This paper describes a constant-time lattice encoder for the NIST-recommended post-quantum encryption algorithm: Kyber. We first refine the analysis of Kyber decoding noise and prove that Kyber decoding noise can be bounded by a sphere. This shows the Kyber encoding problem is essentially a sphere packing in a hypercube. Lattice codes are then constructed to ensure denser packing and a lower decryption failure rate (DFR). For a fixed ciphertext size, the proposed lattice encoder reduces the communication cost by up to 32.6%, and decreases the DFR by a factor of up to 2^{85}. For a fixed plaintext size, e.g., 256 bits, we propose a bit-interleaved coded modulation (BICM) approach, which combines a BCH code and the proposed lattice encoder. The proposed BICM scheme significantly reduces the DFR of Kyber, thus enabling further compression of the ciphertext. Compared with the original Kyber encoder, the communication cost is reduced by 24.49%, while the DFR is decreased by a factor of 2^{39}. The proposed encoding scheme is a constant-time algorithm, thus resistant against the timing side-channel attacks.

翻译：本文针对美国国家标准与技术研究院推荐的后量子加密算法Kyber，提出了一种恒定时间格编码器。首先，我们改进了Kyber解码噪声的分析，并证明该噪声可被球体界定。这表明Kyber编码问题本质上是超立方体内的球体堆积问题。随后构造了格编码以实现更密集的堆积和更低的解密失败率。在固定密文尺寸下，所提格编码器降低通信开销达32.6%，并将解密失败率降低至原来的2^{85}分之一。对于固定明文尺寸（如256比特），我们提出了一种结合BCH码与所提格编码器的比特交织编码调制方案。该方案显著降低了Kyber的解密失败率，从而进一步压缩密文。与原始Kyber编码器相比，通信开销降低24.49%，同时解密失败率降低至原来的2^{39}分之一。所提编码方案为恒定时间算法，因此能够抵御计时侧信道攻击。