Re: RSA: more than one secret exponent d exists ???
- From: Kristian Gjøsteen <kristiag+news@xxxxxxxxxxxx>
- Date: Tue, 6 Jun 2006 18:15:38 +0000 (UTC)
Sebastian Gottschalk <seppi@xxxxxxxxx> wrote:
Kristian Gjøsteen wrote:
Sorry. I'll try to sketch the argument below, with as little
mathematics as possible.
[...]
Still too complicated. Why not the easy way with some algebra?
The point was to minimize mathematical content. Applying algebra (or
whatever you are applying) is not minimizing mathematical content.
The ring Z_n is a multiplicative composition of the mutually exclusive
rings Z_p and Z_q (with respect to multiplication).
This doesn't mean anything, it's nonsense. What you probably wanted to
say is that as Z_n* is isomorphic to Z_p* x Z_q* (drop the stars if you
prefer rings). For those who care, the isomorphism is given by CRT.
This also shows that RSA can be applied to any finite fields and their
composition, where the decomposition of the composite is a well-known
hard problem.
RSA-type problems aren't factorization-like problems. They are e'th
root problems.
--
Kristian Gjøsteen
.
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