Abstract
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.
This research was further partially funded by the Singapore Ministry of Education and the National Research Foundation under grant R-710-000-012-135.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
In particular, \(\mathcal{{F}}\) should not include “re-encoding functions” \(f(c) = \mathsf {Enc}(f'(\mathsf {Dec}(c)))\) for any non-trivial function \(f'\), as \(m'=\mathsf {Dec}(f(\mathsf {Enc}(m)))=f'(m)\) is obviously related to m.
References
Aggarwal, D.: Affine-evasive sets modulo a prime. Inf. Process. Lett. 115(2), 382–385 (2015)
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). https://doi.org/10.1007/978-3-662-49099-0_15
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)
Aggarwal, D., Dodis, Y., Kazana, T., Obremski, M.: Leakage-resilient nonmalleable codes. In: The 47th ACM Symposium on Theory of Computing (STOC) (2015)
Aggarwal, D., Dodis, Y., Lovett, S.: Non-malleable codes from additive combinatorics. In: STOC. ACM (2014)
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). https://doi.org/10.1007/978-3-662-46494-6_17
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). https://doi.org/10.1007/978-3-319-70503-3_10
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). https://doi.org/10.1007/978-3-662-46494-6_16
Agrawal, S., Gupta, D., Maji, H.K., Pandey, O., Prabhakaran, M.: Explicit non-malleable codes resistant to permutations. In: Advances in Cryptology - CRYPTO (2015)
Bogdanov, I.: Deathzone generation lemma (2016). https://mathoverflow.net/questions/252396/inner-product-over-finite-fields
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)
Chattopadhyay, E., Zuckerman, D.: Non-malleable codes in the constant split-state model. In: FOCS (2014)
Cheraghchi, M., Guruswami, V.: Capacity of non-malleable codes. In: ITCS (2014)
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). https://doi.org/10.1007/978-3-642-54242-8_19
Chor, B., Goldreich, O.: Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J. Comput. 17(2), 230–261 (1988)
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. 532–560
Dodis, Y., Nielsen, J.B. (eds.): TCC 2015. LNCS, vol. 9014. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46494-6
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)
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). https://doi.org/10.1007/978-3-642-40084-1_14
Dziembowski, S., Pietrzak, K., Wichs, D.: Non-malleable codes. In: ICS, pp. 434–452. Tsinghua University Press (2010)
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). https://doi.org/10.1007/978-3-642-54242-8_20
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). https://doi.org/10.1007/978-3-662-46447-2_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). https://doi.org/10.1007/978-3-642-55220-5_7
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). https://doi.org/10.1007/978-3-540-24638-1_15
Jafargholi, Z., Wichs, D.: Tamper detection and continuous non-malleable codes. In: Dodis and Nielsen [17], pp. 451–480
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)
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). https://doi.org/10.1007/978-3-642-32009-5_30
Nisan, N., Zuckerman, D.: Randomness is linear in space. J. Comput. Syst. Sci. 52(1), 43–53 (1996)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 International Association for Cryptologic Research
About this paper
Cite this paper
Aggarwal, D., Döttling, N., Nielsen, J.B., Obremski, M., Purwanto, E. (2019). Continuous Non-Malleable Codes in the 8-Split-State Model. In: Ishai, Y., Rijmen, V. (eds) Advances in Cryptology – EUROCRYPT 2019. EUROCRYPT 2019. Lecture Notes in Computer Science(), vol 11476. Springer, Cham. https://doi.org/10.1007/978-3-030-17653-2_18
Download citation
DOI: https://doi.org/10.1007/978-3-030-17653-2_18
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-17652-5
Online ISBN: 978-3-030-17653-2
eBook Packages: Computer ScienceComputer Science (R0)