Re: VMs: Cardan grille

[Jacques Guy <jguy@xxxxxxxxxxxxxxxx>]

2/12/2004 4:53:21 PM, "jan" <hurychj@xxxxxxxxx> wrote:

> I quote:  
>
>"Cardan grill is different from  special grill called Fleissner-Wustrovitz,  where the grill 
is 
>designed such way it can  be rotated and eventually all  places are filled with valid 
>letters

That is "les grilles" I learnt about many years ago in
a sub-teenager's weekly magazine that ran a tutorial in
cryptography (they had interesting magazines back then. Alas,
I do not remember its title. Benjamin? That was one.
But there were others which I read).


> therefore it is a kind of transposition cipher.  
>Cardan grille is a seismographical method that brakes the mutual bonds and deforms the 
>statistics. We take  say  the matrix 15x15 and  cut-out randomly not more then quarter 
>openings. The grill is then used such way that we write plaintext into the openings (in 
>forward or backward direction). It is not rotated but put away  and remaining spaces 
>are filled with nulls (random, not valid letters).



>That makes all statistics and cracking 
>methods useless, including bigraphs.

Yes.

>The solution is possible only when the same grill 
>is used many times and  the text is long enough.

Yes. Another kind of one-time pad.

I searched for "cardan grille" with "-voynich" (yes,
it shows that, now, "cardan grilles" are primarily 
associated with the VMS, fancy that!

I found, among others: "http://en.wikipedia.org/wiki/Cardan_grille";
which said:

"In cryptography, a Cardan grille (introduced by Renaissance 
mathematician Gerolamo Cardano, also known as Jerome Cardan, 
in 1550) is an important tool in the reading of a message 
obfuscated through steganography. The grille is usually 
a piece of card with holes poked through at random places. 
One takes the card and lays it over a page of text that 
contains a hidden message, reading only the letters that 
appear through the holes in the grille."

This suggests to me that the filler text, far from being 
constructed from meaningless gibberish, was made to 
resemble a meaningful text ("steganography").

 
> using the true  Cardan grill  will provide the text which is 75 percent  
>"gibberish"! Such text cannot be handled by statistical nor by grammatical  methods.

It can be handled by standard cryptological methods if the same grilles 
have been used and reused enough times each. In particular, the pages
written with the same grille will all show "squares" containing a
single character _always_ at the same coordinates. But, since the
manuscript was written by hand, the characters of the filler text
will appear in slightly different places from page to page (not
a very clear explanation, I'm afraid. Try encrypting "hello world"
with a small 7x7 grill with 10 holes in it, filling the spaces
in between with text written by hand. Then try again on another
sheet of paper, with a different 10-letter plaintext. And again.
Now compare the three. The plaintext letters are the only ones
to be positioned exactly the same relatively to one another)

 
>The repetitions of signs are irregular and I wonder what can be said about Zip's laws 
>and second entropy of such text, provided that even the spaces between words ( or 
>rather "packets") are put in by random. 

If the spaces between words have been inserted at random,
the Zipf's law holds. If they follow a set pattern, e.g.
every 5th and 7th letters, it does not hold. If the filler
characters have been inserted truly randomly, then the
second-order entropy will be approximately equal to the
first, itself approximately equal to the zeroeth.



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