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Exponential secrecy against unbounded adversary using joint encryption and privacy amplification

In this paper without tailoring to any presumed condition on communication channel or any restriction on adversary's resources we design a secrecy scheme with information leakage that decays at an exponential rate. 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. A key extractor based on a sampler and a Rényi extractor derives secret keys with the required entropy from this source. A general cipher uses this key to ensure the required equivocation for the plaintext and to establish the first layer of secrecy. Using privacy amplification on top of this cipher based on inverse universal2 hashing constitutes the second layer of secrecy for highly confidential message transmission with information leakage that is exponentially decreasing. We provide exponent analysis and optimization to minimize information leakage in terms of Eve's distinguishability based on L1 norm distance from uniformity. The required key rate is characterized for different source entropies in order to guarantee the secrecy that is demanded in terms of secrecy exponent for the second layer and Eve's error rate for the first layer.