Securing Circuits against Constant-Rate Tampering

  • Dana Dachman-Soled
  • Yael Tauman Kalai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7417)

Abstract

We present a compiler that converts any circuit into one that remains secure even if a constant fraction of its wires are tampered with. Following the seminal work of Ishai et. al. (Eurocrypt 2006), we consider adversaries who may choose an arbitrary set of wires to corrupt, and may set each such wire to 0 or to 1, or may toggle with the wire. We prove that such adversaries, who continuously tamper with the circuit, can learn at most logarithmically many bits of secret information (in addition to black-box access to the circuit). Our results are information theoretic.

Keywords

side-channel attacks tampering circuit compiler PCP of proximity 

References

  1. 1.
    Akavia, A., Goldwasser, S., Vaikuntanathan, V.: Simultaneous Hardcore Bits and Cryptography against Memory Attacks. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 474–495. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Applebaum, B., Harnik, D., Ishai, Y.: Semantic security under related-key attacks and applications. Cryptology ePrint Archive, Report 2010/544 (2010), http://eprint.iacr.org/
  3. 3.
    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)Google Scholar
  4. 4.
    Ben-Sasson, E., Goldreich, O., Harsha, P., Sudan, M., Vadhan, S.P.: Robust PCPs of proximity, shorter PCPs, and applications to coding. SIAM J. Comput. 36(4), 889–974 (2006)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    Bitansky, N., Canetti, R., Goldwasser, S., Halevi, S., Kalai, Y.T., Rothblum, G.N.: Program Obfuscation with Leaky Hardware. In: Lee, D.H.,Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 722–739. Springer, Heidelberg (2011)Google Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    Brakerski, Z., Gentry, C., Vaikuntanathan, V.: Fully homomorphic encryption without bootstrapping. IACR Cryptology ePrint Archive, 2011:277 (2011)Google Scholar
  9. 9.
    Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) IWE. In: FOCS, pp. 97–106 (2011)Google Scholar
  10. 10.
    Canetti, R., Dodis, Y., Halevi, S., Kushilevitz, E., Sahai, A.: Exposure-Resilient Functions and All-or-Nothing Transforms. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 453–469. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  11. 11.
    Canetti, R., Feige, U., Goldreich, O., Naor, M.: Adaptively secure multi-party computation. In: STOC, pp. 639–648 (1996)Google Scholar
  12. 12.
    Choi, S.G., Dachman-Soled, D., Malkin, T.,Wee, H.: Improved Non-committing Encryption with Applications to Adaptively Secure Protocols. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 287–302. Springer, Heidelberg (2009)Google Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    Dachman-Soled, D., Kalai, Y.T.: Securing circuits against constant-rate tampering (2012), http://www.cs.columbia.edu/~dglasner/MyPapers/tamper_pcp.pdf
  15. 15.
    Damgård, I., Nielsen, J.B.: Improved Non-committing Encryption Schemes Based on a General Complexity Assumption. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 432–450. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  16. 16.
    Dobrushin, R.L., Ortyukov, S.I.: Upper bound for the redundancy of self-correcting arrangements of unreliable functional elements, vol. 13, pp. 203–218 (1977)Google Scholar
  17. 17.
    Dodis, Y., Goldwasser, S., Kalai, Y.T., Peikert, C., Vaikuntanathan, V.: Public-Key Encryption Schemes with Auxiliary Inputs. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 361–381. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Dodis, Y., Kalai, Y.T., Lovett, S.: On cryptography with auxiliary input. In: STOC, pp. 621–630 (2009)Google Scholar
  19. 19.
    Dodis, Y., Pietrzak, K.: Leakage-Resilient Pseudorandom Functions and Side-Channel Attacks on Feistel Networks. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 21–40. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  20. 20.
    Dziembowski, S., Pietrzak, K.: Leakage-resilient cryptography. In: FOCS, pp. 293–302 (2008)Google Scholar
  21. 21.
    Dziembowski, S., Pietrzak, K.,Wichs, D.: Non-malleable codes. In: ICS, pp. 434–452 (2010)Google Scholar
  22. 22.
    Evans, W., Schulman, L.: On the maximum tolerable noise of k-input gates for reliable computation by formulasGoogle Scholar
  23. 23.
    Evans, W., Schulman, L.: Signal propagation and noisy circuits. IEEE Trans. Inform. Theory 45(7), 2367–2373 (1999)MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Faust, S., Kiltz, E., Pietrzak, K., Rothblum, G.N.: Leakage-Resilient Signatures. In:Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 343–360. Springer, Heidelberg (2010)Google Scholar
  25. 25.
    Faust, S., Pietrzak, K., Venturi, D.: Tamper-Proof Circuits: How to Trade Leakage for Tamper-Resilience. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part I. LNCS, vol. 6755, pp. 391–402. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  26. 26.
    Faust, S., Rabin, T., Reyzin, L., Tromer, E., Vaikuntanathan, V.: Protecting Circuits from Leakage: the Computationally-Bounded and Noisy Cases. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 135–156. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  27. 27.
    Feder, T.: Reliable computation by networks in the presence of noise. IEEE Trans. Inform. Theory 35(3), 569–571 (1989)MathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Gács, P., Gál, A.: Lower bounds for the complexity of reliable boolean circuits with noisy gates. IEEE Transactions on Information Theory 40(2), 579–583 (1994)CrossRefMATHGoogle Scholar
  29. 29.
    Gál, A., Szegedy, M.: Fault tolerant circuits and probabilistically checkable proofs. In: Structure in Complexity Theory Conference, pp. 65–73 (1995)Google Scholar
  30. 30.
    Gandolfi, K., Mourtel, C., Olivier, F.: Electromagnetic Analysis: Concrete Results. In: Koç, Ç.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol. 2162, pp. 251–261. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  31. 31.
    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
  32. 32.
    Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC, pp. 169–178 (2009)Google Scholar
  33. 33.
    Goldwasser, S., Rothblum, G.N.: How to compute in the presence of leakage. Electronic Colloquium on Computational Complexity (2012)Google Scholar
  34. 34.
    Goldwasser, S., Rothblum, G.N.: Securing Computation against Continuous Leakage. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 59–79. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  35. 35.
    Govindavajhala, S., Appel, A.W.: Using memory errors to attack a virtual machine. In: IEEE Symposium on Security and Privacy, pp. 154–165 (2003)Google Scholar
  36. 36.
    Hajek, B.E.,Weller, T.: On the maximum tolerable noise for reliable computation by formulas. IEEE Transactions on Information Theory 37(2), 388–391 (1991)Google Scholar
  37. 37.
    Ishai, Y., Prabhakaran, M., Sahai, A., Wagner, D.: Private Circuits II: Keeping Secrets in Tamperable Circuits. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 308–327. Springer, Heidelberg (2006)Google Scholar
  38. 38.
    Ishai, Y., Sahai, A., Wagner, D.: Private Circuits: Securing Hardware against Probing Attacks. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 463–481. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  39. 39.
    Juma, A., Vahlis, Y.: Protecting Cryptographic Keys against Continual Leakage. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 41–58. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  40. 40.
    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)CrossRefGoogle Scholar
  41. 41.
    Kalai, Y.T., Rao, A., Lewko, A.: Formulas resilient to short-circuit errors (2011) (manuscript)Google Scholar
  42. 42.
    Katz, J., Vaikuntanathan, V.: Signature Schemes with Bounded Leakage Resilience. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 703–720. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  43. 43.
    Kelsey, J., Schneier, B., Wagner, D., Hall, C.: Side Channel Cryptanalysis of Product Ciphers. In: Quisquater, J.-J., Deswarte, Y., Meadows, C., Gollmann, D. (eds.) ESORICS 1998. LNCS, vol. 1485, pp. 97–110. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  44. 44.
    Kleitman, D.J., Leighton, F.T.,Ma, Y.: On the design of reliable boolean circuits that contain partially unreliable gates. In: FOCS, pp. 332–346 (1994)Google Scholar
  45. 45.
    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
  46. 46.
    Kocher, P.C., Jaffe, J., Jun, B.: Differential Power Analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388–397. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  47. 47.
    Kuhn, M.G., Anderson, R.J.: Soft Tempest: Hidden Data Transmission Using Electromagnetic Emanations. In: Aucsmith, D. (ed.) IH 1998. LNCS, vol. 1525, pp. 124–142. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  48. 48.
    Liu, F.-H., Lysyanskaya, A.: Algorithmic Tamper-Proof Security under Probing Attacks. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 106–120. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  49. 49.
    Micali, S., Reyzin, L.: Physically Observable Cryptography (Extended Abstract). In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 278–296. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  50. 50.
    Naor,M., Segev, G.: Public-Key Cryptosystems Resilient to Key Leakage. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 18–35. Springer, Heidelberg (2009)Google Scholar
  51. 51.
    Pietrzak, K.: A Leakage-Resilient Mode of Operation. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 462–482. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  52. 52.
    Pippenger, N.: Reliable computation by formulas in the presence of noise. IEEE Trans. Inform. Theory 34(2), 194–197 (1988)MathSciNetCrossRefMATHGoogle Scholar
  53. 53.
    Pippenger, N.: On networks of noisy gates. In: FOCS, pp. 30–38. IEEE (1985)Google Scholar
  54. 54.
    Quisquater, J.-J., Samyde, D.: ElectroMagnetic Analysis (EMA): Measures and Counter-Measures for Smart Cards. In: Attali, S., Jensen, T. (eds.) E-smart 2001. LNCS, vol. 2140, pp. 200–210. Springer, Heidelberg (2001)Google Scholar
  55. 55.
    Rao, J.R., Rohatgi, P.: Empowering side-channel attacks. Cryptology ePrint Archive, Report 2001/037 (2001), http://eprint.iacr.org/
  56. 56.
    von Neumann, J.: Probabilistic logics and the synthesis of reliable organisms from unreliable components (1956)Google Scholar

Copyright information

© International Association for Cryptologic Research 2012 2012

Authors and Affiliations

  • Dana Dachman-Soled
    • 1
  • Yael Tauman Kalai
    • 1
  1. 1.Microsoft Research New EnglandCambridgeUSA

Personalised recommendations