The Voynich Ninja

(09-01-2022, 12:59 PM)Mark Knowles Wrote: You are not allowed to view links. Register or Login to view.What you have written about the Polybius square is definitely interesting.

In Meister's book we can see that by 1424 the Florentine ciphers had advanced some way....

There is a very interesting cipher key, I think, also from 1424 that Gabrielli generated from enciphered letters..... Meister isn't alive to answer why he did not include that key in his book; I suspect as it is a bit unusual and he was not sure what to make of it or who produced it.

My fingers are crossed that you'll find it and that it will be as interesting as you're hoping!

As to the Polybius Square, I know less than I'd like to about how knowledge of it was diffused during and after the Renaissance, including how and when it came to be imagined as a "square" -- that seems like a natural enough way to picture it, but Polybius himself writes about the idea in terms of five different tablets with five divisions on each.  Here's a link to an English translation of the relevant passage, for any who are interested:

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That cipher was originally for fire-signaling, too, rather than for written messages.  But I suppose that might open up a new line of investigation in itself -- i.e., what *semaphore* systems were in use at the time of the VM, if any?  Was anyone trying to send messages by lights rather than by letters?  If Bruni had read Polybius, he for one should at least have recognized the possibility.

The Polybius square (with a slight modification) was what I meant in You are not allowed to view links. Register or Login to view..

If you use one sub-alphabet for rows, another one for columns, then you obtain intra-bigram positional rigidity not unlike one the VMS exhibits. What results is in its essence a verbose cipher, so the conditional character entropy drops - even more than with the trivial verbose cipher which I provided as an example in my recent blog post, but less than for the VMS. The procedure of course doubles the average word length, but then one is free to introduce fake spaces to bring it back down, and what's valuable is that fake spaces can be introduced arbitrarily on sub-alphabet 1 to sub-alphabet 2 transition, since "real" spaces would always be on the opposite transition, which makes the two easily detectable.

I will make a blog post about that when I have more time. There are further simple developments of the Polybius square concept, I still have to check what opportunities they bring in terms of "bringing it closer to Voynichese".

The concept of the Polybius square is very simple and very easily re-invented. I can imagine it being independently re-invented by the VMS creator, especially given such famous example of matrix placement of a sequence of characters as the Sator square.

(09-01-2022, 04:39 PM)Anton Wrote: You are not allowed to view links. Register or Login to view.The Polybius square (with a slight modification) was what I meant in You are not allowed to view links. Register or Login to view..

Great!  I was going to suggest this and try to get cross references between this idea and your litoreia idea. 

Ironically enough, I, personally have extremely poor spatial sense.  It means I almost always turn the wrong way when lost while driving (to the point where I turn the opposite way "I think" I should go in hopes of being more likely to be right); routinely get very lost in open world video games (although maybe continuing to challenge myself with this kind of thinking is a low risk way to "train" my brain a bit?); and just have a very poor innate sense of how things are related to each other in space (makes parking a real pain).

But I still can perceive the real possibilities in the combination of one or more verbose ciphers (where one involves a kind of transposition) from the point of view of the kind of visual, associative, and entropic characteristics the Voynich exhibits.

Thanks so much for working on this and I'll keep trying -- but it certainly isn't my mental strong point.  If I come up with any insights, I will definitely post -- but for now I'm just trying to get an initial wrap around how these things could be combined.

Maybe I'll see if I can find anything about the transfer of Polybius from a semaphore to a written "square" -- such history could be useful.

(09-01-2022, 04:39 PM)Anton Wrote: You are not allowed to view links. Register or Login to view.The concept of the Polybius square is very simple and very easily re-invented. I can imagine it being independently re-invented by the VMS creator, especially given such famous example of matrix placement of a sequence of characters as the Sator square.

I agree that it seems simple.  But many inventions seem obvious once you know about them, in hindsight, even if they weren't obvious at all before someone invented them.

On the topic of "mapping," then, it would be especially interesting to know if there's any evidence of a fractionating cipher of any kind being used (or even just speculated about) in the century or so before 1450, and if so, where and how.

One other thing it would be nice to know is the history of access to the specific part of Polybius that describes a fractionating cipher.  This passage is in a fragment of Book Ten, so people who had access to other parts of Polybius's Histories didn't necessarily have access to *that* part.  (How this affects the Leonardo Bruni connection, I'm not sure.)  The editio princeps of the Book Ten fragment(s) seems to have been You are not allowed to view links. Register or Login to view., for what it's worth: nineteen years after Books One through Five.  As for secondary references in the cryptological literature, the Polybius Square comes up in You are not allowed to view links. Register or Login to view. -- don't know offhand if there's anything earlier.  Here's how Della Porta displays it:

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And prior to 1549, if we're trying to get back the first half of the 1400s, doesn't that potentially lead to Byzantine sources?

It has already been shown that Shirakatsi was available in Byzantine sources at that time (1400s).

(09-01-2022, 09:11 PM)R. Sale Wrote: You are not allowed to view links. Register or Login to view.And prior to 1549, if we're trying to get back the first half of the 1400s, doesn't that potentially lead to Byzantine sources?

First, I can confirm that the chances that Leonardo Bruni saw the Chapter X fragment are probably zero. His work that relied upon Polybius, Commentarii deprive bello punio used Book 1, chapter 7 through Book 2, chapter 34 (so a part of the "known" first five books of the time).  This analysis is in an academic article by G. Ianziti, You are not allowed to view links. Register or Login to view. Renaissance Quarterly, 51(2): 367-391, 377-378 (1998).  Bruni died in 1444, so a solid 100 years before the likely discovery date of the fragments that include Book X (see discussion below).

With that established, I took a quick look at what I could find beyond what pfeaster discussed and I found a bit of possible information from a source dated 1853.  Here's the clip from Charles Anthon, You are not allowed to view links. Register or Login to view. (p. 395):

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It would seem that the fragment of Book X we're interested was from an unknown source from an unknown location at an unknown time that was found (or at least traversed through) Corfu.  This now Greek island was a colony of the Republic of Venice at the time (e.g. 1549).

This discussion seems to be at least partial basis for a later discussion of the various publications of Polybius in the preface of Evelyn Shuckburgh's 1889 translation into English of the text of Frederick Hultsch, which expands the possible mystery source into even more speculation with this:

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You are not allowed to view links. Register or Login to view. is the link to the full preface.  You are not allowed to view links. Register or Login to view. is a link to an article partially about Casaubon, the translator who speculated it was Marcus Brutus' copy of Polybius (this paper also talks about Bruni so we've come full circle here).  This identification by Casaubon feels a bit too convenient to me to be probable, like the people who are reincarnated that are always Cleopatra or someone else equally famous in their prior lives, but I guess it's possible.

I haven't been able to find any contemporary attempts to find out more about this mysterious source of the fragments including Chapter X -- but it could be out there and does seem to be an interesting topic for study.  If I find anything else, I'll come back.

(08-01-2022, 07:43 PM)pfeaster Wrote: You are not allowed to view links. Register or Login to view.The favored strategy for increasing security was, I take it, to increase the number of different characters in the key.  The result always seems to be a much larger character set than we see in the bulk of the VM.

Hello Patrick,

you are quite right. This has been pointed out several times in the past, in different fora (*) and by several people, well before you joined here. The subject has essentially been 'beaten to death', given that threads had to be closed by the admins, and for that reason I hesitate to point back to them.

René

*) At least: here and in Nick Pelling's Cipher Mysteries

(10-01-2022, 01:56 AM)MichelleL11 Wrote: You are not allowed to view links. Register or Login to view.First, I can confirm that the chances that Leonardo Bruni saw the Chapter X fragment are probably zero. 

That does seem to be how it's looking.  Here's a further You are not allowed to view links. Register or Login to view. in Arnaldo Momigliano's Essays in Ancient and Modern Historiography that leans strongly in this direction while acknowledging a (seemingly weak) argument to the contrary:

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On the other hand, that point about Byzantine sources is a fair one: Polybius could have been read and known continuously in Constantinople up to 1453.

I see that there's a monograph by J. M. Moore about the manuscript tradition of Polybius which could be worth a look, but in the meantime, there's also a survey of manuscripts online You are not allowed to view links. Register or Login to view..  The name Excerpta Antiqua seems to have been given to the collection of excerpts including the pieces of Book X, which may help in searching for references to it.  Of manuscripts of the Excerpta Antiqua mentioned on that website, one copy listed as from the fifteenth century (at the BnF) is online You are not allowed to view links. Register or Login to view., but identified in the catalog record as sixteenth century.  Other possible early copies at the Vatican, but unclear from just this how early and when they got there.

Polybius certainly isn't the only known older source for a cipher with a reduced character set.  As JKP has pointed out, any numerically-based notation can have a similar effect.  And I don't mean to beat a dead horse by rehashing old points about the sizes of cipher character sets, much less to claim that there's anything original about the observations themselves.  But on the current topic of "mapping," I'd assume we'd want to be especially attentive to ciphers involving reduced character sets, however they achieve them.  So if and when anyone's going hunting, it's a good (if obvious) thing to know to watch for.

While you can't hang your hat on a hypothetical coat-hook, it's not the connection to a specific text, which is probably too late for VMs connections, it is about the transmission of an idea.

It seems to me that there would have been a wealth of historical opportunity for this knowledge to exist, for whomever could find and read Polybius *all the way to* Book Ten. It's going to be an exclusive group. So, starting with the fourth Crusade (1204), and the Latin Kingdom of Constantinople tied to Flanders, the trade into the Black Sea by the Genoese and Venetians, how many members of this exclusive group might there be who could access the knowledge of Polybius?

Even after the fall of Constantinople, Trebizond held on till 1461. There were ambassadors from the east in Burgundy at the time. If the ideas of Polybius hadn't transferred by then, perhaps that is too late.

So, back to the map. A number of dots in Italy. Are there some examples from Spain?
What about Venice and Genoa? What types of ciphers did they use? What about Byzantine ciphers? Is there even evidence extant?

When it comes to compiling ciphers from the early 15th century there are a few perspectives it seems to me:

1) The Voynich is not written in cipher and therefore a knowledge of ciphers of the time is irrelevant
2) The Voynich is written in cipher, but it has no relationship to ciphers used or invented at the time therefore knowledge of ciphers of the time is irrelevant
3) The Voynich is written in cipher and is related to ciphers used or invented at the time therefore compiling ciphers of the time can give insights into the Voynich cipher