ECC point compression trick

Think about what mm said ... why can't we just always use one of the
roots?

e.g. you have

y == +/- sqrt(x^3 - 3x + b)

Why not always just use the positive root [adjusting your secret
multiplier as required since (-k)P == k(-P)].

You still have to compute the root to find y but now you don't even
send the one bit. You just send x.

This halves the key space but I don't see how that causes any practical
problems. You're still going to have to cycle find it.

Tom

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Relevant Pages

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  • Re: complex numbers
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  • Re: ECC point compression trick
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  • Re: ECC point compression trick
    ... The negative root would be the one you find by negating the other root ... (But typical Tom reply) ... define the positive root as the one that is less than p/2. ...
    (sci.crypt)