# Is there a Mathematician Cryptographr in the House.

*From*: adacrypt <austin.obyrne@xxxxxxxxxxx>*Date*: Sun, 18 Jul 2010 02:41:47 -0700 (PDT)

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

.

**Follow-Ups**:**Re: Is there a Mathematician Cryptographr in the House.***From:*David Eather

**Re: Is there a Mathematician Cryptographr in the House.***From:*adacrypt

**Re: Is there a Mathematician Cryptographr in the House.***From:*Sebastian

**Re: Is there a Mathematician Cryptographr in the House.***From:*Joseph Ashwood

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