Re: Funny Thing About Number-Theoretic Vector Ciphertext .

On Wed, 08 Feb 2012 23:54:30 +1000, adacrypt <austin.obyrne@xxxxxxxxxxx> wrote:

On Feb 8, 12:45 pm, adacrypt <austin.oby...@xxxxxxxxxxx> wrote:
Ciphertext that has been generated using random keysets as I do in
this new displacement cryptography is secured against all attacks in
several ways. The attack I have in mind here is when an external
statistical attack is made on the ciphertext string on the basis of
frequency of occurrence of the elements of the string that might
enable probabilistic mapping of the ciphertext directly to plaintext
(as message text) thus successfully circumventing the proper
decryption algorithm by an illegal cryptanalyst.

I’m speaking of vector ciphertext here that has three columns of non-
zero integers that may contain elements that may be variously positive
or negative.

Usually ciphertext strings in any form are usually not random (i.e.
having equal probability) albeit created using internal random keysets
that make them secure against other more direct attack there is always
the chance therefore of external attack by Eve hoping that there is
sufficient discernable giveaway correlations in the frequency of the
ciphertext elements that might enable a Kasiski-Babbage style attack
on the ciphertext, using frequency as the basis of a statistical
mapping operation.

Random ciphertext here means the elements of the ciphertext string
having equal probability and supposing the ciphertext string to be
considered as a keyset itself in some attack such as the one I
described above i.e. a statistical attack.

With this in mind I have been conducting experiments on finding the
frequency of large ciphertext strings of numeric ciphertext via the
three column vector coefficients of (i, j, k) using a file of
encrypted 10852 alphanumeric characters that comprise the ciphertext
i.e. the ciphertext that emanates when this file of plaintext is
encrypted into the number-theoretic ciphertext. I am seeking to
secure that back door from ever being opened by Eve.

The experiment is still ongoing but one interesting result is this
(might be obvious to many readers), the larger the integers involved
as coefficients of (i, j, k) in the ciphertext the nearer the
ciphertext string gets to becoming truly random and of course stronger
in resisting statistical attack.

I must explain here that I rate anything less than 100% truly random
as the inferior pseudo random type – that latter level is not
acceptable as true random quality keys for ‘internal’ encryption but
as an external property of ciphertext it is very welcome when it is up
in the 95% level – virtually random you might say in the context of
being external and not as crucially important as the internal
encryption keysets. It is possible to make it totally random however
i.e. 100% truly random but the law of diminishing returns comes into
effect then because the volume of the enchanced cipher text becomes
very great by comparison with AES for instance and it becomes
expensive to process secured information then by vector means.

I have no hesitation meanwhile in saying that “Displacement
Cryptography” implemented by vector means can be summarised as being
demonstrated as rock solid on all fronts.

A down side of displacement cryptography is of course the very large
ciphertext expansion ratio - that may have to be seen as a price to be
paid for cryptography that is both theoretically unbreakable and
immune to computer power for all time

More later as it evolves.

- adacrypt

Supplementary Thread to “Funny Thing etc …. “

This is the frequency spread of the cipher results to hand. The
experiment was totally unrehearsed and unbiased.

10852 characters were encrypted

9181 no repeats of numbers as ciphertext => 9181 = 84.6 % random
746 numbers as ciphertext repeated once => 1492 = 13 .7 % random
57 numbers as ciphertext repeated twice => 114 = 1 % random
2 numbers as ciphertext repeated three times => 4 = 0

Clearly, this data would be worthless to any adversary as a means of
statistical attack on the ciphertext. Alice could even hand the
ciphertext to Eve outrightly and be assured that It cannot be broken.

- adacrypt

Um, the German Enigma was what you are calling 96% random - and it was badly flawed and broken. By your own figures your's is 4 times worse.

We have failed to address the fundamental truth that endless growth is impossible in a finite world.