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

This is the authors' abstract. We don't add key points for this paper.

A wiretap coding scheme (Wyner in Bell Syst Tech J 54(8):1355–1387, 1975) enables Alice to reliably communicate a message m to an honest Bob by sending an encoding c over a noisy channel ChB ChB , while at the same time hiding m from Eve who receives c over another noisy channel ChE ChE . Wiretap coding is clearly impossible when ChB ChB is a degraded version of ChE ChE , in the sense that the output of ChB ChB can be simulated using only the output of ChE ChE . A classic work of Csiszár and Korner (IEEE Trans Inf Theory 24(3):339–348, 1978) shows that the converse does not hold. This follows from their full characterization of the channel pairs (ChB,ChE) ( 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 ChB is not a degraded version of ChE ChE . Our construction assumes the existence of virtual black-box 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 ChB and not on ChE ChE .