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Old 2006-12-21, 18:19   #6
R.D. Silverman
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Nov 2003

22·5·373 Posts

Originally Posted by akruppa View Post
I asked Pierrick Gaudry, who has worked on elliptic curve arithmetic before, about this and he replied simply that he didn't know about this idea, either. Someone may well have investigated this before, but if so, it's not very commonly known, apparantly. Sounds like an interesting topic to delve into some more.

It is simple.

For a curve in the form y^2 = x^3 + ax + b, the parameter b does
not occur in the arithmetic when adding two points. So given
y^2 = x^3 + Ax + B for given A,B, a point (x1, y1) not on this curve
is instead on the curve y^2 = x^3 + Ax + B', where B' != B.

You are still adding points, but it is on a DIFFERENT curve from the one
you expect.
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