Coding-Based Hybrid Post-Quantum Cryptosystem for Non-Uniform Information

Abstract

We introduce for non-uniform messages a novel hybrid universal network coding cryptosystem (NU-HUNCC) in the finite blocklength regime that provides Post-Quantum (PQ) security at high communication rates. Recently, hybrid cryptosystems offered PQ security by premixing the data using secure linear coding schemes and encrypting only a small portion of it. The data is assumed to be uniformly distributed, an assumption that is often challenging to enforce. Standard fixed-length lossless source coding and compression schemes guarantee a uniform output in normalized divergence. Yet, this is not sufficient to guarantee security. We consider an efficient compression scheme uniform in non-normalized variational distance for the proposed hybrid cryptosystem, that by utilizing a uniform sub-linear shared seed, guarantees PQ security. Specifically, for the proposed PQ cryptosystem, first, we provide an end-to-end practical coding scheme, NU-HUNCC, for non-uniform messages. Second, we show that NU-HUNCC is information-theoretic individually secured (IS) against an eavesdropper with access to any subset of the links and provide a converse proof against such an eavesdropper. Third, we introduce a modified security definition, individual semantic security under a chosen ciphertext attack (ISS-CCA1), and show that against an all-observing eavesdropper, NU-HUNCC satisfies its conditions. Finally, we provide an analysis of NU-HUNCC's high data rate, low computational complexity, and the negligibility of the shared seed size.

Parts of this work were accepted for publication at the IEEE International Symposium on Information Theory, ISIT 2024