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Update ch04.asciidoc

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Added 8G for completeness and as depicted by image.
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krupawan5618 2021-02-24 20:45:50 -05:00 committed by GitHub
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@ -232,7 +232,7 @@ y = 07CF33DA18BD734C600B96A72BBC4749D5141C90EC8AC328AE52DDFE2E505BDB
To visualize multiplication of a point with an integer, we will use the simpler elliptic curve over real numbers—remember, the math is the same. Our goal is to find the multiple _kG_ of the generator point _G_, which is the same as adding _G_ to itself, _k_ times in a row. In elliptic curves, adding a point to itself is the equivalent of drawing a tangent line on the point and finding where it intersects the curve again, then reflecting that point on the x-axis. To visualize multiplication of a point with an integer, we will use the simpler elliptic curve over real numbers—remember, the math is the same. Our goal is to find the multiple _kG_ of the generator point _G_, which is the same as adding _G_ to itself, _k_ times in a row. In elliptic curves, adding a point to itself is the equivalent of drawing a tangent line on the point and finding where it intersects the curve again, then reflecting that point on the x-axis.
<<ecc_illustrated>> shows the process for deriving _G_, _2G_, _4G_, as a geometric operation on the curve. <<ecc_illustrated>> shows the process for deriving _G_, _2G_, _4G_, and _8G_ as a geometric operation on the curve.
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