# Re: Elliptic curves

• From: mm <nowhere@net>
• Date: Wed, 05 Aug 2009 17:23:35 +0200

a écrit :
mm <nowhere@net> wrote:
As a matter of fact, to mimic RSA, there is no need of a ring. All we
need is a group whose order is difficult to compute (except to the one
who built this group). So we could do RSA with ECs but it would cost
too much in space as well as in time.

No. You need a group where computing e'th roots is hard. Computing e'th
roots isn't hard unless it is hard to compute the order of the group,
but the converse need not be true.

But I was not writing a math paper, I was just saying that what we need
is a group, not a ring. (Of course, we cannot make use of any group.)

Univariate polynomial equations are easy to solve over finite fields.
Therefore it is easy to compute e'th roots (at least for small e) on an
elliptic curve over a finite field without computing the group order.

Who did talk of a curve over a finite field?

mm
.

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