Beyond the Csiszár-Körner Bound: Best-Possible

Transcript:Beyond the Csiszár-Körner Bound: Best-Possible:
Beyond the Csiszár-Körner Bound: Best-Possible Wiretap Coding via Obfuscation Paul Lou UCLA Amit Sahai UCLA Alexis Korb UCLA Yuval Ishai Technion Wiretap Channel [Wyn75] ChB ChE Xn Yn Zn M M Alice Bob Eve Encode Decode Goal: Alice wants to send a message to Bob without Eve learning it. Wiretap Channel [Wyn75] ChB ChE Xn Yn Zn M M Alice Bob Eve Encode Decode Goal: Alice wants to send a message to Bob without Eve learning it. Discrete memoryless channels (DMCs) Non-interactive No shared secrets Formal Definition Formal Definition Formal Definition Our results also generalize to larger message spaces. Simple Impossibility ChE ChB ChS = Observation: In this case, Eve can learn the same distribution Bob learns, so wiretap coding is impossible. Def: ChB is a degradation of ChE if there exists a channel ChS such that Simple Impossibility BEC2p BSCp Assign erasures to random bits = Observation: In this case, Eve can learn the same distribution Bob learns, so wiretap coding is impossible. Def: ChB is a degradation of ChE if there exists a channel ChS such that ex) Information Theoretic Setting Can we create a wiretap coding scheme whenever ChB is not a degradation of ChE? Information Theoretic Setting [CK78] Wiretap coding schemes are possible if and only if ChE is not less noisy than ChB. Can we create a wiretap coding scheme whenever ChB is not a degradation of ChE? No (Not) Less Noisy [CK78] ChB ChE X Y Z M “Encode” H(M | Y) < H(M | Z) Def: ChE is not less noisy than ChB if there exists a Markov chain M→X→YZ where pY|X(y|x) corresponds to ChB, pZ|X(z|x) corresponds to ChE, and Bob has an advantage over Eve in terms of conditional entropy. X is a one symbol encoding of M Information Theoretic Impossibility Less Noisy Degraded (Impossibility) Less Noisy (Impossibility) Secure Wiretap Coding p ε – 2p (BSC0.1, BEC0.3) ex) ChB = BSCp ChE = BECε [Nair10] Information Theoretic Impossibility Less Noisy Degraded (Impossibility) Less Noisy (Impossibility) Secure Wiretap Coding p ε – 2p (BSC0.1, BEC0.3) ex) ChB = BSCp ChE = BECε [Nair10] Can we do better in the computational setting? Computational Assumptions and Feasibility Results Computational Setting Can we create a wiretap coding scheme whenever ChB is not a degradation of ChE? Recall: Impossible (even computationally) if ChB is a degradation of ChE. Computational Setting Our Work: Assuming secure evasive function obfuscation