基于新型压缩感知的图像加密构建方法与分析机制研究

From the perspective of cryptography, compressed sensing (CS) naturally contains the features of encryption algorithms, and it does not need any additional compression steps in the framework. It has been widely used to construct cryptographic primitives, such as image encryption, identity authentication and secret sharing. In the aspect of designing cryptographic schemes, based on the computational security of three new types of CS (i.e., chaotic CS, semi-tensor CS and finite CS), this project studies the model of one-to-many image encryption based on chaotic CS, proposes image encryption system based on semi-tensor CS, studies the security of the model of finite CS, and constructs image encryption schemes based on finite CS. In the aspect of analyzing cryptographic schemes, on the basis of the fact that most existing chaotic image encryption schemes lack the theoretical proofs of security, this project establishes the transformation relationship between different attack models and the reconstruction algorithms of chaotic CS, and explores the intrinsic mechanism of using the reconstruction algorithms of finite CS to analyze the cryptographic schemes based on inhomogeneous small integer solution problems. The overall aims of this project are to clarify the general operational principles and security levels of the proposed schemes, establish the designing method and cryptanalysis mechanism for image encryption schemes based on new types of CS, and then form a complete theoretical framework for image encryption schemes based on new types of CS.

从密码学的角度看，压缩感知过程蕴藏了天然的加密特征且无需额外的压缩步骤，已被广泛地应用于图像加密、身份认证以及秘密共享等密码方案的设计之中。在构建方法方面，本项目拟以混沌压缩感知、半张量压缩感知以及有限域压缩感知三种新型压缩感知过程的计算安全性为基础，研究基于混沌压缩感知的一对多图像加密新模型，提出基于半张量积压缩感知的图像加密体制，研究有限域压缩感知模型的安全性，构建基于有限域压缩感知图像加密方案；在分析机制方面，以现有混沌图像加密方案缺乏严格的安全性证明为事实依据，建立不同攻击模型与混沌压缩感知重构算法之间的转换关系，探索运用有限域压缩感知重构算法分析基于非齐次小整数解难题密码方案的内在机制。本项目的总体目标是明确所提方案的通用工作原理和安全层级，建立新型压缩感知图像密码方案的构造方法与分析机制，形成一套完整的新型压缩感知图像加密方案的理论框架。

基于压缩感知新模型，本项目研究图像加密体制的构造方法与分析体制，建立适用于图像数据的新型压缩感知压缩加密方法。本项目以提高效率与扩展功能性为目标，研究混沌压缩感知、半张量积压缩感知以及离散空间压缩感知三种新型压缩感知在图像加密领域的应用，明确所提方案的基本过程和工作机理。在混沌压缩感知新模型加密方面，设计一种高效的多图像联合加密方案，提出针对云环境的一对多加密新体制。在半张量积压缩感知新模型加密方面，设计了一个多方安全的加密-共享融合方案，对传统图像加密方案容错性低的问题进行了探究。在离散空间压缩感知新模型加密方面，提出构造离散空间压缩感知测量矩阵的方法，设计了基于压缩感知的公钥图像加密方案。基于本项目的科学研究促进了图像加密领域的发展，具有一定的理论与现实意义。