Counting points on an elliptic curve
SMRTR summary
Counting points on elliptic curves can be done using three methods: brute force, checking x values, and Schoof's algorithm. Brute force takes O(p²) time, checking x values takes O(p log³ p), and Schoof's algorithm takes O(logᵏ p). For cryptographically large curves with p ≈ 2²⁵⁶, only Schoof's algorithm is feasible, requiring about 2⁶⁴ operations, while the other methods are impractical.
SMRTR provides this summary for quick context. The original article belongs to John D. Cook.
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