Speeding 2x isn't enough to enable attacks when they already take exponential time. It applies most commonly to curves with an equation of the form y^3 = x² +

Speeding 2x isn't enough to enable attacks when they already take exponential time. It applies most commonly to curves with an equation of the form y^3 = x² + b which mathematically imply that (x, y) and (x, cuberoot(y)) are both points on a curve and so you can split a n bits scalar into two n/2 bits scalar and do double scalar multiplication.