8.1 Point Counting
نویسنده
چکیده
We now consider the problem of determining the number of points on an elliptic curve E over a finite field Fq. The most näıve approach one could take would be to evaluate the curve equation y2 = x3 + Ax + B for E at every pair (x, y) ∈ Fq , count the number of solutions, and add 1 for the point at infinity. This takes O(q2M(log q)) time. Note that the input to this problem is the pair of coefficients A,B ∈ Fq, which each have O(n) bits, where n = log q. Thus in terms of the size of its input, this algorithm takes
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