Continuous Non-Malleable Codes in the 8-Split-State Model

  • Divesh Aggarwal
  • Nico Döttling
  • Jesper Buus NielsenEmail author
  • Maciej Obremski
  • Erick Purwanto
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11476)


Non-malleable codes (NMCs), introduced by Dziembowski, Pietrzak and Wichs [20], provide a useful message integrity guarantee in situations where traditional error-correction (and even error-detection) is impossible; for example, when the attacker can completely overwrite the encoded message. NMCs have emerged as a fundamental object at the intersection of coding theory and cryptography. In particular, progress in the study of non-malleable codes and the related notion of non-malleable extractors has led to new insights and progress on even more fundamental problems like the construction of multi-source randomness extractors. A large body of the recent work has focused on various constructions of non-malleable codes in the split-state model. Many variants of NMCs have been introduced in the literature, e.g., strong NMCs, super strong NMCs and continuous NMCs. The most general, and hence also the most useful notion among these is that of continuous non-malleable codes, that allows for continuous tampering by the adversary. We present the first efficient information-theoretically secure continuously non-malleable code in the constant split-state model. We believe that our main technical result could be of independent interest and some of the ideas could in future be used to make progress on other related questions.


  1. 1.
    Aggarwal, D.: Affine-evasive sets modulo a prime. Inf. Process. Lett. 115(2), 382–385 (2015)MathSciNetCrossRefGoogle Scholar
  2. 2.
    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. LNCS, vol. 9563, pp. 393–417. Springer, Heidelberg (2016). Scholar
  3. 3.
    Aggarwal, D., Briët, J.: Revisiting the Sanders-Bogolyubov-Ruzsa theorem in \({\rm f}_{\rm p}^{\rm n}\) and its application to non-malleable codes. In: 2016 IEEE International Symposium on Information Theory (ISIT), pp. 1322–1326. IEEE (2016)Google Scholar
  4. 4.
    Aggarwal, D., Dodis, Y., Kazana, T., Obremski, M.: Leakage-resilient nonmalleable codes. In: The 47th ACM Symposium on Theory of Computing (STOC) (2015)Google Scholar
  5. 5.
    Aggarwal, D., Dodis, Y., Lovett, S.: Non-malleable codes from additive combinatorics. In: STOC. ACM (2014)Google Scholar
  6. 6.
    Aggarwal, D., Dziembowski, S., Kazana, T., Obremski, M.: Leakage-resilient non-malleable codes. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9014, pp. 398–426. Springer, Heidelberg (2015). Scholar
  7. 7.
    Aggarwal, D., Kazana, T., Obremski, M.: Inception makes non-malleable codes stronger. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 319–343. Springer, Cham (2017). Scholar
  8. 8.
    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. LNCS, vol. 9014, pp. 375–397. Springer, Heidelberg (2015). Scholar
  9. 9.
    Agrawal, S., Gupta, D., Maji, H.K., Pandey, O., Prabhakaran, M.: Explicit non-malleable codes resistant to permutations. In: Advances in Cryptology - CRYPTO (2015)Google Scholar
  10. 10.
  11. 11.
    Chattopadhyay, E., Goyal, V., Li, X.: Non-malleable extractors and codes, with their many tampered extensions. In: Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing, pp. 285–298. ACM (2016)Google Scholar
  12. 12.
    Chattopadhyay, E., Zuckerman, D.: Non-malleable codes in the constant split-state model. In: FOCS (2014)Google Scholar
  13. 13.
    Cheraghchi, M., Guruswami, V.: Capacity of non-malleable codes. In: ITCS (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). Scholar
  15. 15.
    Chor, B., Goldreich, O.: Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J. Comput. 17(2), 230–261 (1988)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Coretti, S., Maurer, U., Tackmann, B., Venturi, D.: From single-bit to multi-bit public-key encryption via non-malleable codes. In: Dodis and Nielsen [17], pp. 532–560CrossRefGoogle Scholar
  17. 17.
    Dodis, Y., Nielsen, J.B. (eds.): TCC 2015. LNCS, vol. 9014. Springer, Heidelberg (2015). Scholar
  18. 18.
    Dodis, Y., Ostrovsky, R., Reyzin, L., Smith, A.: Fuzzy extractors: how to generate strong keys from biometrics and other noisy data. SIAM J. Comput. 38(1), 97–139 (2008)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Dziembowski, S., Kazana, T., Obremski, M.: Non-malleable codes from two-source extractors. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8043, pp. 239–257. Springer, Heidelberg (2013). Scholar
  20. 20.
    Dziembowski, S., Pietrzak, K., Wichs, D.: Non-malleable codes. In: ICS, pp. 434–452. Tsinghua University Press (2010)Google Scholar
  21. 21.
    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). Scholar
  22. 22.
    Faust, S., Mukherjee, P., Nielsen, J.B., Venturi, D.: A tamper and leakage resilient von neumann architecture. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 579–603. Springer, Heidelberg (2015). Scholar
  23. 23.
    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). Scholar
  24. 24.
    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). Scholar
  25. 25.
    Jafargholi, Z., Wichs, D.: Tamper detection and continuous non-malleable codes. In: Dodis and Nielsen [17], pp. 451–480CrossRefGoogle Scholar
  26. 26.
    Li, X.: Improved non-malleable extractors, non-malleable codes and independent source extractors. In: Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing, pp. 1144–1156. ACM (2017)Google Scholar
  27. 27.
    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). Scholar
  28. 28.
    Nisan, N., Zuckerman, D.: Randomness is linear in space. J. Comput. Syst. Sci. 52(1), 43–53 (1996)MathSciNetCrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  • Divesh Aggarwal
    • 1
  • Nico Döttling
    • 2
  • Jesper Buus Nielsen
    • 3
    Email author
  • Maciej Obremski
    • 1
  • Erick Purwanto
    • 1
  1. 1.National University of SingaporeSingaporeSingapore
  2. 2.CISPA Helmholtz Center for Information SecuritySaarbrückenGermany
  3. 3.Aarhus UniversityAarhusDenmark

Personalised recommendations