Simultaneous Secrecy and Reliability Amplification for a General Channel Model
We present a general notion of channel for cryptographic purposes, which can model either a (classical) physical channel or the consequences of a cryptographic protocol, or any hybrid. We consider simultaneous secrecy and reliability amplification for such channels. We show that simultaneous secrecy and reliability amplification is not possible for the most general model of channel, but, at least for some values of the parameters, it is possible for a restricted class of channels that still includes both standard information-theoretic channels and keyless cryptographic protocols.
Even in the restricted model, we require that for the original channel, the failure chance for the attacker must be a factor c more than that for the intended receiver. We show that for any \(c > 4 \), there is a one-way protocol (where the sender sends information to the receiver only) which achieves simultaneous secrecy and reliability. From results of Holenstein and Renner (CRYPTO’05), there are no such one-way protocols for \(c < 2\). On the other hand, we also show that for \(c > 1.5\), there are two-way protocols that achieve simultaneous secrecy and reliability.
We propose using similar models to address other questions in the theory of cryptography, such as using noisy channels for secret agreement, trade-offs between reliability and secrecy, and the equivalence of various notions of oblivious channels and secure computation.
We thank Yevgeny Dodis, Noah Stevens-Davidowitz, Giovanni di Crescenzo, Daniele Micciancio, Thomas Holenstein and Steven Rudich for helpful comments and discussions. Russell Impagliazzo’s work was partially supported by the Simons Foundation and NSF grant CCF-121351; this work was done [in part] while Russell Impagliazzo was visiting the Simons Institute for the Theory of Computing, supported by the Simons Foundation and by the DIMACS/Simons Collaboration in Cryptography through NSF grant #CNS-1523467. Valentine Kabanets was partially supported by the NSERC Discovery grant. Bruce Kapron’s work was supported in part by the NSERC Discovery Grant “Foundational Studies in Privacy and Security”. Stefano Tessaro was partially supported by NSF grants CNS-1423566, CNS-1553758, CNS-1528178, IIS-1528041 and the Glen and Susanne Culler Chair.
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