基于裁剪后的Hopfield神经网络的多变量加密系统研究

Neural networks which possess rich dynamic characteristics are emerging as an important branch in cryptographic design. As a post-quantum crypto algorithm, multivariate cryptosystem has the advantage of low operation complexity and power consumption. However, the lack of security proof, low decryption efficiency, the possibility of decryption failure and the large amount of memory consumption limit its applications in the security design for resource constrained devices. It’s noted that the high nonlinear feature, parallel distributed way and the iteration nature of its input and output of Clipped Hopfield Neural Network allow its well mapping to multivariate exponential modular sequences. This research program investigates a new multivariate cryptosystem utilizing the multivariate exponential modular sequences constructed under the Clipped Neural Network infrastructure. It’s expected to solve the decryption issues in terms of low decryption efficiency and decryption failure caused by the large amount of equivalent keys, which existing in almost all traditional multivariate cryptosystems. Moreover, this work tries to reduce the memory consumption of these key matrices to improve the practicality by constructing key matrices with sparsity feature and supporting fast implementation algorithms. This study expands and promotes the lightweight post-quantum cryptographic applications of neural networks both theoretically and practically.

神经网络丰富的动力学特性在密码学领域具有重要的研究价值和广阔的应用空间。多变量公钥密码系统算法作为一种后量子加密算法具有计算操作简单、功耗低等优点，但它存在着安全性不明确、解密效率低及可能解密失败、存储空间消耗过大等问题，严重阻碍了其在轻量级加密算法设计中的应用。裁剪的Hopfield神经网络所具有的高度非线性、大规模分布式特性及输入输出迭代方式使其与多变量模幂序列具有良好的映射关系。本课题在改进裁剪的Hopfield神经网络架构下，探索基于多变量模幂序列的迭代式多变量加密系统，以期解决传统多变量公钥密码系统存在指数级等价解而导致的解密结果不唯一或存在解密失败可能性等问题。此外，本项目还针对多变量公钥密码系统在存储消耗过大等问题，尝试通过构造具有稀疏性、支持快速实现算法的密钥矩阵提高算法实用价值。本项目的研究成果可为基于神经网络的后量子轻量级密码研究奠定理论基础，并提供应用示范。

本项目针对传统多变量加密算法安全性不明确、解密效率低及可能解密失败、存储空间消耗过大等问题，基于对Hopfield神经网络高度非线性、迭代特性研究，项目构建了多变量模幂序列与神经网络映射关系理论，提出了基于裁剪的、Hopfiled神经网络的多变量加密算法。传统多变元算法存在多组等价解揭秘结果不唯一等问题，项目本提出基于Diffie-Hellman 秘钥交换协议生成基矩阵，通过选取该基矩阵环上任意个数、任意元素的和矩阵构建通信双方的公钥向量，进而可以通过将明文作为神经网络初始状态输入系统，将系统迭代次后各神经元对应的状态输出为密文而实现基于Hopfield神经网络架构的、迭代式多变量加密算法。物联网环境动态多变等特性，项目从多目标优化的角度，提出了一种混合智能算法框架，该算法综合基于角度的分解、基于奖励的边界插入分解方法的优势，灵活、有效平衡搜索过程中解的多样性及收敛性，可有效匹配资源与安全能。