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From: adacrypt on 29 Jun 2010 08:15

The cryptography of sporadic mapping of plaintext to wildly disparate
integer points in space that I am promoting on my website http://www.adacrypt.com
has one or two ‘sinister’ points that are worth noting. Mathematician
readers will appreciate the curio value also of these truisms in three-
dimensional space methodology although it is not being allowed to
affect the crypto strength of the ciphers here that use it.

The encryption transformation in this spatial crypto type is from a
character in ASCII to an integer point in space that is defined by the
coordinates of a position vector that mark its position on a directed
number line in space. The position vector is given a reversible
change-of-origin before it is ascribed as the cipher text
corresponding to that plaintext. That is the backbone of the one-way
function that underpins this cryptography. Decryption is largely
comprised of the symmetric inverting of this process after first
reversing the change-of-origin in the cipher text.

Note well – as a generalisation: (the point being made)
Every point in three-dimensional space is the common intersection
point of an infinite number of invisible hidden lines in space –
particular lines (encryption lines) might be there for the finding by
a cryptanalyst.

Also, and more important to this cryptography:
Every straight line in space is the line of intersection of an
infinite number of hidden planes – again, these planes are there for
the finding by a cryptanalyst.

These geometric facts were investigated by me during a search for
latent ‘back doors’ in the vector ciphers that are to hand. My
initial reaction on finding this perceived weakness was grief until I
realised that these facts could be used with profit as the basis for a
particular version of vector cipher in the series of four ciphers that
I have invented.

All of the vector ciphers currently to hand are unbreakably secured by
means of the change-of-origin ploy that is used in the algorithm.
There is no implied weakness in this exposition of what might be
called a possible back door to cryptanalysis. This extraordinary
cipher version is largely of academic interest. There is no danger
whatever in using the derived method that emanates from it.

The cipher in question uses the position vector above i.e the one that
Alice computes in her encryption algorithm in the transformation of a
plaintext, as the direction vector of the line of intersection of a
hidden family of planes that all intersect along it – i.e. each plane
in the family contains Alice’s position vector. This fact enables Bob
to evaluate her message text without any knowledge of how she created
it by selecting one of the planes in the family and using it to derive
a decryption key.

How it Works.
Normally, Alice sends a position vector within her cipher text that is
called called Pn to which Bob pairs another vector called N with it,
(he reads N directly from his mutual database to hand) and these two
vectors comprise the decryption keys that enable the decryption
process to be completed.

In this extraordinary vector cipher i.e.Vector Cipher_4, Bob uses Pn
twice - 1) as Pn in its designated role as a position vector and 2) he
uses it again to double as the normal vector in a substitution for N.
This latter dispenses with the need for knowing N explicitly. Bob
then proceeds with the decryption process as usual, using these as
decryption keys.

The resulting cipher, Vector Cipher_4 is no more or no less secure
than any of the other ciphers in the series but it is very novel and
may yet have unseen particular uses in future infrastructure
management plans.

Visitor readers to my website will be assured therefore that the
possibility of attack by means of latent back door geometry has been
considered and pre-empted.

The cipher, Vector Cipher_4 is being offered (complete with working
compiler and descriptive PDF) as a free download from my website
http://www.adacrypt.com in the title box “ Download - Extraordinary
Cipher with Program Sourcecode “.

Cheers - adacrypt


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