### Beyond the Csiszár-Körner Bound: Best-Possible Wiretap Coding via Obfuscation

##### Abstract

A wiretap coding scheme (Wyner, Bell Syst. Tech. J. 1975) enables Alice to reliably communicate a message m to an honest Bob by sending an encoding c over a noisy channel chB, while at the same time hiding m from Eve who receives c over another noisy channel chE. Wiretap coding is clearly impossible when chB is a degraded version of chE, in the sense that the output of chB can be simulated using only the output of chE. A classic work of Csiszár and Körner (IEEE Trans. Inf. Theory, 1978) shows that the converse does not hold. This follows from their full characterization of the channel pairs (chB, chE) that enable information-theoretic wiretap coding. In this work, we show that in fact the converse does hold when considering computational security; that is, wiretap coding against a computationally bounded Eve is possible if and only if chB is not a degraded version of chE. Our construction assumes the existence of virtual black-box (VBB) obfuscation of specific classes of evasive'' functions that generalize fuzzy point functions, and can be heuristically instantiated using indistinguishability obfuscation. Finally, our solution has the appealing feature of being universal in the sense that Alice's algorithm depends only on chB and not on chE.

Note: Minor edits and revisions

Available format(s)
Publication info
A minor revision of an IACR publication in CRYPTO 2022
Contact author(s)
yuvali @ cs technion ac il
alexiskorb @ cs ucla edu
pslou @ cs ucla edu
sahai @ cs ucla edu
History
2022-09-01: last of 2 revisions
See all versions
Short URL
https://ia.cr/2022/343

CC BY

BibTeX

@misc{cryptoeprint:2022/343,
author = {Yuval Ishai and Alexis Korb and Paul Lou and Amit Sahai},
title = {Beyond the Csiszár-Körner Bound: Best-Possible Wiretap Coding via Obfuscation},
howpublished = {Cryptology ePrint Archive, Paper 2022/343},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/343}},
url = {https://eprint.iacr.org/2022/343}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.