## spatial ciphers/cryptanalysis techniques? [closed]

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Are there spatial ciphers/cryptanalysis techniques based on neighborhood spaces in a grid? More specially are there 5 orientation "spaces" with the values being north, south, east, west, neutral?

I know this sounds more like rigorous math, but just need a simple explanation or some direction, as in resources or keywords or links (springerlink, arxiv, etc.)?

Thanks for the help everyone.

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(update)

Well, in the context of the way I am handling the problem, I assigned these 5 values/symbols (N,S,E,W,I). Basically, I have globular shapes (whose descriptors don't matter) that are in a n x n grid of these "neighborhood spaces". They are not given - just a method I am tackling the problem with. I base these values (N,S,E,W,I) on whether these globules cross into neighboring spaces or are strictly inside a grid-cell. I treated globules extending/touching the grid lines shared between two neighboring cells as still crossing over into a neighboring space.

Also, it may not use a cipher, but a code. So foremost, I am looking for ways to construct a cipher or a code based on spatial alignments. I hope this is clear, so let me know if clarifications are needed.

Note: I - inside/ neutral.

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The obvious answer is that any string of symbols could encode data, and this is no different from just having a string of digits between $1$ and $5$. I don't know of any standard encoding which is formatted this way. I really can't imagine what there could be to say mathematically about this sort of data as compared to just strings of symbols from a $5$ character alphabet. – David Speyer Sep 7 2010 at 11:25

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I only answered this as below because it hasn't been deleted yet, despite multiple downvotes, and the question's author has at least tried to amend and clarify the question, though it still remains very unclear to me, particularly his cipher vs code, and the comments about globs. Perhaps describing the problem itself would make things clearer... – sleepless in beantown Sep 8 2010 at 1:13

## 3 Answers

There is a classic substitution cipher technique that uses a 25-square ($5 \times 5$) grid which holds 25 of the 26 letters of the roman alphabet:

````- + 1 2 3 4 5
- 1 A B C D E
- 2 F G H I J
- 3 K L M N O
- 4 P Q R S T
- 5 U V W X Y
````

It's effectively a short-hand technique for creating a substitution cipher by viewing it as a toroidal lattice, letting NORTH define the mapping {'A'$\to$'U', 'B'$\to$'V', ... 'Y'$\to$'T'}, etc. Effectively, north maps the coordinates (x,y) to ($NORTH_x(x),NORTH_y(y)$), for $x,y \in$ {1,2,3,4,5},

$NORTH_x(t)=t$, for $1 \le t \le 5$

$NORTH_y(t)=$ $t-1$ for $2\le t \le 5$,

$NORTH_y(t)=5$ for $t=1$.

Similar definitions exist for SOUTH, EAST, and WEST. The Identity direction or NULL direction stands for the identity function, $NULL(t)=t$.

A message can be encoded with a single direction, meaning only one substitution cipher is used for the entire message. A message can be encoded with multiple directions, meaning that each sequential letter is encoded by a different direction, rolling over when you get to the end of the cipher.

Napoleon used a variation of this, with two $5 \times 5$ grids, with a pass-phrase used for the second grid.

This may have nothing to do with what you're asking for. Your explanation thus far is not illuminating enough for me to grasp what it is exactly that you are trying to do. Can you explain your ultimate end-goal? Is it to create an encrytion cipher? Is it to analyze an already existing encrypted message? Is it to analyze a particular encoding algorithm or technique?

What exactly is the underlying problem which you are attempting to solve?

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Please do not leave comments as answers. – David Speyer Sep 7 2010 at 19:25

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Please do not leave comments as answers – Yemon Choi Sep 7 2010 at 18:55
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