Re: Elliptic curves



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".
.