[论文解读] Embedding Cryptographic Features in Compressive Sensing

Yushu Zhang, Kwok‐Wo Wong+3 more|arXiv (Cornell University)|Mar 25, 2014

Sparse and Compressive Sensing Techniques参考文献 38被引用 4

一句话总结

本文提出了一种两级保护模型（TLPM），通过在并行压缩感知（PCS）中嵌入基于混沌的随机置换和混沌测量矩阵，实现安全压缩感知（SCS）的联合压缩、加密及性能提升。该方法确保了高安全性，对噪声和裁剪具有鲁棒性，同时保持或提升压缩比，优于传统联合方案。

ABSTRACT

Compressive sensing (CS) has been widely studied and applied in many fields. Recently, the way to perform secure compressive sensing (SCS) has become a topic of growing interest. The existing works on SCS usually take the sensing matrix as a key and the resultant security level is not evaluated in depth. They can only be considered as a preliminary exploration on SCS, but a concrete and operable encipher model is not given yet. In this paper, we are going to investigate SCS in a systematic way. The relationship between CS and symmetric-key cipher indicates some possible encryption models. To this end, we propose the two-level protection models (TLPM) for SCS which are developed from measurements taking and something else, respectively. It is believed that these models will provide a new point of view and stimulate further research in both CS and cryptography. Specifically, an efficient and secure encryption scheme for parallel compressive sensing (PCS) is designed by embedding a two-layer protection in PCS using chaos. The first layer is undertaken by random permutation on a two-dimensional signal, which is proved to be an acceptable permutation with overwhelming probability. The other layer is to sample the permuted signal column by column with the same chaotic measurement matrix, which satisfies the restricted isometry property of PCS with overwhelming probability. Both the random permutation and the measurement matrix are constructed under the control of a chaotic system. Simulation results show that unlike the general joint compression and encryption schemes in which encryption always leads to the same or a lower compression ratio, the proposed approach of embedding encryption in PCS actually improves the compression performance. Besides, the proposed approach possesses high transmission robustness against additive Gaussian white noise and cropping attack.

研究动机与目标

• 为解决现有安全压缩感知（SCS）方案中缺乏具体、可操作的加密模型的问题，这些方案仅将感知矩阵视为密钥。
• 通过将压缩感知与对称密钥密码体制进行类比，系统性地研究SCS。
• 为并行压缩感知（PCS）设计一种高效、安全的加密方案，将加密直接集成到压缩过程中。
• 在确保高安全性及对常见攻击（如加性高斯白噪声和裁剪）的鲁棒性的同时，提升压缩性能。
• 提出一种新框架——两级保护模型（TLPM），以激发压缩感知与密码学领域的进一步研究。

提出的方法

• 第一级保护通过混沌系统对二维信号实施随机置换，确保置换后信号每列的稀疏度水平以极高概率降低。
• 第二级保护采用具有独立同分布亚高斯条目的混沌测量矩阵，该矩阵以极高概率满足压缩感知的限制等距性质（RIP）。
• 随机置换与混沌测量矩阵均由单一混沌系统生成，确保编码器与解码器之间的密钥同步。
• 该方法利用混沌的内在特性——对初始条件的敏感性与遍历性——生成安全、不可预测且均匀分布的变换。
• 加密过程直接嵌入PCS框架中，避免了传统方案中加密导致压缩比下降的典型权衡。
• 理论分析证明，置换在概率趋近于1时是可接受的（即降低最大列稀疏度），且测量矩阵在RIP条件下可保持信号的恢复能力。

实验结果

研究问题

• RQ1 能否开发一种系统化且实用的安全压缩感知模型，将加密直接集成到压缩与采样过程中？
• RQ2 如何利用压缩感知与对称密钥密码体制之间的关系，设计一种安全高效的加密机制？
• RQ3 与传统联合压缩-加密方案相比，将加密嵌入PCS框架是否改善或降低压缩比？
• RQ4 所提出的方案对常见信号攻击（如加性高斯白噪声和裁剪）的鲁棒性如何？
• RQ5 基于混沌的两级保护模型（TLPM）能否在PCS中同时实现高安全性与优异的压缩性能？

主要发现

• 所提方案通过将加密直接嵌入PCS过程，提升了压缩性能，与传统联合压缩-加密方案中常见的性能下降相反。
• 随机置换层以极高概率降低最大列稀疏度，其证明基于类似“球与盒子”问题的概率分析。
• 混沌测量矩阵以极高概率满足限制等距性质（RIP），确保信号恢复的稳定与鲁棒。
• 该方案对加性高斯白噪声和裁剪攻击表现出高度鲁棒性，保持了信号完整性和恢复质量。
• 加密方案表现出高度的密钥敏感性，即密钥的微小变化将导致显著不同的加密输出。
• 仿真结果证实，所提方法在实现高安全性的同时提升了压缩效率，验证了理论结论。