š§® **The GLV Endomorphism: Why secp256k1 Is Fast**
The curve y² = x³ + 7 has a secret weapon: because a = 0, the curve has j-invariant 0, which means it possesses an endomorphism of degree 3 ā an algebraic map from the curve to itself that is not just a scalar multiplication. This endomorphism, discovered and exploited by Gallant, Lambert, and Vanstone (GLV) in 2001, enables a technique that reduces the number of point doublings in scalar multiplication by half, yielding a roughly 33% speedup.
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