  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 coding
schemes and encrypting only a small portion of it, assuming the data is
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, his is not sufficient to
guarantee security. We consider an efficient almost uniform compression scheme
in non-normalized variational distance for the proposed hybrid cryptosystem,
that by utilizing uniform sub-linear shared seed, guarantees PQ security.
Specifically, for the proposed PQ cryptosystem, first, we provide an end-to-end
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. Third, we introduce a
modified security definition, individually semantically secure 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 that shows the high communication rate of NU-HUNCC and the
negligibility of the shared seed size.
