# Re: could it be a trapdoor

*From*: Kristian Gjøsteen <kristiag+news@xxxxxxxxxxxx>*Date*: Wed, 29 Mar 2006 19:27:55 +0200

laicko <yichun.zhang@xxxxxxxxx> 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?

As Tom said, you only need 1/e mod N, not mod phi(N). It does not

matter if you publish N, point counting is easy in this context.

Second: I believe it is possible to extract e'th roots on an elliptic

curve even if you do not know N, at least if e is small. Simply

compute symbolic equations for multiplication by e, then solve them.

You can try yourself with e=2 and e=3.

--

Kristian Gjøsteen

.

**Follow-Ups**:**Re: could it be a trapdoor***From:*laicko

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