Abstract: Finding suitable non-supersingular elliptic curves for
pairing-based cryptosystems becomes an important issue for the
modern public-key cryptography after the proposition of id-based
encryption scheme and short signature scheme. In previous work
different algorithms have been proposed for finding such elliptic
curves when embedding degree k ∈ {3, 4, 6} and cofactor h ∈ {1, 2, 3,
4, 5}. In this paper a new method is presented to find more
non-supersingular elliptic curves for pairing-based cryptosystems with
general embedding degree k and large values of cofactor h. In
addition, some effective parameters of these non-supersingular elliptic
curves are provided in this paper.