A burst of research activity has lead me to a set of relatively simple
congruences that change everything with factoring by allowing you to
calculate z mod p and y mod p, when z^2 = y^2 + nT, and the first
thing that happens when I get to a new research result is that I look
for problems in my reasoning or anything that might mean that I'm just
wishing for an answer versus having found one.

Thanks to some arguing back and forth on the newsgroups where some
people did notice problems I was pushed to find a full existence proof
and now have a complete theory, so I can puzzle over all the details.

Importantly as well, as I argued the ideas simplified, so that, for
instance, for a while I thought you had to resolve quadratic residues
to find y, but with the existence proof I got congruences that just
give you y.

Also, importantly, I can now begin a full evaluation of resistance to
my mathematical research across the board with the continuing silence
from the official mathematical community with this result giving
important clues.

When i first started taking my pet project seriously, I was told I should
look into compression as part of the encryption scheme, that is to say
encyphering a message and then compressing it. Unfortunately I have only
ever found one suitable implementation, but that method was so intertwined
as to make it almost impossible to distinguish the compression with the
encryption (the message string was compressed and then encrypted), so I let
it fall by the wayside for many moons.

Recently I have become interested in the compression side of the idea again
but still can not find any suitable implementations.

What I am looking for is an implementation that will accept a string,
compress it, and then pass it back to the encryption module for processing,
I am after the actual implementation not the modules that comprise the
implementation.

The idea (possibly a bad idea) is to compress a string, encrypt it and then
pass the string back to the compression algorithm for further compression.

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