lsfr with odd charecteristics

[Mike Rosing]

On Tue, 11 Jun 2002, gfgs pedo wrote:

> Book says, a construction  that involved computing
> LSFR's  over a field of 'odd charecteristics'
> is insecure.
> Does that mean a register with odd number of bits is
> insecure which would mean a tap sequence which
> uses an odd degree polynomial is insecure?

No, if you use bits for coefficients you are still in GF(2^n).
What "odd characteristic" means is that you are in GF(p^m) with
p odd (say 3 or 5 or 9).  So you have a polynomial of the form
x^3 + 4x^2 + 3 mod 5 is GF(5^4).  5 is the characteristic of
the base field, and since it's odd it's a bad lfsr for crypto.

Patience, persistence, truth,
Dr. mike