[cryptography] New Hand Cipher - The Drunken Bishop

Aaron Toponce aaron.toponce at gmail.com
Fri Dec 27 09:02:44 EST 2013

On Fri, Dec 27, 2013 at 12:25:47AM +0000, Peter Maxwell wrote:
> If you view the moving-the-bishop as an s-box lookup, and apply it to
> itself three times (composition), you end up with another s-box of the same
> size, lets call it S.  Given S doesn't change, things should be rather easy
> indeed.  If your cipher is then roughly akin to C[n] = P[n] + S[ C[n-1] ]
> with all operations taken modulo 2^6 the problem should now be a little
> more obvious.

When designing it, this was the first thing I asked myself: Is this an S-box
lookup? It sure feels like it. There has been a lot of research into S-boxes
since the release of DES, and unless I can change the state of the S-box, I
might be sunk. I think you just confirmed it.

> ​Can I suggest doing some preliminary reading on group theory and
> finite-field maths, and also paying more attention ​to how existing strong
> steam ciphers are constructed.  One of the reasons Solitaire is useful is
> because you can mathematically prove certain properties about the cipher
> operation; also you'll note the entire internal state of Solitaire changes,
> while your design stays static.

I immediately recognized this: the board stays static, and the cards adjust
position. I've asked myself, and fellow mathematicians and programmers thoughts
on making the board much more dynamic. Everything we run into, shows that a
dynamic 8x8 board, where the rows, columns, and diagnals are changing, would be
much more difficult to maintain by hand. The only thing that has come to mind,
is treating the board as an 8x8 matrix, and runing standard mathematical
operations on the matrix, such as the multiplicative inverse, rotations, and
exclusive OR. An HP-48 calculator could do this for you, but then you're
relying on computing tools, and it looses the allure of a pure hand cipher.

This might be possible with magnets on a cookie sheet, or something magnetic,
where the numbers are on the magnets themselves. But this seems difficult to
carry around, and highly suspicious.

Other questions that have plagued my mind:

    1. Even though the keyspace is 64!, how many boards will cause the bishop
       to land on the same square after 3 walks (compositions)?
    2. If generating a "heat map" of the visits a bishop makes to each square
       on the board, given a certain key and plaintext, what can I infer about
       the probabilities of his walk?
    3. After our discussion on this list, it appears that the cipher is very
       linear, which is unfortunate. Is it possible to inttroduce non-linearity
       into the system with a static board?

The more I look into it, the more I see a dead end. Even though some of the
abstract algebra is eluding me, I think this is just a poor choice for a hand
cipher. However, it's taught me a great deal about designing hand ciphers, and
that it's more difficult than it seems. Heh.

Thanks for the feedback everyone. I think I'll hang this one up as a learning
exercise, and head back to the drawing board, as I have really enjoyed creating
this, even though it sucks, and most of you are probably laughing your ass off
at my lame attempt. It also appears that I need to study my abstract algebra
and linear algebra a bit better.


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