Joint Thin Tile Cryptography - Bqatch and Real Time.
- From: austin.obyrne@xxxxxxxxxxx
- Date: Tue, 31 Mar 2009 03:35:30 -0700 (PDT)
The writer has invented “Thin Tile Cryptography”.
This is a powerful implementation of “Vector Cryptography”. A salient
thing about this cipher design is that it demonstrates the strong
cryptography that emanates from the use of definitively structure-less
data i.e. lumpy, discontinuous, volatile thin tiles as the raw
encryption data in vector cryptography, compared with the highly
structured scalar-numbers data in current number-theoretic
cryptography, (scalar numbers means the use of numbers as a type of
scalar in the context of scalar cryptography – not all scalars are
numbers but all numbers are scalars => scalars as non-vectors might be
more explicit.
The alphanumeric data of ASCII and Unicode are scalars.
A Thin Tile working program is up and running. A download will be
made available later to readers of sci crypt that contains 1) working
program source code, 2) a language compiler and 3), a pdf description
document.
Comment.
Vector Cryptography.
In vector cryptography number lines are defined by their vector
equation and are not just of arbitrary direction as in scalar
cryptography. Integers retain their names and their iconic shapes but
they are not scalable per se, any more. Furthermore, integers and
float values may be represented by a scalene triangle that is of a
different shape for each value of integer and float. Only integers are
needed here for cryptography. A scalene triangle is one in which no
two angles are equal. In this cryptography, the triangles also have
planar attitude, i.e. orientation in space relative to an XYZ frame of
reference.
In this method of presenting numbers in vector cryptography, any
integer may be graphically represented by any one of an infinite
number of permutations of scalene triangle. All computations are done
by manipulations of such scalene triangles, larger triangles are tiled
by smaller triangles to perform division, etc. The scalene triangle
representation of integers is volatile from case to case and it is
virtually certain that a different set of scalene triangles will be
used next time to represent the same set of integers as of now,
although this is not essential to secrecy. The implications to
cryptography are very obvious here.
It may seem that this is a very tedious time-consuming matter of
laborious trigonometrical computations involving the ‘cosine’ rule but
that is not so, thanks to the invention of physical vector mathematics
by Rowan Hamilton circa two centuries ago, all calculations are
resolved by simple vector methods.
Thin Tile Cryptography.
This is an implementation of vector cryptography in which integers are
always represented by scalene triangles. The integer representing a
plaintext is encoded by vector methods into a unique scalene triangle
at each enciphering of a plaintext. The scope of the set of scalene
triangles is infinite, the scalene triangle in hand is next encrypted
into vector cipher text. The benefit of using scalene triangles is to
provide data that has minimal structure and minimal methodology thus
avoiding residual structure in the cipher text that is exploitable by
a cryptanalyst. A simple to understand algorithm provides an equation
that has to be satisfied, this involves nothing more than the vector
cross product and scalar multiplication of a vector. It is to be
assumed that a computer is de rigueur in any modern crypto
infrastructure and once the algorithm is understood then all theory
goes under the bonnet (hood) of the computer automobile and the crypto
‘driver’ just forgets about it. Longhand working by means of a
handheld computer is quite feasible also if that is required for
whatever reason.
Strong cryptography becomes self evident as the reader comes to
understand the mathematics of this cipher and the writer is strongly
of the belief that this cryptography will figure a lot in future
secure communications especially after the arrival of quantum
computers which could be much nearer than we think.
The writer holds that theoretically unbreakable cryptography is the
only cryptography worth bothering with and even if it comes at a high
price it is still cheap in today’s world of terrorism. Nice, highly
articulate, aesthetically pleasing cryptography is not an option.
The software to hand by the writer requires very little daily
administration and minimal training by a keyboard operator. It is
comprised of open source code in the Ada-95 programming language and
the only knowledge needed by an operator is being able to change some
parameters in the lines of source code on a regular basis and
responding to on-screen prompts during encryption sessions. The
office administrator simply decides on the parameters to be used for
the duration of a session.
In the writer’s view there is no ‘if ‘about quantum computers becoming
available to cryptanalysts in the coming years ahead, instead it is
more a question now of when will happen. When that happens it is
going to be the end of all modern ciphers – these will be shot to
pieces by the speed of these powerful machines. So what will
cryptographers do then is a good question. The writer believes that
these wonderful machines can only be used to cryptanalyse ciphers that
are ‘practically’ unbreakable. They will be stymied by the
theoretically unbreakable ciphers that are available here. Countdown
to the arrival of quantum computers has already started on the
international scene.
In other words then, the quest may then be on at national level for a
mathematically proven unbreakable cipher – a theoretically unbreakable
cipher in short. The focus shifts from a quantum computer that is
capable of breaking all modern ciphers to a cipher that is
theoretically unbreakable by that same computer, such a cipher does
not exist in the tool box of secure communications in the status quo.
The cipher described in the download pdf that is called , “Joint Thin
Tile –Batch and Real Time” is mathematically proven to fit that bill
however, it can be demonstrated with complete proof at the highest
level in mathematics.
Any advances in computer manufacture can only benefit this vector
cipher unlike the current scalar ciphers that are in constant jeopardy
from that same possibility. A very significant step nearer to the
realization of a working quantum computer was reached on (25/03/09) –
see internet - due to groundbreaking work by researchers in Manchester
and Edinburgh universities. Progress in Russia, Iran, China and India
is not to hand.
The writer is convinced that our number system that is so good at
what the Arabs meant it to do initially is totally unsuited for
today’s number-theoretic cryptography because very simply, it
possesses so much indelible structure and such vast methodology that
it will always leave footprints of residual structure in the cipher
text. It is amazing to the writer that this fact has gone on
unnoticed for so long right up to the present day, beginning with the
early breed of number- theoretic cryptographers in the seventies, who
relied entirely on pure mathematics and number theory and eschewed the
burgeoning power of the then new computer science and the long
established applied mathematics that was available to them. The
result is today’s partly secure industry, one that will never stop
wrestling with its defects.
Not all of the number system and its axioms is usually necessary at
the time of any encryption but the cryptographer isn’t allowed to be
selective – using the arbitrary number line of number theory alone is
committing him/her to huge redundancy, hence the need for a customized
number system of analogue representation of numbers that has less
structure and methodology to it but is sufficient for a dedicated,
isolated one-off application to cryptography only. Crypto readers
should not have difficulty agreeing to this, you should not have to
take on a dairy farm when figuratively all you need is a pint of milk
by analogy.
At the risk of excessively laboring the point, using arithmetical
methods and integers taken from an arbitrary number-line in current
cryptography opens the back door to a huge array of extra methods that
are not needed by the cryptographer but are very useful to a
cryptanalyst – to the cryptographer it is the equivalent of a
figurative infection being picked up at vaccination time.
The benefit of using an analogue to represent integers is that the
analogue will almost certainly not have the hugely pervasive structure
of the scalar number it is representing nor will it have such a huge
methodology. Using analogues of the numbers solves the problem of
excessive structure and the profusion of cryptanalytic methods of
cipher text that are grist to the mill for cryptanalysts but are
unwanted and problematic to cryptographers.
Any analogue, other than vectors which is just one instance from
mathematics in this case, or physics or engineering will do fine if
the methodology of that data-type can include being reversible at
decryption time. Readers may know of some others.
The substitution that is used in some cases in integral calculus might
be taken as a role model here for cryptography. That is done in
calculus when the integrand cannot easily be integrated and a
substitution data type is used to temporarily represent it during the
integration metamorphosis making it easier to integrate. The
methodology of the substitution is used to take it through the
integration process and it is then changed back to the original data-
type at the end, thus completing the operation of that particular
integration. Similarly, encryption – transmission – decryption may be
modeled on this.
It could be logically said that this encryption ploy is an adaptation
of the universal set of integers. By means of a vector transformation
it changes the Arabic integers of the universal number system into a
substitution set of area analogue units, thus changing the raw
encryption data from integers into scalene triangles. It could be
jargonized as graphical algebra or data preparation. The scalene
triangles themselves are more the effect than the cause of anything.
They are ‘fallout’ of the vector encryption methods being used, useful
more as pragmatic proof of the vector encryption methods, rather than
the active creators of cipher text.
“Thin Tile” is an instance of vector cryptography that has other
methods also such as “Skew Curve” (see website).
Summarising,
Encryption is done by defining the vector sides and the planar
attitude in space of scalene triangles that represent the plaintext.
Decryption is done by reading these scalene triangles and converting
them back to plaintext. The result is theoretically unbreakable vector-
driven cryptography.
Abstract.
Let the reader allow that scaling means separating integers by means
of equal short line segments of arbitrary direction in two
dimensions. Then in three dimensions these line segments become areas
i.e area analogue representation of integers is the equivalent scaling
in three dimensions. Each scalene triangle is then a distinct extra
icon (tertiary to its Arabic icon) that is unique to that integer for
that particular direction of number line in three-dimensional space.
A whole new branch of mathematics is imminent. This is pursuable as
mathematical research but under a different banner. So far, the
writer has defined multiplication, division, addition, subtraction,
logarithms by tiling. Any body interested in pursuing this further?
Enjoy - adacrypt
.
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