These are ordinary curves of with embedding degree 6, whose orders are prime or a prime multiplied by a small constant.

A type D curve is defined over some field F_q and has order h * r where
r is a prime and h is a small constant. Over the field F_q^{6} its order is
a multiple of r^{2}.

Typically the order of the curve E is around 170 bits, as is F_q, the base
field, thus q^{k} is around the 1024-bit mark which is commonly considered
good enough.

`d_param`

struct fields:

q F_q is the base field n # of points in E(F_q) r large prime dividing n h n = h * r a E: y^2 = x^3 + ax + b b nk # of points in E(F_q^k) hk nk = hk * r * r coeff0 coefficients of a monic cubic irreducible over F_q coeff1 coeff2 nqr quadratic nonresidue in F_q

These were discovered by Miyaji, Nakabayashi and Takano, "New explicit conditions of elliptic curve traces for FR-reduction".