# Re: Elliptic curves

*From*: mm <nowhere@net>*Date*: Thu, 06 Aug 2009 23:32:08 +0200

pubkeybreaker a écrit :

In my 2nd post to E. S�ylemez, I wrote

|With a curve E(A,B)/N, N being the product of two "big" different

|primes, the order is not easy to compute (but we can build such a curve

|with a known order when we know the factorization of N).

I thought it made it clear that the computations are done with the curve

E(A,B)/N where N is not a prime.

E(A,B) mod N where N is composite does not even form an

Elliptic Curve.

Exactly like 0..N-1 is not a group with the multiplication and it does

not prevent RSA to work.

Using the bijection E(A,B)/N ~ E(A,B)/P x E(A,B)/Q, we can define an

addition on E(A,B)/N such that, with this addition, E(A,B)/N is a group.

And this is sufficient in order "to mimic RSA with ECs".

.

**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

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

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

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