Security evaluation and design elements for a class of randomised encryptions

Abstract

This study considers a class of randomised encryption techniques, where the encrypted data suffers from noise through transmission over a communication channel. It focuses on the encoding–encryption framework, where the data is first encoded using error correction coding for reliability, then encrypted with a stream cipher. A dedicated homophonic encoder is added to enhance the protection of the stream cipher key, on which relies the security of all the system transmissions. This study presents a security evaluation of such systems in a chosen plaintext attack scenario, which shows that the computational complexity security is lower bounded by the related LPN (learning from parity with noise) complexity in both the average and worst cases. This gives guidelines to construct a dedicated homophonic encoder which maximises the complexity of the underlying LPN problem for a given encoding overhead. A generic homophonic coding strategy that fulfils the proposed design criteria is then given, which thus both enhances security while minimising the induced overhead. Finally, a comparison of encryption schemes based on the LPN problem with and without homophonic coding is considered.