In continuation to earlier works where the problem of joint information embedding and lossless compression (of the composite signal) was studied in the absence \cite{MM03} and in the presence \cite{MM04} of attacks, here we consider the additional ingredient of protecting the secrecy of the watermark against an unauthorized party, which has no access to a secret key shared by the legitimate parties. In other words, we study the problem of joint coding for three objectives: information embedding, compression, and encryption.Our main result is a coding theorem that provides a single--letter characterization of the best achievable tradeoffs among the following parameters: the distortion between the composite signal and the covertext, the distortion in reconstructing the watermark by the legitimate receiver, the compressibility of the composite signal (with and without the key), and the equivocation of the watermark, as well as its reconstructed version, given the composite signal. In the attack--free case, if the key is independent of the covertext, this coding theorem gives rise to a {\it threefold} separation principle that tells that asymptotically, for long block codes, no optimality is lost by first applying a rate--distortion code to the watermark source, then encrypting the compressed codeword, and finally, embedding it into the covertext using the embedding scheme of \cite{MM03}. In the more general case, however, this separation principle is no longer valid, as the key plays an additional role of side information used by the embedding unit.
Information- and Coding-Theoretic Analysis of the RLWE Channel
在NIST后量子密码学标准化过程中已经提出了基于\emph{Ring Learning with Errors}（RLWE）问题的几种密码系统，例如，新希望此外，还有像Kyber这样的系统，它们基于密切相关的MLWE假设。前面提到的两种方案都导致非零的解密失败率（DFR）。这些算法的加密和解密的组合可以被解释为在噪声信道上的数据传输。据我们所知，本文是第一个工作，分析了该通道的容量。我们展示了如何修改加密方案，使得相应通道的输入字母增加。特别是，我们提出了他们的能力，这表明，传输速率可以显着增加的下限相比，在文献中的标准建议。此外，在随机独立系数失效的共同假设下，我们给出了基于Gilbert-Varshamov界和使用BCH码的具体码构造的可实现速率的下界。通过我们的构造，我们可以在保证相同DFR的同时增加总比特率（对于Kyber增加$1.84$的因子，对于NewHope增加$7$的因子），或者对于相同的比特率，我们可以显著降低本工作中考虑的所有方案的DFR（例如，对于NewHope，从$2^{-216}$到$2^{-12769}$）。
Intelligent Wiretap Code Design: Exploiting Wireless Endogenous Security via Information Theory and Deep Learning Integration
Xidian University（西安电子科技大学）；Information Engineering University（信息工程大学）；Peng Cheng Laboratory（鹏城实验室）；National Mobile Communications Research Laboratory, Southeast University（东南大学移动通信国家重点实验室）；James Watt School of Engineering, University of Glasgow（格拉斯哥大学詹姆斯·瓦特工程学院）；China Industrial Control Systems Cyber Emergency Response Team（中国工业控制系统网络安全应急响应中心）；School of Electrical Engineering and Telecommunications, University of New South Wales（新南威尔士大学电气与电信工程学院）；Faculty of Electrical Engineering and Computer Science at the Technical University of Berlin（柏林工业大学电气与计算机科学学院）
