could it be a trapdoor



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?

.



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