Advertisement

INDOCRYPT 2018: Progress in Cryptology – INDOCRYPT 2018 pp 307-328

# Non-malleable Codes Against Lookahead Tampering

• Divya Gupta
• Hemanta K. Maji
• Mingyuan Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11356)

## Abstract

There are natural cryptographic applications where an adversary only gets to tamper a high-speed data stream on the fly based on her view so far, namely, the lookahead tampering model. Since the adversary can easily substitute transmitted messages with her messages, it is farfetched to insist on strong guarantees like error-correction or, even, manipulation detection. Dziembowski, Pietrzak, and Wichs (ICS–2010) introduced the notion of non-malleable codes that provide a useful message integrity for such scenarios. Intuitively, a non-malleable code ensures that the tampered codeword encodes the original message or a message that is entirely independent of the original message.

Our work studies the following tampering model. We encode a message into $$k\geqslant 1$$ secret shares, and we transmit each share as a separate stream of data. Adversaries can perform lookahead tampering on each share, albeit, independently. We call this k-lookahead model.

First, we show a hardness result for the k-lookahead model. To transmit an $$\ell$$-bit message, the cumulative length of the secret shares must be at least $$\frac{k}{k-1}\ell$$. This result immediately rules out the possibility of a solution with $$k=1$$. Next, we construct a solution for 2-lookahead model such that the total length of the shares is $$3\ell$$, which is only 1.5x of the optimal encoding as indicated by our hardness result.

Prior work considers stronger model of split-state encoding that creates $$k\geqslant 2$$ secret shares, but protects against adversaries who perform arbitrary (but independent) tampering on each secret share. The size of the secret shares of the most efficient 2-split-state encoding is $$\ell \log \ell /\log \log \ell$$ (Li, ECCC–2018). Even though k-lookahead is a weaker tampering class, our hardness result matches that of k-split-state tampering by Cheraghchi and Guruswami (TCC–2014). However, our explicit constructions above achieve much higher efficiency in encoding.

## Keywords

Non-malleable codes Lookahead tampering Split-state Constant-rate

## 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. LNCS, vol. 9563, pp. 393–417. Springer, Heidelberg (2016).
2. 2.
Aggarwal, D., Dodis, Y., Kazana, T., Obremski, M.: Non-malleable reductions and applications. In: Servedio, R.A., Rubinfeld, R. (eds.) 47th Annual ACM Symposium on Theory of Computing, 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 Annual ACM Symposium on Theory of Computing, New York, NY, USA, 31 May–3 June 2014, pp. 774–783. ACM Press (2014)Google Scholar
4. 4.
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).
5. 5.
Ball, M., Dachman-Soled, D., Kulkarni, M., Malkin, T.: Non-malleable codes for bounded depth, bounded fan-in circuits. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 881–908. Springer, Heidelberg (2016).
6. 6.
Chandran, N., Goyal, V., Mukherjee, P., Pandey, O., Upadhyay, J.: Block-wise non-malleable codes. In: Chatzigiannakis, I., Mitzenmacher, M., Rabani, Y., Sangiorgi, D. (eds.) 43rd International Colloquium on Automata, Languages and Programming, ICALP 2016. LIPIcs, Rome, Italy, 11–15 July 2016, vol. 55, pp. 31:1–31:14. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2016)Google Scholar
7. 7.
Chattopadhyay, E., Li, X.: Explicit non-malleable extractors, multi-source extractors, and almost optimal privacy amplification protocols. In: Dinur, I. (ed.) 57th Annual Symposium on Foundations of Computer Science, New Brunswick, NJ, USA, 9–11 October 2016, pp. 158–167. IEEE Computer Society Press (2016)Google Scholar
8. 8.
Chattopadhyay, E., Zuckerman, D.: Non-malleable codes against constant split-state tampering. In: 55th Annual Symposium on Foundations of Computer Science, Philadelphia, PA, USA, 18–21 October 2014, pp. 306–315. IEEE Computer Society Press (2014)Google Scholar
9. 9.
Cheraghchi, M., Guruswami, V.: Capacity of non-malleable codes. CoRR, abs/1309.0458 (2013)Google Scholar
10. 10.
Cheraghchi, M., Guruswami, V.: Capacity of non-malleable codes. In: Naor, M. (ed.) 5th Innovations in Theoretical Computer Science, ITCS 2014, Princeton, NJ, USA, 12–14 January 2014, pp. 155–168. Association for Computing Machinery (2014)Google Scholar
11. 11.
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).
12. 12.
Cramer, R., Dodis, Y., Fehr, S., Padró, C., Wichs, D.: Detection of algebraic manipulation with applications to robust secret sharing and fuzzy extractors. In: Smart, N. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 471–488. Springer, Heidelberg (2008).
13. 13.
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)
14. 14.
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).
15. 15.
Dziembowski, S., Pietrzak, K., Wichs, D.: Non-malleable codes. In: Yao, A.-C.-C. (ed.) 1st Innovations in Computer Science, ICS 2010, Tsinghua University, Beijing, China, 5–7 January 2010, pp. 434–452. Tsinghua University Press (2010)Google Scholar
16. 16.
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).
17. 17.
Goyal, V., Kumar, A.: Non-malleable secret sharing. In: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018, Los Angeles, CA, USA, 25–29 June 2018 (2018)Google Scholar
18. 18.
Gupta, D., Maji, H.K., Wang, M.: Non-malleable codes against lookahead tampering. Cryptology ePrint Archive, report 2017/1048 (2017). https://eprint.iacr.org/2017/1048
19. 19.
Guruswami, V., Umans, C., Vadhan, S.P.: Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes. In: 22nd Annual IEEE Conference on Computational Complexity (CCC 2007), 13–16 June 2007, San Diego, California, USA, pp. 96–108 (2007)Google Scholar
20. 20.
Kanukurthi, B., Obbattu, S.L.B., Sekar, S.: Four-state non-malleable codes with explicit constant rate. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017. LNCS, vol. 10678, pp. 344–375. Springer, Cham (2017).
21. 21.
Kanukurthi, B., Obbattu, S.L.B., Sekar, S.: Non-malleable randomness encoders and their applications. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 589–617. Springer, Cham (2018).
22. 22.
Li, X.: Improved non-malleable extractors, non-malleable codes and independent source extractors. In: Hatami, H., McKenzie, P., King, V. (eds.) 49th Annual ACM Symposium on Theory of Computing, Montreal, QC, Canada, 19–23 June 2017, pp. 1144–1156. ACM Press (2017)Google Scholar
23. 23.
Li, X.: Pseudorandom correlation breakers, independence preserving mergers and their applications. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 25, p. 28 (2018)Google Scholar
24. 24.
Vadhan, S.P.: Pseudorandomness. Foundations and Trends in Theoretical Computer Science. Now Publishers (2012)Google Scholar

## Copyright information

© Springer Nature Switzerland AG 2018

## Authors and Affiliations

1. 1.Microsoft ResearchBangaloreIndia
2. 2.Department of Computer SciencePurdue UniversityWest LafayetteUSA