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Non-malleable Codes for Bounded Depth, Bounded Fan-In Circuits

  • Marshall BallEmail author
  • Dana Dachman-Soled
  • Mukul Kulkarni
  • Tal Malkin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9666)

Abstract

We show how to construct efficient, unconditionally secure non-malleable codes for bounded output locality. In particular, our scheme is resilient against functions such that any output bit is dependent on at most \(n^{\delta }\) bits, where n is the total number of bits in a codeword and \(0\le \delta < 1\) a constant. Notably, this tampering class includes \(\mathsf {NC}^0\).

Notes

Acknowledgments

We thank Seung Geol Choi and Hoeteck Wee for sharing with us an in-submission journal version of [15], as well as the manuscript [16]. We also thank Yevgeniy Dodis for helpful discussions and clarifications regarding [2] and other previous work. Finally, we thank Eran Tromer for enlightening discussions on practical tampering attacks, which inspired the class of attacks considered in this work.

This work was done in part while all authors were visiting the Simons Institute for the Theory of Computing, supported by the Simons Foundation and by the DIMACS/Simons Collaboration in Cryptography through NSF grant #CNS-1523467. The first and fourth authors are supported in part by the Defense Advanced Research Project Agency (DARPA) and Army Research Office (ARO) under Contract #W911NF-15-C-0236, and NSF grants #CNS-1445424 and #CCF-1423306. The second and third authors are supported by an NSF CAREER award #CNS-1453045 and by a Ralph E. Powe Junior Faculty Enhancement Award. Any opinions, findings and conclusions or recommendations expressed are those of the authors and do not necessarily reflect the views of the Defense Advanced Research Projects Agency, Army Research Office, the National Science Foundation, or the U.S. Government.

References

  1. 1.
    Aggarwal, D., Agrawal, S., Gupta, D., Maji, H.K., Pandey, O., Prabhakaran, M.: Optimal computational split-state non-malleable codes. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016-A. LNCS, vol. 9563, pp. 393–417. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49099-0_15 CrossRefGoogle Scholar
  2. 2.
    Aggarwal, D., Dodis, Y., Kazana, T., Obremski, M.: Non-malleable reductions and applications. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th ACM STOC, Portland, OR, USA, 14–17 June 2015, pp. 459–468. ACM Press (2015)Google Scholar
  3. 3.
    Aggarwal, D., Dodis, Y., Lovett, S.: Non-malleable codes from additive combinatorics. In: Shmoys, D.B. (ed.) 46th ACM STOC, NY, USA, May 31–Jun 3, 2014, pp. 774–783 (2014)Google Scholar
  4. 4.
    Aggarwal, D., Dziembowski, S., Kazana, T., Obremski, M.: Leakage-resilient non-malleable codes. Cryptology ePrint Archive, Report 2014/807 (2014). http://eprint.iacr.org/2014/807
  5. 5.
    Agrawal, S., Gupta, D., Maji, H.K., Pandey, O., Prabhakaran, M.: Explicit non-malleable codes against bit-wise tampering and permutations. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 538–557. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-47989-6_26 CrossRefGoogle Scholar
  6. 6.
    Agrawal, S., Gupta, D., Maji, H.K., Pandey, O., Prabhakaran, M.: A rate-optimizing compiler for non-malleable codes against bit-wise tampering and permutations. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part I. LNCS, vol. 9014, pp. 375–397. Springer, Heidelberg (2015)Google Scholar
  7. 7.
    Applebaum, B.: Cryptography in Constant Parallel Time. Information Security and Cryptography. Springer, Heidelberg (2014). http://dx.doi.org/10.1007/978-3-642-17367-7 CrossRefzbMATHGoogle Scholar
  8. 8.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: 20th ACM STOC, Chicago, Illinois, USA, 2–4 May 1988, pp. 1–10. ACM Press (1998)Google Scholar
  9. 9.
    Chabanne, H., Cohen, G.D., Flori, J., Patey, A.: Non-malleable codes from the wire-tap channel. CoRR abs/1105.3879 (2011). http://arxiv.org/abs/1105.3879
  10. 10.
    Chabanne, H., Cohen, G.D., Patey, A.: Secure network coding and non-malleable codes: protection against linear tampering. In: Proceedings of the 2012 IEEE International Symposium on Information Theory, ISIT 2012, Cambridge, MA, USA, 1–6 July 2012, pp. 2546–2550. IEEE (2012). http://dx.doi.org/10.1109/ISIT.2012.6283976
  11. 11.
    Chandran, N., Kanukurthi, B., Raghuraman, S.: Information-theoretic local non-malleable codes and their applications. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016-A. LNCS, vol. 9563, pp. 367–392. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49099-0_14 CrossRefGoogle Scholar
  12. 12.
    Chattopadhyay, E., Zuckerman, D.: Non-malleable codes against constant split-state tampering. In: 55th FOCS, Philadelphia, PA, USA, 18–21 October 2014, pp. 306–315. IEEE Computer Society Press (2014)Google Scholar
  13. 13.
    Cheraghchi, M., Guruswami, V.: Capacity of non-malleable codes. In: Naor, M. (ed.) ITCS, Princeton, NJ, USA, 12–14 January 2014, pp. 155–168. ACM (2014)Google Scholar
  14. 14.
    Cheraghchi, M., Guruswami, V.: Non-malleable coding against bit-wise and split-state tampering. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 440–464. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  15. 15.
    Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.M.: Black-box construction of a non-malleable encryption scheme from any semantically secure one. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 427–444. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Choi, S.G., Dachman-Soled, D., Malkin, T., Wee, H.: A note on improved, black-box constructions of non-malleable encryption from semantically-secure encryption. Manuscript (2015)Google Scholar
  17. 17.
    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
  18. 18.
    Coretti, S., Dodis, Y., Tackmann, B., Venturi, D.: Non-malleable encryption: Simpler, shorter, stronger. Cryptology ePrint Archive, Report 2015/772 (2015). http://eprint.iacr.org/2015/772 Google Scholar
  19. 19.
    Coretti, S., Dodis, Y., Tackmann, B., Venturi, D.: Non-malleable encryption: simpler, shorter, stronger. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016-A. LNCS, vol. 9562, pp. 306–335. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49096-9_13 CrossRefGoogle Scholar
  20. 20.
    Dachman-Soled, D., Liu, F.-H., Shi, E., Zhou, H.-S.: Locally decodable and updatable non-malleable codes and their applications. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part I. LNCS, vol. 9014, pp. 427–450. Springer, Heidelberg (2015)Google Scholar
  21. 21.
    Decatur, S.E., Goldreich, O., Ron, D.: Computational sample complexity. SIAM J. Comput. 29(3), 854–879 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM J. Comput. 30(2), 391–437 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Dziembowski, S., Kazana, T., Obremski, M.: Non-malleable codes from two-source extractors. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 239–257. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  24. 24.
    Dziembowski, S., Pietrzak, K., Wichs, D.: Non-malleable codes. In: Yao, A.C.C. (ed.) ICS, 5–7 January 2010, pp. 434–452. Tsinghua University Press, Tsinghua University, Beijing, China (2010)Google Scholar
  25. 25.
    Faust, S., Mukherjee, P., Nielsen, J.B., Venturi, D.: Continuous non-malleable codes. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 465–488. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  26. 26.
    Faust, S., Mukherjee, P., Venturi, D., Wichs, D.: Efficient non-malleable codes and key-derivation for poly-size tampering circuits. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 111–128. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  27. 27.
    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
  28. 28.
    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)CrossRefGoogle Scholar
  29. 29.
    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
  30. 30.
    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
  31. 31.
    Liu, F.-H., Lysyanskaya, A.: Tamper and leakage resilience in the split-state model. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 517–532. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  32. 32.
    Nisan, N.: Pseudorandom generators for space-bounded computation. Combinatorica 12(4), 449–461 (1992)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  • Marshall Ball
    • 1
    Email author
  • Dana Dachman-Soled
    • 2
  • Mukul Kulkarni
    • 2
  • Tal Malkin
    • 1
  1. 1.Columbia UniversityNew YorkUSA
  2. 2.University of MarylandCollege ParkUSA

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