# Re: Elliptic curves

• From: mm <nowhere@net>
• Date: Thu, 06 Aug 2009 11:59:57 +0200

a écrit :
mm <nowhere@net> wrote:
But I was not writing a math paper, [...]

Correctness still matters.

Like telling me that we cannot use ECs to mimic RSA because computing
"e'th roots (at least for small e) on an elliptic curve over a finite
field" is easy? In short, you do not even know what I am thinking of
but that's not what can prevent you to explain me why it cannot work!
Correctness still matters... :-)

The only goal of my post to E. Söylemez was that we can make RSA with
ECs because we need a group, not a ring. Now, maybe I should have
written "a group with the good properties", it would have been
sufficiently fuzzy to avoid misplaced comma hunters. (Btw, since you
knew that what we need is a group and not a ring, why didn't you tell
him? Did correctness not matter two days ago?)

Let's say, E(A,B)/N (E_N for short) is an elliptic curve modulo N.
What I am thinking of is to use a bijection between E(A,B)/N and
E(A mod P,B mod P)/P x E(A mod Q,B mod Q)/Q with N = PQ, P and Q
primes and 3 < P < Q.
This bijection maps a point (X,Y,Z) of E_N to the couple of points
((X mod P,Y mod P,Z mod P),(X mod Q,Y mod Q,Z mod Q)) of E_P x E_Q.

Now you have enough information in order to explain me why it will
not work.
.