# Is there a Mathematician Cryptographr in the House.

Both ‘Key’ and ‘Plaintext’ belong in the ASCII printable subset
(elements 32 to 126 incl – 95 elements)

Treat these names ‘Key’ and ‘Plaintext’ as variable names in this
model.

X is a positive integer.

Consider now,

[(X +Key) + (X +Plaintext)] (Mod N) = a residue (Mod N)

Call, [(X +Key) + (X +Plaintext)], Sum.

N must divide Sum just once (and once only) and leave the residue (Mod
N) >= 0

Every possible combination of key and Plaintext is to be considered as
usable for both key and plaintext at any instant.

Then, question

1)

What is the minimum starting value for X that enables any N to be
deduced – i.e. what is the value of this first N that satisfies the
equation,

[(X +Key) + (X +Plaintext)] (Mod N) = a residue (Mod N) >= 0

What is the value of X that will give me a discreet number of N’s say
14000.

Theory.

This is the algorithm that produces two sets of random keys in the
following cipher in modular arithmetic.

Encryption.

[(X +Key) + (X +Plaintext)] (Mod N) = a residue (Mod N) >=0

Cipher text = residue – N
Decryption.

Decryption Key = residue + N

Plaintext (as messagetext) = Ciphertext + 2N – Key

Comment.

This cipher comes from the same stable as your RSA cipher except that
this cipher is totally, utterly and irrefutably unbreakable by any
means. It is secured by two sets of random keys i.e. the set of
eponymous keys (Key) and the set of N’s. Each of these two sets of
random keys is made equal in length to the message length during
encryption. Each of these two sets of random keys is used only once
in any message.

The cipher uses the concept of mutual database technology, i.e. the
keys are read in sequential order from the synchronised arrays in the
entities’ databases. The plaintext is either read in from external
batch files (produced by non-specialist operators) or is keyed
interactively at the computer keyboard (by non-specialist operators).
The arrays are periodically ‘scrambled’ and ‘sliced’ in a controlled
way by the entities.

If there are readers who are academics and would like to justify this
brainwave into formal presentation then I would welcome your interest
and contribution.

As I see it.

Residue, Ciphertext and Decryption key are congruent modulo N.
(editing restriction forces me to print it this way)

There are N elements in each residue class, there N classes of
residue.

It would be nice to formalise this using proper mathematical notation
but again the restrictions of this editor won’t go that far. How
would you do it just for comparison.

Comment.

This not a boring one-time pad cipher.

This is a cipher for mathematicians.

It is an adaptation of the Vigenere cipher that undocks the eponymous
square from its static position at (0,0) and moves it along the line Y
= - (X+x).

The OTP is also another adaptation of the Vigenere cipher although
sadly, no one seems to realise this. Major Joseph Mauborgne who was
Head of the US Army Cryptological Research in 1920 did however and
designed the OTP in conjunction with his contemporary Gilbert Vernam.

In my opinion, one of the first things that should have been done with
the inception of computer-driven cryptography is to have had another
look at the OTP that had become a popular joke paradox in the previous
half century. That is being done now albeit more a renaissance of the
Vigenere cipher than the OTP.

May I repeat, this is not a One-Time Pad cipher despite the
resemblance in the caveats of the operation. Please don’t make any
comparison-based arguments.

Please give this modular arithmetic your best shot, it is a cipher for
the future.

The theory is fully expounded on my website http://www.scalarcryptography.co.uk
- adacrypt
.

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