elliptic curve reference point P0; an encoder, configured to perform binary coding on an input elliptic curve coefficient; a divider, configured to divide the elliptic curve coefficient binary code into N segme
The remaining points that are allowed to run through the math routines may not be order q. Recall that about 3/4ths of the points on the curve are of order 4q rather than of order q. Despite the use of efficient endomorphisms during point multiplication, these exceptional points are handl...
We will rely on some Magma calculations [26] that can be verified in the free calculator on the official site of this computer algebra system. The next lemmas are proved by means of the reduction to a Weier- strass form of . Lemma 1. [26] The F-curve is elliptic with the j-...
) on the elliptic curve Ec(a, b): y2≡x3+ab+b(mod p) is made into the ordinary sentence at the original point (xp, yp) if this cipher sentence is further subjected to dp multiplication, where p is the least common multiple calculated by a first least common multiple calculator ...
PURPOSE: To decrease the number of times of addition, subtraction multiplication and division and to shorten the time for forming keys by determining integers (u), (v) satisfying p=u2-uv+v2 required for formation of the keys without making computation of complex integers. ;CONSTITUTION: A ...