I've tried to use this algorithm in PARI/GP with the following code, just to check if it works, it doesn't output m but the indexes [i,j] of R+iQ=jP. Ellpoint finds a random point on the curve, ellsum makes the sum between two points, ellpow(E,P,n) compute the scalar multiplication nP. But it...
The baby-step-giant-step method to compute the number m of rational points over an elliptic curve defined over \mathbb{F}_p
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In the second part R=(p+1)P, but for every point on the curve (p+1)P is the identity...
I found that the endomorphism group over an elliptic curve is isomorphic to a complex quadratic order:
End(E)\simeq \mathbb{Z}[\delta]=\mathbb{Z}+\delta\mathbb{Z},
where
\delta=\frac{\sqrt{\Delta}}{2} if \Delta is even
\delta=\frac{1+\sqrt{\Delta}}{2} if \Delta is odd
Does anyone know where...