[Cryptography] Yet another dumb crypto system

Viktor Dukhovni cryptography at dukhovni.org
Thu Sep 24 23:24:26 EDT 2015

On Thu, Sep 24, 2015 at 02:58:53AM +0000, Viktor Dukhovni wrote:

> To avoid such problems you'd want x and y to be roots of distinct
> irreducible quadratic polynomials.  This then turns your system
> into a degree 4 Galois extension of F_p.

For the record the degree would of course be 2 not 4.  For odd p,
all quadratic irreducible polynomials split once the F_p is augmented
with a square-root of any non-square element.  (And for p=2, there
is only one quadratic irreducible polynomial over F_p in the first


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