Existing error correction mechanisms in lattice-based public key encryption (PKE) rely on either trivial modulation or its concatenation with error correction codes (ECC). This paper demonstrates that lattice coding, as a combined ECC and modulation technique, can replace trivial modulation in current lattice-based PKEs, resulting in improved error correction performance. We model the FrodoPKE protocol as a noisy point-to-point communication system, where the communication channel resembles an additive white Gaussian noise (AWGN) channel. To utilize lattice codes for this specific channel with hypercube shaping, we propose an efficient labeling function that converts binary information bits to lattice codewords and vice versa. The parameter sets of FrodoPKE are enhanced to achieve higher security levels or smaller ciphertext sizes. For instance, the proposed Frodo-1344-E\(_\text {8}\) offers a 10-bit classical security improvement over Frodo-1344. The code for reproducing our main experiments is available at https://github.com/shx-lyu/lattice-codes-for-pke.

基于格的公钥加密 (PKE) 中现有的纠错机制依赖于简单的调制或其与纠错码 (ECC) 的串联。本文证明，点阵编码作为 ECC 和调制技术的结合，可以取代当前基于点阵的 PKE 中的简单调制，从而提高纠错性能。我们将 FrodoPKE 协议建模为一个噪声点对点通信系统，其中通信信道类似于加性高斯白噪声 (AWGN) 信道。为了利用超立方体成形的特定通道的点阵码，我们提出了一种有效的标记函数，可以将二进制信息位转换为点阵码字，反之亦然。FrodoPKE 的参数集得到增强，以实现更高的安全级别或更小的密文大小。例如，提议的 Frodo-1344-E \(_\text {8}\)比 Frodo-1344 提供了 10 位经典安全性改进。用于重现我们主要实验的代码可在 https://github.com/shx-lyu/lattice-codes-for-pke 上找到。