一种基于格的联合加密、编码和调制方案
A Lattice Based Joint Encryption, Encoding and Modulation Scheme
摘要：
提出了一种新的非线性Rao-Nam型对称密钥加密方案。在我们的设计中使用了QC-LDPC格，由于其低复杂度的编码和解码算法，实际上可以在高维中实现。在此基础上，提出了一种能够同时进行加密、编码和数据调制的联合方案。该密码系统经受住所有变种的选择明文攻击Rao-Nam像密码系统，由于其非线性。QC-LDPC格的奇偶校验矩阵的稀疏性、其生成元和奇偶校验矩阵的准循环性质、用于生成故意误差向量的简单硬件结构、置换和非线性函数，导致我们的方案具有较小的密钥大小。与本文所用格相关的格码具有较高的码率，适用于带限AWGN信道。因此，基于这些格的联合方案有助于在带限AWGN信道中安全、可靠和高效地传输数据。
英文摘要：
A new nonlinear Rao-Nam like symmetric key encryption scheme is presented in this paper. QC-LDPC lattices that are practically implementable in high dimensions due to their low complexity encoding and decoding algorithms, are used in our design. Then, a joint scheme is proposed which is capable of encrypting, encoding and data modulation simultaneously. The proposed cryptosystem withstands all variants of chosen plaintext attacks applied on Rao-Nam like cryptosystems due to its nonlinearity. The sparseness of the parity-check matrix of QC-LDPC lattices, quasi-cyclic nature of their generator and parity-check matrices, simple hardware structure for generating intentional error vector, permutation and nonlinear functions, result in a small key size for our scheme. The lattice codes related to the lattices used in this paper have high rate which are suitable for bandlimited AWGN channels. Therefore, the joint scheme based on these lattices facilitates secure, reliable and efficient data transmission in bandlimited AWGN channels.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
