# Re: Funny Thing About Number-Theoretic Vector Ciphertext .

*From*: "David Eather" <eather@xxxxxxxxxx>*Date*: Fri, 10 Feb 2012 06:22:17 +1000

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.

.

**References**:**Funny Thing About Number-Theoretic Vector Ciphertext .***From:*adacrypt

**Re: Funny Thing About Number-Theoretic Vector Ciphertext .***From:*adacrypt

- Prev by Date:
**Re: Is this a side-channel attack?** - Next by Date:
**Random Numbers from Text Files** - Previous by thread:
**Re: Funny Thing About Number-Theoretic Vector Ciphertext .** - Next by thread:
**Re: Funny Thing About Number-Theoretic Vector Ciphertext .** - Index(es):