A joint Shannon cipher and privacy amplification approach to attaining exponentially decaying information leakage

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In this paper, we propose a novel layering approach to achieve end-to-end exponential security without resorting to presumed physical layer conditions. The only requirement for such an exponentially secure system is existence of a common key source between legitimate users that is partially known by Eve. The novel framework includes a random cipher and key stream generating scheme constituting the first layer and universal hash forming the second layer. The key generating scheme is based on a novel definition of a randomness extractor that derives a key stream with the required entropy from the common source, to be used for cipher. All metrics involved in characterizing the quality of secrecy of two-layer components are related to Rényi entropy and conditional Rényi entropy, which are all ultimately captured in the adopted information leakage metrics: mutual information and Eve's distinguishability based on L1 norm distance from uniformity. Such relationships are exploited to optimize the resulting bounds for secrecy exponents by selecting appropriate operating parameters including required key rate and source entropies, as well as the required guessing error rate by Eve to attack the first layer.

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Information Sciences

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