A survey that frames the security of lattice-based post-quantum cryptography as classical geometry-of-numbers problems: SVP/CVP, ball packing and covering, and quadratic forms.
The Mathematical Foundation of Post-Quantum Cryptography
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abstract
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.
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Some Mathematical Problems Behind Lattice-Based Cryptography
A survey that frames the security of lattice-based post-quantum cryptography as classical geometry-of-numbers problems: SVP/CVP, ball packing and covering, and quadratic forms.