  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.
