An Introduction to Elliptic Curve Cryptography - Introduction to Cryptography with Maple - page 622

y := numtheory:-msqrt(z, p);
if y <> 0 then
EP := [op(EP), [x, y], [x, -y mod p]]
else
EP := [op(EP), [x, y]]
end if;
end if;
end do;
[0, op(EP)]
end proc:

Example 11.4 Let us compute the list of all points on the elliptic curve over F 2017

given by the equation y 2 x 3 669. We do not print the list as it is too

long but we will plot the curve to appreciate its appearance:

= + 578 x +

> ep :=EllipticPoints(EllipticCurve(578, 669, 2017)):
nops(%);

2087

We see that the curve has exactly 2087 points. Next we plot it:

> epp := plots:-pointplot(ep[2 .. -1], symbol = solidcircle, symbolsize = 9):
> plots:-display(epp);