Public-Key Cryptosystems Resilient to Key Leakage
Most of the work in the analysis of cryptographic schemes is concentrated in abstract adversarial models that do not capture side-channel attacks. Such attacks exploit various forms of unintended information leakage, which is inherent to almost all physical implementations. Inspired by recent side-channel attacks, especially the “cold boot attacks”, Akavia, Goldwasser and Vaikuntanathan (TCC ’09) formalized a realistic framework for modeling the security of encryption schemes against a wide class of side-channel attacks in which adversarially chosen functions of the secret key are leaked. In the setting of public-key encryption, Akavia et al. showed that Regev’s lattice-based scheme (STOC ’05) is resilient to any leakage of L / polylog(L) bits, where L is the length of the secret key.
In this paper we revisit the above-mentioned framework and our main results are as follows:
We present a generic construction of a public-key encryption scheme that is resilient to key leakage from any universal hash proof system. The construction does not rely on additional computational assumptions, and the resulting scheme is as efficient as the underlying proof system. Existing constructions of such proof systems imply that our construction can be based on a variety of number-theoretic assumptions, including the decisional Diffie-Hellman assumption (and its progressively weaker d-Linear variants), the quadratic residuosity assumption, and Paillier’s composite residuosity assumption.
We construct a new hash proof system based on the decisional Diffie-Hellman assumption (and its d-Linear variants), and show that the resulting scheme is resilient to any leakage of L(1 − o(1)) bits. In addition, we prove that the recent scheme of Boneh et al. (CRYPTO ’08), constructed to be a “circular-secure” encryption scheme, is resilient to any leakage of L(1 − o(1)) bits. These two proposed schemes complement each other in terms of efficiency.
We extend the framework of key leakage to the setting of chosen-ciphertext attacks. On the theoretical side, we prove that the Naor-Yung paradigm is applicable in this setting as well, and obtain as a corollary encryption schemes that are CCA2-secure with any leakage of L(1 − o(1)) bits. On the practical side, we prove that variants of the Cramer-Shoup cryptosystem (along the lines of our generic construction) are CCA1-secure with any leakage of L/4 bits, and CCA2-secure with any leakage of L/6 bits.
KeywordsEncryption Scheme Leakage Function Valid Ciphertext Cold Boot Attack Residuosity Assumption
- 2.Akavia, A., Goldwasser, S., Vaikuntanathan, V.: Simultaneous hardcore bits and cryptography against memory attacks. In: TCC, pp. 474–495 (2009)Google Scholar
- 11.Dodis, Y., Tauman Kalai, Y., Lovett, S.: On cryptography with auxiliary input. To appear in STOC (2009)Google Scholar
- 13.Dorrendorf, L., Gutterman, Z., Pinkas, B.: Cryptanalysis of the windows random number generator. In: ACM CCS, pp. 476–485 (2007)Google Scholar
- 14.Dziembowski, S., Pietrzak, K.: Leakage-resilient cryptography. In: FOCS, pp. 293–302 (2008)Google Scholar
- 17.Gutterman, Z., Pinkas, B., Reinman, T.: Analysis of the linux random number generator. In: IEEE Symposium on Security and Privacy, pp. 371–385 (2006)Google Scholar
- 18.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. In: USENIX, pp. 45–60 (2008)Google Scholar
- 19.Heninger, N., Shacham, H.: Improved RSA private key reconstruction for cold boot attacks. Cryptology ePrint Archive, Report 2008/510 (2008)Google Scholar
- 22.Kiltz, E., Pietrzak, K., Stam, M., Yung, M.: A new randomness extraction paradigm for hybrid encryption. In: EUROCRYPT, pp. 590–609 (2009)Google Scholar
- 23.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
- 28.Naor, M., Segev, G.: Public-key cryptosystems resilient to key leakage. Cryptology ePrint Archive, Report 2009/105 (2009)Google Scholar
- 29.Naor, M., Yung, M.: Public-key cryptosystems provably secure against chosen ciphertext attacks. In: STOC, pp. 427–437 (1990)Google Scholar
- 30.Petit, C., Standaert, F.-X., Pereira, O., Malkin, T., Yung, M.: A block cipher based pseudo random number generator secure against side-channel key recovery. In: ASIACCS, pp. 56–65 (2008)Google Scholar
- 31.Pietrzak, K.: A leakage-resilient mode of operation. In: EUROCRYPT, pp. 462–482 (2009)Google Scholar
- 32.Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC, pp. 84–93 (2005)Google Scholar
- 34.Shacham, H.: A Cramer-Shoup encryption scheme from the Linear assumption and from progressively weaker Linear variants. Cryptology ePrint Archive, Report 2007/074 (2007)Google Scholar
- 35.Tauman Kalai, Y., Vaikuntanathan, V.: Public-key encryption schemes with auxiliary inputs and applications (2009)Google Scholar
- 36.Yilek, S., Rescorla, E., Shacham, H., Enright, B., Savage, S.: PRNG PR0N: Understanding the Debian OpenSSL debacle (2008)Google Scholar