The 2018 International Symposium on Information Theory and Its Applications (ISITA2018)
Post Encryption Compression with Affine Encoders for Secrecy Amplification in Distributed Source Encryption with Correlated Keys
Bagus Santoso, Yasutada Oohama,
In this paper, we propose the application of postencryption-compression (PEC) to strengthen the secrecy in the case of distributed encryption where the encryption keys are correlated to each other, without additional randomness. We show that, in the case of one-time-pad encryption, certain affine encoders are sufficient for strengthening the secrecy by using them to compress the ciphertexts before sending them to public communication channels. We show how to explicitly construct those affine encoders using universal code construction paradigm. The universal code construction gives us advantages as follows. ? We can construct good encoders based on the transmission rates only, without knowing the value of the distribution of sources or keys. ? Reliability and secrecy are achievable by construction even in 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 concrete 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 n becomes large.