An end-to-end exponentially secure secrecy scheme against an unbounded adversary

Abstract

In this paper without tailoring to any physical channel condition or any restriction on adversary's computational resources we design a secrecy scheme with information leakage that decays at an exponential rate. The only advantage for legitimate users over eavesdropper is existence of a key source that is partially known by Eve. A key extractor based on a sampler and a Renyi extractor derives secret keys with the required entropy from this source. Encryption using this key with a general cipher maps Eve's uncertainty about the key to uncertainty about the plaintext that can also be interpreted as degradation in her channel. Using privacy amplification on top of this cipher based on inverse universal2 hashing results in information leakage with decreasing exponent that can be optimized to guarantee a higher level of secrecy.