Re: Elliptic Curve RSA
- From: "nathan@xxxxxxxxxxx" <nathan@xxxxxxxxxxx>
- Date: 30 Apr 2006 00:48:58 -0700
Sorry, but your question does not help, even if you found an answer.
The question you probably meant to ask, is: how do you find elliptic
curves with N points, where N is the product of 2 primes? I don't know
the answer to that question.
To answer your question as to why the equation doesn't work for powers
of 2, the answer is very easy: the equation y**2=x**3+a*x+b is in the
so called weierstrass normal form. If the field is not a power of 2,
then every elliptic curve can be transformed to the normal form. If the
field is a power of 2, then 2 has no multiplicative inverse, and so you
can not complete the square. You therefore can not bring every elliptic
curve to the weiserstrass normal form.
Oh, and by the way, RSA lives in a monoid, not a field or group. Since
elliptic curves have a group structure, they are also monoids. That is
why RSA is possible. Just because it is possible does not mean it is
secure.
.
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