## Cryptographic system puzzle

A forum for good logic/math puzzles.

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### Cryptographic system puzzle

Hi everybody,

We start from a square board n*n
We have to place 26 knights on the board. Each knight is representing a distinct letter (A to Z).
2 guys want to use the moves of the knights as cryptographic system.
The 2 have the same starting position for each knight (symmetric key).
They have to crypt texts by sending to each other ONLY the targeted position.
Instead of sending for example C2.E3 they have to send only E3 (the knight landing on E3 represents some letter).
BUT for each targeted position they need to have ONLY one distinct knight reaching that position. I mean no targeted position could be reached by 2 or more knights.
Of course this is possible on big board 1000*1000. They could place them all in starting positions where it is highly unlikely that 2 knights reach the same position after k different moves. It will give them a hudge secret key.
The challenge is : what is the minimal size of the board m*m such as after at most k distinct moves (k=20 for example) for each knight some cyclic moves are allowed to be repeated. k distinct moves means that the targeted cells are distinct.

Thank you.