# Permutation ring

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Preambule:
There are Alice and Bob. Alice got a message and a chest. Both of them have locks.
Alice puts the message into the chest, locks with her lock and sends it to Bob.
Bob can't open Alice's lock btw. So he locks chest with his own lock and sends it back to Alice.
Alice opens her lock and sends.
Bob opens his lock, opens chest and reads the message.
Simple story hows how Diffie-Hellman works. But it can be broken by bruteforce. Anyone can say about long keys and the time... I can't agree with them because of random luck and growing computer potential.
I've decided to find one more oeration that can make this algo brute-proof. So we need second operation that won't affect multiplication ring. I've tried different but the only acceptable I found is permutation ring.
Permutation ring solves the only problem to get second dimention independent from the multiplication ring. So lets look like how it works.
You got your array of ints. Lets make the permutation table. Ex.: First element stays it's place. Second got i-th place. Third element got j-th place...
The assumption was that if we will repeat permutation n-times we'll got the starting array. As far as I could check the assumption, it looks like we got a ring at the n! - round. May be it can be done better.
So... Here we can use as the second dimention. Non-affecting the first one.
To avoid impacts of statistical analysis array should be split into subarrays with uique elements, join separator-element (Ex. 0, MAX_INT) to each one, join rest of "alphabet" after separator. As for the "alphabet" I mean a range of int's acceptable by the system. This array splittig also defines n to alphabet length. This can also make processig more determined.
As a result I see the following algo (symbol=number):
• Get your int array message
• Split into subarrays with unique numbers
• Add the split-symbol and rest of alphabet to the tail of each subarray
-- For each array by each participant (n! times)
• permutation round + multiplication round
• send to another

--

• last permutation+multiplication round
• throw out split-symbol and all after that for each syubarray
• merge subarrays
• profit!

Does someone knows some similar systems? I'll post some sources later if there are no similar...

May be someone had the same research and does have other results...

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There are Alice and Bob. Alice got a message and a chest. Both of them have locks.
Alice puts the message into the chest, locks with her lock and sends it to Bob.
But on its way there the postman picks up a copy
Bob can't open Alice's lock btw. So he locks chest with his own lock and sends it back to Alice.
But on its way there the postman picks up a copy
Alice opens her lock and sends.
But on its way there the postman picks up a copy
Bob opens his lock, opens chest and reads the message.
Alice puts the message into the chest, locks with her lock and sends it to Bob.
But it doesn't get to Bob it goes the postman
The postman puts his lock on the chest and sends it back to Alice
Alice opens her lock and sends it back to Bob
But it doesn't get to Bob it goes to the postman
Postman opens lock sees what is inside
Postman puts his lock on the chest and sends it to Bob
Bob puts his lock on the chest and sends it back to Alice
But it doesn't get to Alice it goes to the postman
Postman removes his lock and sends it back to Bob
Bob opens chest
Morale of the story never trust the postman
There are Alice and Bob. Alice got a message and a chest. Both of them have locks.
Alice puts the message into the chest, locks with her lock and sends it to Bob.
But on its way there the postman picks up a copy
Bob can't open Alice's lock btw. So he locks chest with his own lock and sends it back to Alice.
But on its way there the postman picks up a copy
Alice opens her lock and sends.
But on its way there the postman picks up a copy
Bob opens his lock, opens chest and reads the message.
Alice puts the message into the chest, locks with her lock and sends it to Bob.
But it doesn't get to Bob it goes the postman
The postman puts his bomb on the chest and sends it back to Alice
Alice opens her lock and dies
Postman puts his bomb on the chest and sends it to Bob
Bob puts his lock on the chest and dies
Morale of the story never trust the postman
There are Alice and Bob. Alice got a message and a chest. Both of them have locks.
Alice puts the message into the chest, locks with her lock and sends it to Bob.
But on its way there the postman picks up a copy
Postman dies
Morale of the story never spy on alice

Edited by fiveworlds

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You've just described MITM attack. Diffie-Hellman and this algo don't solve MITM and connection loss.

But for the mitm partitial solving:

1) Because of timings (too many data transfer) Bob can guess that something is got too long and postman may be trying to join the dialog.

2) Message signature should be used for Alice verification.

As for the bomb - buy a watchdog. It would be nice to have such helpful pet.

As for connection problems - change the postman provider in case it fails.

And as for replay attck (you hadn't mentiond but was close) you won't got the same routine because of mulriple ring rounds. As for the normal protection against ordinary replay you should save several outgoing messages for incoming comparison.

Any other materials?

Edited by formalizator

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You've just described MITM attack

Correct

As for connection problems - change the postman provider in case it fails.

There is only one postman. Not an email postman the actual postman and the bomb itself would be a real bomb. In the instance of the bomb to bob. Bob is expecting a letter off Alice there is no reason for Bob to suspect that there has been an abnormal time delay. Delivery of parcels usually takes a few days anyway. The parcel will be handed to Bob by the postman and signed for. The postman then leaves detonating the bomb. In the case of Alice's bomb to the postman the postal service has a drop-box allowing parcels to be left there overnight. Alice in a balaclava leaves the bomb in the postbox at night. Then Alice activates a pressure sensor when the postman picks up the parcel the pressure changes and the bomb explodes. Now in the case of email bomb. Email pings location where opened to remote server if location is not where Bob is supposed to be a missile is fired at location.

Edited by fiveworlds

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