Mathematical Functions not Needed


The Real number-line is the desktop of all number-theoretic
cryptography. A mathematical function simply takes an integer operand
from a point on the line, operates on it and moves it to a different
point along the same line in either directional sense of the line. In
essence then, a function is a spanning rule for that occasion, it
spans the new position of the point using the operand’s original place
as the origin of the spanning process and its terminal place as the
spanned step.

Applying this to number-theoretic cryptography, the encryption process
is simply another such spanning step and the decryption process is the
symmetric reverse.

The important thing to notice is that the spanning process does not
need to be a tortuously complicated function process involving a
difficult function as all modern cryptography seeks to make it and
instead needs to be nothing more than any arbitrary mechanical step
that is reversible by referencing mutual databases. Making it into a
complex function is unnecessary and it simply tells the cryptanalyst
that it can be reversed by some mathematical means instead of that
being impossible due to the step data being random.

Mutual database technology enables large arrays of random keys to be
used in this cryptography that are simply called from their scrambled
state in the arrays in sequential order – no mathematical relationship
is necessary to identify the keys, they are random and are indexed
explicitly by the ciphertext items in sequential order. This totally
precludes all cryptanalysis to the adversary – think about it.

Modern cryptography is about to be reduced by this means to nothing
more complicated than simple arithmetic that uses ordinary
conventional computer management.

How It Works.

Encryption.
Alice reads in the next plaintext for encryption. She makes a primary
transformation to the denary representation of this plaintext that is
say capital ‘P’ that normally is 80 in ASCII such that it now becomes
437 say, this primary transformation includes her digital signature.

This number 437 has a normal, usual place on the real number-line at
437 intervals along the line relative to the origin at 0, but Alice
next gives it change-of-origin by saying that it is 437 intervals
along the line but relative to an origin at some other point that may
be at any positive or negative integer (within the scope of the
computer obviously). Call this the change-of-origin key.

Relative to this new origin Alice gives the number 437 another change
that I will call the spanning step that is made relative to the new
origin – call this step the span key. She adds some integer value to
it in other words. The sum of these step-changes is the ciphertext as
an integer.

Arrays of equal length of these change-of-origin keys and span keys
are stored as integers in the databases and used in sequential order.
These keys are random by design. Any message-length as a subset of
the arrays length may be encrypted and be random itself while also
fulfilling the requirement of key-length being equal to message-length
for the class of “Theoretically Unbreakable”.

The key sets to hand are 14250 in length, this enables a block of
14250 characters to be encrypted in one go, anything more than that is
done in a freshly scrambled database for another block and so on.
The initial block length of 14250 can be made as large as you like – I
just happen to have that array handy from a previous use.

Decryption.

Clearly, decryption simply reverses these steps by calling the keys in
sequential order from the mutual database and reversing the steps
symmetrically until the value 437 is found. This value is decoded
back into the plaintext that it represents in Alice’s original
character set.

Comment.

Heavy mathematics is not needed, (I happen to like mathematics but I
also believe in simplicity) - adacrypt


.

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