Secrecy Amplification for Distributed Encrypted Sources with Correlated Keys using Affine Encoders

TL;DR

This paper introduces a method using affine encoders for distributed encryption with correlated keys, significantly enhancing secrecy by reducing information leakage and enabling reliable data recovery with legitimate keys.

Contribution

It presents a universal code construction employing affine encoders for secure distributed encryption with correlated keys, defining achievable rate regions for secrecy and data retrieval.

Findings

Information leakage is negligible within the rate region.

Legitimate users can recover original data with negligible error.

The method applies to distributed encryption with correlated keys.

Abstract

This paper proposed the application of post-encryption-compression (PEC) to strengthen the secrecy in the case of distributed encryption where the encryption keys are correlated to each other. We derive the universal code construction for the compression and the rate region where codes with achievability and secrecy are obtainable. Our main technique is to use affine encoders which are constructed from certain linear encoders to encode the ciphertexts before sending them to public communication channels. We show that if the rates of linear codes are within a certain rate region:(1) information leakage on the original sources from the encoded ciphertexts without the keys is negligible, while (2) one who has legitimate keys is able to retrieve the original source data with negligible error probability.