Existing error correction mechanisms in lattice-based public key encryption (PKE) rely on either naive modulation or its concatenation with error correction codes (ECC). This paper shows that lattice coding, as a joint ECC and modulation technique, can substitute the naive modulation in existing lattice-based PKEs to enjoy better correction performance. We begin by modeling the FrodoPKE protocol as a noisy point-to-point communication system, where the communication channel is similar to the additive white Gaussian noise (AWGN) channel. To employ lattice codes for this special channel that hinges on hypercube shaping, we propose an efficient labeling function that converts between binary information bits and lattice codewords. The parameter sets of FrodoPKE are improved towards either higher security levels or smaller ciphertext sizes. For example, the proposed Frodo-1344-E$_\text{8}$ has a 10-bit classical security gain over Frodo-1344.

翻译：现有基于格的公钥加密（PKE）中的纠错机制依赖于朴素调制或其与纠错码（ECC）的级联。本文证明，格码作为一种联合ECC与调制技术，可替代现有基于格PKE中的朴素调制，从而获得更优的纠错性能。我们首先将FrodoPKE协议建模为带有噪声的点对点通信系统，该通信信道与加性高斯白噪声（AWGN）信道类似。为了将格码应用于这种依赖超立方体成形的特殊信道，我们提出了一种高效标签函数，可在二进制信息比特与格码字之间进行转换。通过优化FrodoPKE的参数集，实现了更高的安全级别或更小的密文尺寸。例如，所提出的Frodo-1344-E₈相较于Frodo-1344获得了10比特经典安全增益。