The Mathematical Foundation of Post-Quantum Cryptography
<|reference_start|>The Mathematical Foundation of Post-Quantum Cryptography: On July 5, 2022, the National Institute of Standards and Technology announced four possible post-quantum cryptography standards, three of them are based on lattice theory and the other one is based on Hash function. It is well-known that the security of the lattice cryptography relies on the hardness of the shortest vector problem (SVP) and the closest vector problem (CVP). In fact, the SVP is a sphere packing problem and the CVP is a sphere covering problem. Furthermore, both SVP and CVP are equivalent to arithmetic problems of positive definite quadratic forms. This paper will briefly introduce the post-quantum cryptography and show its connections with sphere packing, sphere covering, and positive definite quadratic forms.<|reference_end|>
@article{zong2024the,
    title={The Mathematical Foundation of Post-Quantum Cryptography},
    author={Chuanming Zong},
    journal={arXiv preprint arXiv:2404.19186},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.19186},
    primaryClass={cs.IT cs.CR math.IT math.MG math.NT}
}