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.

翻译：针对非均匀消息，我们提出了一种新颖的有限块长体制下的混合通用网络编码密码系统（NU-HUNCC），该系统能在高通信速率下提供后量子（PQ）安全性。近期，混合密码系统通过使用安全编码方案对数据进行预混合并仅加密其中一小部分来提供PQ安全性，其前提是数据服从均匀分布。然而这一前提往往难以保证。标准定长无损信源编码和压缩方案能在归一化散度下保证均匀输出，但这不足以确保安全性。我们为所提出的混合密码系统考虑了一种在非归一化变分距离下的高效近似均匀压缩方案，该方案通过利用均匀次线性共享种子来保证PQ安全性。具体而言，针对所提出的PQ密码系统：首先，我们为非均匀消息提供了一种端到端编码方案NU-HUNCC。其次，我们证明NU-HUNCC能针对可访问任意链路子集的窃听者实现信息论意义上的个体安全性（IS）。第三，我们引入了改进的安全性定义"选择密文攻击下的个体语义安全性（ISS-CCA1）"，并证明NU-HUNCC能满足全观测窃听者场景下的该条件。最后，分析表明NU-HUNCC具有高通信速率且共享种子尺寸可忽略不计。