# Re: An Adaptation of the Traditional Number Line as a Derived Modular Line in Cryptography.

S1: P = plaintext char or byte?
S2: P' = P * k, where k = 10, being a denary (base 10?) system.
This creates a slot at the units digit of P', into which a binding of a digit from a preformed digital signature array (DS) can be bound to P.
S3: PS = dsbind(P', DS[i])
where DS[i] being a decimal digit replaces the units digit of P' to from PS.

Halt ....
To continue ....
What precisely is the nature (random,; output of a hash. some other mechanism?) of DS. How many bytes does it contain?
How is "7" chosen from the whole of DS?

"adacrypt" <austin.obyrne@xxxxxxxxxxx> wrote in message news:abf343cf-3c91-412c-bc16-e99c02d42ba9@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Mar 17, 3:27 pm, "ping pong" <mosescua...@xxxxxxxx> wrote:

news:94e86d9f-c22a-4aba-b15f-8b09cff2bc02@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

> On Mar 17, 10:46 am, adacrypt <austin.oby...@xxxxxxxxxxx> wrote:
>> I am making a prediction here that a lot, if not all of future
>> cryptography will be number-theoretic in concept and that it will use
>> the traditional number line per se to model integer numbers as points
>> on a straight line that may have arbitrary direction. The
>> construction of this line i.e. the rule or equation of the line is
>> invariably taken for granted and I doubt if anybody ever actually
>> envisages a number as a point on that line when they use it, unless of
>> course you are teaching children to add and subtract line segments as
>> an introduction to arithmetical addition of numbers or else you are
>> talking about numbers at a much higher level say, in number theory.

>> A large part of mathematics depends on a basic assumption that the
>> traditional number line has unitary period and unitary scale i.e. the
>> integers are separated by 1 and the graphic scale of the interval
>> between integers is 1 also i.e. scale of the line is 1 = 1.

>> I have been labouring the point for over ten years that this is the
>> downfall of mathematics in cryptography in that the traditional number
>> line is too transparent to cryptanalysts and no matter what a
>> cryptographer will ever do to obfuscate a plaintext by mathematical
>> means the cryptanalyst will always find another mathematical means to
>> invert it. However accurate this prognosis is or is not, is
>> unimportant, the fact remains that mathematics based on the
>> traditional number line has failed in cryptography. There is nothing
>> to defend in that failure, cryptography is a nefarious business anyway
>> and our beautiful number system was never intended to misinform people
>> in the first place.

>> To get to the point therefore I am promoting Scalable Key
>> Cryptography as something that still uses mathematics but in such a
>> way that the transparency that a cryptanalyst has enjoyed up to now
>> while using the traditional number line is no longer available to
>> him. I am defining number lines in a different way that is compatible
>> and interchangeable with the traditional number line but quite
>> different at the same time. I am using lines that have unitary period
>> but with a scale that is not unitary as in the traditional number line
>> and is instead some thing else, it may be any positive integer taken
>> from a large domain of positive integers (only the computer capacity
>> to store large positive integers restrains this), then the scale of
>> the line is N = 1.

>> This ploy takes me into the realm of modular arithmetic that was
>> invented by the great mathematician Leonard Euler and a contemporary
>> Johann Carl Friedrich Gauss. I don t wish to open a can of
>> argumentive worms here from readers, lets say they did it jointly.
>> The mathematics of modular arithmetic is often called clock arithmetic
>> because of the way it is modelled on rotations of the hands of a
>> clock.

>> For my purposes in scalable key cryptography I am inventing number-
>> lines that have non-unitary periodic scale. When these straight lines
>> are given variable non-unitary periodic scale it becomes tantamount to
>> the clock arithmetic of modular invention being portrayed as opened-
>> out straight lines now. The upshot is that if one of these modular
>> lines is superimposed on a standard traditional number line any
>> integer from the latter line can be mapped onto the modular line as a
>> residue modulo (some N ) if N is known.

>> As applied to cryptography the trick is not to make N known.

>> The upshot in cryptography is that while the ciphertext as a set of
>> integers may still be represented as points on the traditional number
>> line still bearing their iconic Arabic names and shapes, they can only
>> be decrypted by mapping them onto some modular line but which one?
>> there are N possible coincident modular lines where N is numerically
>> equal to the message length. Clearly, the possibility space of these
>> derived modular lines is vast.

>> A different value of N enables a fresh modular line to be used for
>> each plaintext.

>> The upshot of this invention is that the items of ciphertext that are
>> nominally ordinary integers and are still related to each other by
>> periodic scale are now not inductively decipherable by any
>> mathematical means. It is not possible to deduce the operand from the
>> function in other words. This pulls the plug on all mathematical
>> cryptanalysis i.e. cryptanalysis that seeks to invert transformations
>> by inverse functional means.

>> I think I am entitled to claim the credit for this invention of
>> modular lines in cryptography and I hope it does not give offence to

>> PS : Look at the elephants here never mind the pedantic fleas.

> How it Works - Summary.

trying to go through the steps - please be patient - o.k?

> Alice reads in the next plaintext which is say capiatl P. 'P' has
> denary value 80 in ASCII .

She multiplies 80 by 10 so as to create an

> empty units place => 80 now becomes 800.

I shall stop here and ask:
1. Where did 10 come from?
2. Is it randomly chosen?
3. Is it chosen by some other means?
4. Is it a secret? Or Is it published to all?
5. What is the possible range of k? if you see what I mean?

> She next inserts a digit from her Digital Signature array -say 7, into
> the empty units place - 800 becomes 807.

> She uses 807 to index an array of non-repeating integers that range
> from -526 to + 487.

> She calls this indexed integer whatever it is, her representation of
> capital P - lets say it is - 428 (minus 428). - Lets call this Alice's
> Digital Signature.

> She next calls on an array of change-of-origin integers that ranges
> from 300 to 1300.

> She next calls a value of 'N' from another array that might range from
> 14000 to 28000.

> Then,
> Encryption,

> CipherText = "Change-of-Orign" integer + "Alice's Digital Signature"
> integer + n multples of 'N'. = some fairly bulky integer.

> Decryption : Bob simply reverses everything from his identical arrays
> having mapped the ciphertext integer across to his relevant "modular
> line" that has been described above.

> Note : a variation of this algorithm configures this cipher to work
> only between certain bounds that are assigned to it by Alice and Bob.
> Certain situations might require that also.

> - adacrypt.- Hide quoted text -

- Show quoted text -- Hide quoted text -

- Show quoted text -

I shall stop here and ask:
<1. Where did 10 come from?
<2. Is it randomly chosen?
<3. Is it chosen by some other means?
<4. Is it a secret? Or Is it published to all?
<5. What is the possible range of k? if you see what I mean?

Given that I am working in denary evaluations of ASCII, the value of
'P' is 80, a denary integer, For my purpose I wish to bind Alice to
each plaintext. I do this by giving the plaintext text an attachment
of something that is traceable to Alice i.e. a denary integer from a
preformed array that constitutes her "Digital Signature" array. I
need a place to put this integer so I deliberately create an empty
column to put the integer in by multiplying 80 by 10 to make it 800 -
the extreme right column is the units column so I put the 7 in
there. All of this goes on behind the scenes at rutime of the
program.

Obviously only 10 can be used to facilitate this piece of the
algorithm.

Note also there are no powers or multiples of P - its P^ 1 always -
note well 'P' in this case is the instantaeous character being
enciphered at that moment - it is not a variable name - could be Z
or ? or ~ if they happened to be the next character on the external
file of plaintext. - come back if you don't understand - adacrypt

.

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