Secrecy Amplification of Distributed Encrypted Sources With Correlated Keys Using Post-Encryption-Compression

In this paper, we are interested in the problem of strengthening the secrecy of distributed encryption in a particular case where the encryption keys are correlated to each other. We show that the post-encryption-compression (PEC) paradigm provides a suitable solution for the problem without requiring any additional secret randomness. More precisely, we show that in the case of one-time-pad encryption, we can use affine encoders with specific properties to strengthen the secrecy by using them to compress the ciphertexts before sending them to public communication channels. We show how to derive those affine encoders using universal code construction paradigm. The universal code construction gives us advantages as follows. 1) We can construct good encoders based on the transmission rates only, without knowing the value of the distribution of sources or keys. 2) Reliability and secrecy are achievable by construction even in particular cases such as follows: 1) only the range of correlation between keys is known but the exact amount is unknown or 2) the correlation between keys are changing time to time within a certain range. We also derive explicit lower bounds on the achievable reliability and secrecy exponents, i.e., the exponential rates of decay of the probability of decoding error and of the information leakage as the block length becomes large.