# 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.

.

**Follow-Ups**:**Re: Elliptic curves***From:*Kristian Gjøsteen

**Re: Elliptic curves***From:*pubkeybreaker

**Re: Elliptic curves***From:*Tom St Denis

**References**:**Elliptic curves***From:*Giuliano Bertoletti

**Re: Elliptic curves***From:*mm

**Re: Elliptic curves***From:*Kristian Gjøsteen

**Re: Elliptic curves***From:*mm

**Re: Elliptic curves***From:*Kristian Gjøsteen

- Prev by Date:
**Re: DES keys** - Next by Date:
**Re: Elliptic curves** - Previous by thread:
**Re: Elliptic curves** - Next by thread:
**Re: Elliptic curves** - Index(es):