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The Ladder-Step function (given below) used within the ladder is the core of the algorithm and is a combined form of the differential add and doubling operations. The field constant a 24 is defined as a 24 = ( A + 2 ) / 4 {\displaystyle (A+2)/4} , where A {\displaystyle A} is a parameter of the underlying Montgomery curve .
The algorithm always takes a step in the positive direction (upwards), and occasionally takes a step in the slow direction (the negative direction). From the circle equation is obtained the transformed equation x 2 + y 2 − r 2 = 0 {\displaystyle x^{2}+y^{2}-r^{2}=0} , where r 2 {\displaystyle r^{2}} is computed only once during initialization.
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