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Bellare, M., Cash, D., Miller, R.: Cryptography Secure against Related-Key Attacks and Tampering. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 486–503. Springer, Heidelberg (2011); Also Cryptology ePrint Archive, Report 2011/252Google Scholar
  8. 8.
    Biham, E., Shamir, A.: Differential Fault Analysis of Secret Key Cryptosystems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 513–525. Springer, Heidelberg (1997)Google Scholar
  9. 9.
    Boneh, D., Boyen, X.: Efficient Selective-ID Secure Identity-Based Encryption Without Random Oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Boneh, D., DeMillo, R.A., Lipton, R.J.: On the Importance of Checking Cryptographic Protocols for Faults. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 37–51. Springer, Heidelberg (1997)Google Scholar
  11. 11.
    Boyen, X., Mei, Q., Waters, B.: Direct chosen ciphertext security from identity-based techniques. In: ACM CCS, pp. 320–329 (2005)Google Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Cash, D., Kiltz, E., Shoup, V.: The Twin Diffie-Hellman problem and applications. J. Cryptology 22(4), 470–504 (2009)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Choi, S.G., Kiayias, A., Malkin, T.: BiTR: Built-in Tamper Resilience. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 740–758. Springer, Heidelberg (2011)Google Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    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); Also, Cryptology ePrint Archive, Report 2001/085CrossRefGoogle Scholar
  17. 17.
    Cramer, R., Damgård, I.B., Schoenmakers, B.: Proof of Partial Knowledge and Simplified Design of Witness Hiding Protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994)Google Scholar
  18. 18.
    Cramer, R., Dodis, Y., Fehr, S., Padró, C., Wichs, D.: Detection of Algebraic Manipulation with Applications to Robust Secret Sharing and Fuzzy Extractors. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 471–488. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM J. Comput. 30(2), 391–437 (2000)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Dziembowski, S., Pietrzak, K., Wichs, D.: Non-malleable codes. In: ICS, pp. 434–452 (2010)Google Scholar
  21. 21.
    Gennaro, R., Lysyanskaya, A., Malkin, T., Micali, S., Rabin, T.: Algorithmic Tamper-Proof (ATP) Security: Theoretical Foundations for Security against Hardware Tampering. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 258–277. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  22. 22.
    Goldenberg, D., Liskov, M.: On Related-Secret Pseudorandomness. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 255–272. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  23. 23.
    Goyal, V., O’Neill, A., Rao, V.: Correlated-Input Secure Hash Functions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 182–200. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  24. 24.
    Groth, J.: Simulation-Sound NIZK Proofs for a Practical Language and Constant Size Group Signatures. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 444–459. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  25. 25.
    Halderman, J.A., Schoen, S.D., Heninger, N., Clarkson, W., Paul, W., Calandrino, J.A., Feldman, A.J., Appelbaum, J., Felten, E.W.: Lest we remember: cold-boot attacks on encryption keys. Commun. ACM 52(5), 91–98 (2009)CrossRefGoogle Scholar
  26. 26.
    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)CrossRefGoogle Scholar
  27. 27.
    Hofheinz, D., Kiltz, E.: The Group of Signed Quadratic Residues and Applications. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 637–653. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  28. 28.
    Kalai, Y.T., Kanukurthi, B., Sahai, A.: Cryptography with Tamperable and Leaky Memory. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 373–390. Springer, Heidelberg (2011)Google Scholar
  29. 29.
    Katz, J., Malka, L.: Constant-Round Private Function Evaluation with Linear Complexity. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 556–571. Springer, Heidelberg (2011); Also Cryptology ePrint Archive, Report 2010/528CrossRefGoogle Scholar
  30. 30.
    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)CrossRefGoogle Scholar
  31. 31.
    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)CrossRefGoogle Scholar
  32. 32.
    Kocher, P.C.: Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 104–113. Springer, Heidelberg (1996)Google Scholar
  33. 33.
    Lucks, S.: Ciphers Secure against Related-Key Attacks. In: Roy, B., Meier, W. (eds.) FSE 2004. LNCS, vol. 3017, pp. 359–370. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  34. 34.
    MacKenzie, P.D., Reiter, M.K., Yang, K.: Alternatives to Non-malleability: Definitions, Constructions, and Applications. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 171–190. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  35. 35.
    Micciancio, D., Peikert, C.: Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012); Also, Cryptology ePrint Archive, Report 2011/501CrossRefGoogle Scholar
  36. 36.
    Mohassel, P.: One-Time Signatures and Chameleon Hash Functions. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 302–319. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  37. 37.
    Pandey, O., Pass, R., Vaikuntanathan, V.: Adaptive One-Way Functions and Applications. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 57–74. Springer, Heidelberg (2008)Google Scholar
  38. 38.
    Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: STOC, pp. 187–196 (2008)Google Scholar
  39. 39.
    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
  40. 40.
    Ristenpart, T., Tromer, E., Shacham, H., Savage, S.: Hey, you, get off of my cloud: exploring information leakage in third-party compute clouds. In: ACM Conference on Computer and Communications Security, pp. 199–212 (2009)Google Scholar
  41. 41.
    Shamir, A., Tauman, Y.: Improved Online/Offline Signature Schemes. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 355–367. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  42. 42.
    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)Google Scholar

Copyright information

© International Association for Cryptologic Research 2012

Authors and Affiliations

  • Hoeteck Wee
    • 1
  1. 1.George Washington UniversityUSA

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