Elliptic Curves Math

Page #4355473 of Chapter: Crypto-for-the-rest-of-us

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We define an arbitrary way to "add" two points on a curve, called an ECC curve:

Then we cast the curve into the 'straight jacket' of modular arithmetic, such that the values of A, B, X, and Y will be mapped into a modular set: 0,1,2,.....(p-1). We find some k points (X,Y) that satisfy the ECC equation, such that adding (in the ECC way) any two points yields another point from a k-elements set. This defines: Q = nP, and n = logP(Q).

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