Just Think About It.

A point is a geometric figure, it has position but no magnitude.
Let’s give it some magnitude just for discussion purposes and say a
point is the size of a full stop (period) on this page. Given that
I’m talking about points in the whole of three-dimensional space in
the universe I can afford to be generous with the magnitude or ‘size’
of a single point.

Any point in three-dimensional space may also be seen as the point of
intersection of an infinite set of hidden non-parallel straight
lines. Relative to any other point in three-dimensional space each of
these lines can be defined by a unique vector equation.

In passing, it can also be said that any point in space is the
intersection point of an infinite number of sets of three non-parallel
planes in three-dimensional space. (Three non-parallel planes
intersect at a point, two non-parallel planes intersect along a
straight line.)

These hidden lines in para 2 can be commissioned as ‘number-lines’ –
in crypto practice only one line is taken for one only plaintext -a
dedicated line that is for each plaintext. There is a natural
periodic positioning of the integers (the scale) that is always fixed
on such a line. The scale relates to the direction of the line, the
integers are not generally scalable and effectively still have integer
coefficients later on when represented as a displacement vector.

If these lines are used now in an “assign now-retrieve later” ploy as
the obfuscation part of a cipher then any line can be used and the
remainder of the infinite set (minus 1 now), of unused lines are
‘collisions’ per se. Only one line is used to define the positional
point of a single plaintext in hand for encryption by assignment to
that line and the remainder of the unused infinite set of lines are
discarded on this occasion. Because the lines intersect at the same
point that represents the plaintext on the bona fide chosen number
line, the coordinates of the point on this genuine line also satisfy
the equations of all the other (redundant) lines in the infinite set,
since they each also contain the point and the plaintext can therefore
be defined by the equation of any of these other unused lines in
space. The equations of these lines are impossible to find by a
cryptanalyst however. They are collisions in the metaphorical sense of
crypto jargon. (Digressing to another use - as it happens, they would
also constitute unwanted physical collision courses in say air traffic
control or surface ship navigation but would be ideal for aiming
devices probably).

Compare this now to the status quo in cryptography where the same line
is used over and over again for all encryptions. The line in question
was designed by mathematicians so as to have maximum transparency and
to be infinitely scalable. The line may have any direction and it has
no equation worth mentioning. Cryptanalysis is invited by the sheer
simplicity of this beautifully simple model that was never intended to
be devious in the first place so why continue with it in scalar
cryptography is an obvious question. That cryptography then requires
enormous complexity of method to try and hide the innate transparency
of what can only be called ‘weak’ encryption data. The pursuit of
pseudo-randomness so as to achieve this complexity is further
questionable.

Scalar is the scientific name for quantities that are not vector
quantities. Scalars may be defined by their magnitude only, a single
number that may include attached units suffices for scalars while
vectors have two distinct parts, that is both a magnitude and a
direction. The magnitude of a vector is a scalar. The methods of
computation for these two data types are very different and require a
prodigious study for the understanding thereof.

These hidden lines above are perfect for hash functions but why stop
there, a high-speed loop that can repeat the entire point selection
process using a different point from a different infinite set of
points, then sequentially reading in plaintexts from an external file
one at a time and performing ‘encryption by hashing’ of these
plaintexts in one visit, becomes a cipher. It is a vector stream
cipher in fact (don’t bother pointing out minor inexactitudes here,
the focus is on the broader concept). Such a cipher is up and running
by this writer.

The foregoing is a broad outline of vector cryptography.

There is a case for both scalar and vector cryptography to coexist in
today’s world of computer-driven cryptography. There is a case also
for existing office software to be commissioned for creating both hash
functions and full length encryption of messages. Microsoft ‘Excel’
software is in mind. No knowledge of vector methods is needed for a
keyboard operator to make a repetitious, unchanging sequence of simple
arithmetical computations using that software to produce vector cipher
text or indeed alphanumeric cipher-text also. The result is
theoretically secure communication of information by operators of
database and spread*** software doubling now as crypto operators –
an attractive prospect. A high speed loop for inclusion in the
software source code should be possible by the owners of ‘Excel’.

This concept could prove to be an enormous boost to business methods
and commercial office software in general as well as being an
enhancement of the ‘Excel’ software.

Go to http://www.adacrypt.com and see - “A New Approach to
Cryptography”

God Bless Barack Obama.

Cheers – Adacrypt

.

Loading