Abstract
In \cite{QPKC}, a knapsack based cryptosystem is proposed using number fields as a scheme of quantum public key cryptosystems. We studied on key generation of this scheme in the case of imaginary quadratic fields \cite{Nishi}. In this paper, we study the cases of real quadratic fields and cubic fields. We first give some propositions for practical key generation. We then estimate various densities of the generated knapsack problems for these cases and for the imaginary quadratic case. We further generate explicit public keys and knapsack problems for several special cases and test the resistance against low-density attacks.
