Re: Elliptic Curve RSA

xmath wrote:
> hassan.jameel@gmail.com wrote:
>
>>Let p,q be two primes and let n=pq. Let 'e' be the public key and 'd'
>>be the private key such that ed is congruent to 1 mod phi(n) . (just as
>>in RSA). Now let EC denote an elliptic curve over the field Zn
>
> You can stop there. Zn is a field if and only if n is prime.

   Elliptic curves cryptography using y**2=x**3+a*x+b works when x and y
range over a prime-order set. The equation y**2+x*y=x**3+a*x+b (IIRC)
works when x and y range over a set of 2**n elements. To keep the OP's
question interesting can we reformulate to "Is there an equation that
can be used for ECC when x and y range over a set of N elements, where N
is the product of two primes?"?
   Note: I'm over my head here. I have no idea why y**2=x**3+a*x+b
wouldn't work for powers of 2, nor, if they don't, why prime order sets
don't work with y**2+x*y=x**3+a*x+b.

--Mike Amling
Received on Mon May 1 02:06:13 2006