Abstract
A wiretap coding scheme for a pair of noisy channels \((\textsf{ChB},\textsf{ChE})\) enables Alice to reliably communicate a message to Bob by sending its encoding over \(\textsf{ChB}\), while hiding the message from an adversary Eve who obtains the same encoding over \(\textsf{ChE}\).
A necessary condition for the feasibility of wiretap coding is that \(\textsf{ChB}\) is not a degradation of \(\textsf{ChE}\), namely Eve cannot simulate Bob’s view. While insufficient in the information-theoretic setting, a recent work of Ishai, Korb, Lou, and Sahai (Crypto 2022) showed that the non-degradation condition is sufficient in the computational setting, assuming idealized flavors of obfuscation. The question of basing a similar feasibility result on standard cryptographic assumptions was left open, even in simple special cases.
In this work, we settle the question for all discrete memoryless channels where the (common) input alphabet of \(\textsf{ChB}\) and \(\textsf{ChE}\) is binary, and with arbitrary finite output alphabet, under standard (sub-exponential) hardness assumptions: namely those assumptions that imply indistinguishability obfuscation (Jain-Lin-Sahai 2021, 2022), and injective PRGs. In particular, this establishes the feasibility of computational wiretap coding when \(\textsf{ChB}\) is a binary symmetric channel with crossover probability p and \(\textsf{ChE}\) is a binary erasure channel with erasure probability e, where \(e>2p\).
On the information-theoretic side, our result builds on a new polytope characterization of channel degradation for pairs of binary-input channels, which may be of independent interest.
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References
Agrawal, S., et al.: Secure computation from one-way noisy communication, or: anti-correlation via anti-concentration. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12826, pp. 124–154. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84245-1_5
Alekhnovich, M.: More on average case vs approximation complexity. In: 44th Symposium on Foundations of Computer Science (FOCS 2003), 11–14 October 2003, Cambridge, MA, USA, Proceedings, pp. 298–307. IEEE Computer Society (2003). https://doi.org/10.1109/SFCS.2003.1238204
Barak, B., Bitansky, N., Canetti, R., Kalai, Y.T., Paneth, O., Sahai, A.: Obfuscation for evasive functions. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 26–51. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54242-8_2
Barak, B., et al.: On the (Im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1–18. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44647-8_1
Blum, A., Furst, M., Kearns, M., Lipton, R.J.: Cryptographic primitives based on hard learning problems. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 278–291. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48329-2_24
Bogdanov, A., Qiao, Y.: On the security of Goldreich’s one-way function. Comput. Complex. 21(1), 83–127 (2012)
Csiszár, I., Korner, J.: Broadcast channels with confidential messages. IEEE Trans. Inf. Theory 24(3), 339–348 (1978)
Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. SIAM J. Comput. 45(3), 882–929 (2016). https://doi.org/10.1137/14095772X
Guruswami, V.: List decoding of binary codes–a brief survey of some recent results. In: Chee, Y.M., Li, C., Ling, S., Wang, H., Xing, C. (eds.) IWCC 2009. LNCS, vol. 5557, pp. 97–106. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01877-0_10
Guruswami, V., Sudan, M.: List decoding algorithms for certain concatenated codes. In: 32nd ACM STOC, pp. 181–190. ACM Press, May 2000
Ishai, Y., Korb, A., Lou, P., Sahai, A.: Beyond the Csiszár-Körner bound: best-possible wiretap coding via obfuscation. In: Crypto 2022 (2022)
Ishai, Y., Korb, A., Lou, P., Sahai, A.: Beyond the csiszár-korner bound: Best-possible wiretap coding via obfuscation. In: Dodis, Y., Shrimpton, T. (eds.) Advances in Cryptology - CRYPTO 2022, Part II. LNCS, vol. 13508, pp. 573–602. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-15979-4_20
Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from well-founded assumptions. In: Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing, pp. 60–73 (2021)
Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from LPN over \(\mathbb{F}_p\), dlin, and prgs in nc\({}^{\text{0}}\). In: Dunkelman, O., Dziembowski, S. (eds.) Advances in Cryptology - EUROCRYPT 2022. Part I. LNCS, vol. 13275, pp. 670–699. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-06944-4_23
Nair, C.: Capacity regions of two new classes of two-receiver broadcast channels. IEEE Trans. Inf. Theory 56(9), 4207–4214 (2010)
Poor, H.V., Schaefer, R.F.: Wireless physical layer security. In: Proceedings of the National Academy of Sciences, vol. 114, no. 1, 19–26 (2017). https://www.pnas.org/content/114/1/19
Sahai, A., Waters, B.: How to use indistinguishability obfuscation: deniable encryption, and more. SIAM J. Comput. 50(3), 857–908 (2021). https://doi.org/10.1137/15M1030108
Sudan, M.: List decoding: algorithms and applications. In: van Leeuwen, J., Watanabe, O., Hagiya, M., Mosses, P.D., Ito, T. (eds.) TCS 2000. LNCS, vol. 1872, pp. 25–41. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-44929-9_3
Sudan, M., Trevisan, L., Vadhan, S.P.: Pseudorandom generators without the XOR lemma (extended abstract). In: 31st ACM STOC, pp. 537–546. ACM Press, May 1999
Wyner, A.D.: The wire-tap channel. Bell Syst. Tech. J. 54(8), 1355–1387 (1975)
Acknowledgments
Y. Ishai was supported in part by ERC Project NTSC (742754), BSF grant 2018393, ISF grant 2774/20, and a Google Faculty Research Award. A. Jain is supported in part by the Google Research Scholar Award and through various gifts from CYLAB, CMU. A. Sahai was supported in part from a Simons Investigator Award, DARPA SIEVE award, NTT Research, BSF grant 2018393, a Xerox Faculty Research Award, a Google Faculty Research Award, and an Okawa Foundation Research Grant. This material is based upon work supported by the Defense Advanced Research Projects Agency through Award HR00112020024.
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Ishai, Y., Jain, A., Lou, P., Sahai, A., Zhandry, M. (2023). Computational Wiretap Coding from Indistinguishability Obfuscation. In: Handschuh, H., Lysyanskaya, A. (eds) Advances in Cryptology – CRYPTO 2023. CRYPTO 2023. Lecture Notes in Computer Science, vol 14084. Springer, Cham. https://doi.org/10.1007/978-3-031-38551-3_9
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