This paper describes a constant-time lattice encoder for the National Institute of Standards and Technology (NIST) recommended post-quantum encryption algorithm: Kyber. The first main contribution of this paper is to refine the analysis of Kyber decoding noise and prove that Kyber decoding noise can be bounded by a sphere. This result shows that the Kyber encoding problem is essentially a sphere packing in a hypercube. The original Kyber encoder uses the integer lattice for sphere packing purposes, which is far from optimal. Our second main contribution is to construct optimal lattice codes to ensure denser packing and a lower decryption failure rate (DFR). Given the same ciphertext size as the original Kyber, the proposed lattice encoder enjoys a larger decoding radius, and is able to encode much more information bits. This way we achieve a decrease of the communication cost by up to 32.6%, and a reduction of the DFR by a factor of up to 2^{85}. Given the same plaintext size as the original Kyber, 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：本文描述了一种针对美国国家标准与技术研究院（NIST）推荐后量子加密算法Kyber的常数时间格编码器。本文的第一个主要贡献是改进了Kyber解码噪声的分析，并证明Kyber解码噪声可由一个球体界定。该结果表明Kyber编码问题本质上是超立方体内的球体堆积。原始Kyber编码器使用整数格进行球体堆积，远非最优解。我们的第二个主要贡献是构造最优格编码以确保更密集的堆积和更低的解密失败率（DFR）。在保持与原始Kyber相同密文大小的前提下，所提出的格编码器具有更大的解码半径，能够编码更多的信息比特。通过这种方式，我们实现了通信成本最高降低32.6%，同时DFR最多降低2^{85}倍。在保持与原始Kyber相同明文大小（例如256比特）的条件下，我们提出了一种比特交织编码调制（BICM）方法，该方法结合了BCH码与所提出的格编码器。所提出的BICM方案显著降低了Kyber的DFR，从而实现了密文的进一步压缩。与原始Kyber编码器相比，通信成本降低了24.49%，而DFR降低了2^{39}倍。所提出的编码方案为常数时间算法，因此能够抵抗时序侧信道攻击。