nzmath.elliptic
The class is for elliptic curves over finite (odd) prime field. It is usually called E/F_p.
The class is a subclass of ECGeneric.
characteristic can be odd prime. for characteristic == 2, use ECoverF2.
In general, given EC characteristic specified, you should call EC for your profit.
Returns a random point on elliptic curve.
computes t such that #E(Fp)=p+1-t, where #E(Fp) stands for the number of points of elliptic curve over Fp. This uses the Schoof's method.
computes t such that #E(Fp)=p+1-t, where #E(Fp) stands for the number of points of elliptic curve over over Fp. This uses the Shanks-Mestre method.
computes t such that #E(Fp)=p+1-t, where #E(Fp) stands for the number of points of elliptic curve over Fp. This uses the Legendre-symbol method.
computes #E(Fp). If p<1000, this uses the Legendre method. If 10^4<p<10^30, this uses the Shanks-Mestre method. Otherwise, it uses Schoof's method. If flag=r, this computes #E(Fp^r) .
returns <P,Q>_m by using Miller's algorithm.
returns T_m(P,Q):=<P,Q>_m^((ch-1)/m) by using Miller's algorithm.
returns e_m(P,Q) by using Miller's algorithm. suppose divisor class is [0].
returns m such that mP=[0].
returns m such that Q=mP. P, Q are in the subgroup of order n.
returns the group structure (n1, n2) of the E(Fp) by using Weil Pairing.