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elliptic_curves [2025/06/17 15:07] – [Operations] transatoshi | elliptic_curves [2025/06/17 15:08] (current) – [Operations] transatoshi | ||
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If we draw a line passing through P and Q, this line will cross a third point on the curve, R (so that P, Q and R are aligned). If we take the inverse of this point, which is simply the one symmetric to it about the x-axis, we have found the result of adding two curve points, P + Q. Let’s illustrate: | If we draw a line passing through P and Q, this line will cross a third point on the curve, R (so that P, Q and R are aligned). If we take the inverse of this point, which is simply the one symmetric to it about the x-axis, we have found the result of adding two curve points, P + Q. Let’s illustrate: | ||
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In other words, addition of points is basically hopping around on the curve to a different, seemingly random point; It looks random unless you know the exact operation performed to reach it. | In other words, addition of points is basically hopping around on the curve to a different, seemingly random point; It looks random unless you know the exact operation performed to reach it. | ||
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To calculate 8*P for e.g. wouldn’t take 8 operations, but only 3; you can find 2*P, then add it onto itself, and then add 4*P onto itself, for the final result of 8*P. | To calculate 8*P for e.g. wouldn’t take 8 operations, but only 3; you can find 2*P, then add it onto itself, and then add 4*P onto itself, for the final result of 8*P. | ||