Re: could it be a trapdoor

laicko wrote:
> if E(K) is a elliptic curve over a finite field K, then we could
> construct a subgroup with order N.
> Let N=p*q, p and q are both big prime.
>
> Then here comes my question:
> if we make N in public , let p and q in secret,
> let the points in this subgroup is the plaintext space,
>
> then could we can conclude that: if we let e<N, then to compute eM from
> M is easy and compute M from eM is hard?

No, because counting the order of a composite order curve is no harder
than a prime order curve.

Also we need 1/e mod N not phi(N) so whether you give out N or they
find it themselves they can find 1/e and decrypt.

Tom
Received on Mon May 1 01:53:22 2006