Re: Trithemius progressive cipher

[Jorge Stolfi <stolfi@xxxxxxxxxxxxx>]

    > [Claus Anders:] [Trithemius progressive cipher] has some
    > interesting features (Garbriel Landini poited to this too) 
    > 2. The word structure will be preserved

I don't know what you mean here.

Consider for example the core-mantle-crust model described in my
Voynich page. Since the components of that model have varying lengths,
any component after the first one would be encoded with different
shifts in different words. This variation should prevent us from
seeing any structure. Thus I think that the progressive cipher is
pretty much ruled out.

    > 3. This cipher will not change the entropy of the text.

Indeed, in theory --- since the original can be recovered without loss.

However, the probability distribution of the letters will become
flatter, since the same plain letter will be mapped to several
different cipher letters, depending on its position in the word.
Therefore, the single character entropy will increase.

This observation applies also to the k-letter entropies.

Indeed, almost any mechanical cipher other than plain Caesar will
increase the computed value of h_k.  

    > So, if (and why not) our author of VMS used a cipher like this,
    > how did he produce a code with such low h2 entropy?

The statistics h_k can be manipulated in infinitely many ways. One way
of lowering h_2 is to insert after each plaintext letter x_i a null
letter y_i = f(x_i) where f is a fixed function. This "encoding" will
set h2 to half of the original h1. If f is chosen so that Prob(f(x_i))
is close to Prob(x_i), then h1 itself won't change much.


But I would say that no theory (criptological or linguistic) for the
VMs is worth spending any time on, unless it can explain (a) the
compact word-length distribution, (b) the core-mantle-crust structure,
and (c) the gallows-bit correlation.

All the best,

--stolfi