In a post-quantum asymmetric key generation method and system, a processing unit generates, based on a prime and an arithmetic function or a classical string, a prime vector which has an infinite number of components; generates a prime array based on the prime vector; generates an associated matrix based on the prime array; obtains, based on the associated matrix and a first reference prime, a first reference inverse prime array that serves as a private key; and obtains a public key that is paired with the private key based on a second reference inverse prime array. The second reference inverse prime array is obtained based on the associated matrix, the first reference prime, a second reference prime, and a randomization array.