Here’s a nice little thing that might possibly earn a Cipher Mysteries reader 100 US$!
Once upon a time in Copenhagen, a bright mathematics professor called Julius Petersen briefly stepped into the world of codes and ciphers. He wrote and published a pamphlet on cryptography called Système cryptographique, as well as a series of eight fortnightly articles on the subject for the weekly magazine NÆR OG FJERN (‘NEAR AND FAR AWAY’) – these ran from issue 150 (16 May 1875) to issue 164 (22 August 1875).
Though the articles did not actually say Petersen had written them, they are very much à la main de Petersen: and according to Professor Bjarne Toft, “we know from other sources that [Petersen] was the author (or one of the authors)“.
The point of interest for us is that the author(s) signed his / their name(s) in this unusual encrypted fashion:-
By 46, 9, 4-57, 3, 5.
This has left Bjarne Toft so mystified that he has offered money to anyone who can crack it:-
Does the dash ‘-‘ indicate that there are two authors? If so, the other could be Frederik Bing, who was an extremely good mathematician and a close friend of Petersen. Bing was mathematical director in the state life insurance company. And are the numbers dates? Or what??
I have offered a prize of 100 US$ to anyone who can give a convincing solution (convincing for me that means!).
Here are some things that might possibly help you crack such a tiny cryptogram (even smaller than the Dorabella Cipher!):
- Petersen’s full name was “Julius Peter Christian Petersen”, so his initials were presumably JPCP;
- Petersen’s friend’s full name was “Frederik Moritz Bing”, so his initials were FMB;
- The cryptogram looks an awful lot like a tiny book cipher (along the lines of the Beale Papers);
- If it is a book code, no obvious attempt has been made to use high numbers;
- If it is a book code, common letters would presumably tend to appear as smaller numbers, less common letters slightly larger numbers, with extremely rare letters potentially very large numbers: so the pattern here would seem to be “rare common common dash rare common common“;
- Surely the number one candidate book for testing the “book code” hypothesis would be Petersen’s Système cryptographique. Yet Worldcat lists no copies in the UK, so it would be down to someone to have a look at one of the scant few copies owned elsewhere…
Over to you, armchair cryptogram detectives…
Numbering the book title three times = 1 to 84 gives
Systemecryptographique.
46 = Y
9 = R
4 = T
57 = 0
3 = S
5 = E
You aRe TO SEe I presume the book,
perhaps Edward Elgar wrote it, his style,
Hello Nick.
Nice one!
I agree — it looks like a book code. For my .02 dollars, I’d speculate that it goes something like:
Page 46 — Line 9 — Word 4 = Julius
Page 57 — Line 3 — Word 5 = Petersen
It would make sense if the book used as the key had an alphabetical listing of names and ran to about 90 pages. Worldcat says that “Système cryptographique” has 15 pages so no joy there.
But then, who really knows!
Cheers!
Erni
From my armchair, it could be a matrix using 0 as a space, and if 4-57=(4-5)7=17 then we have 46,09,17,03,05
Using (won’t align unless you use courier new font or equiv.):
-01234
6fghij
7klmno
5pqrst
9uvwxy
0zabcd
8e—-
which gives: Jul. C. P.
There are few constraints here, thus many plausible solutions, but it’s more fun over a coffee than Sudoku.
TT
Hi Nick —
If the magazine used volume pagination that spanned multiple issues (and the eight article installments fell within one volume), the “book” could be the magazine itself. If there was consecutive page numbering, has anyone checked pages 46 and 57 of that volume of the magazine?
As another alternative, the reference could be to letters on a magazine page whose contents remained constant from issue to issue, at least through the first 57 characters (e.g. the title page or table of contents). If so, then the reader of any one installment would (literally) have the solution in hand.
Jim
Here’s a thought. “by” in Danish means “town”.
@Jim: Wouldn’t that assume that Petersen knew at the time of writing his article what the exact layout of the printed volume would be? How else could he predict what would appear on page 46 etc.?
(Unless, as you pointed out, JCP indeed referred the cover or some other unchanging elements of the magazin.)
46= T
9= I
4= D
57=E
3 C
5=E
TIDECE REARRANGED = DECIET,
Unsolved historical code…
Hi,
I’m Petros Petrosyan.
I now live in Chicago.
Attention Please!
Please Go to: http://www.world-mysteries.com/pex_PPetrosyan1.htm
1. The pyramid is not a sepulcher of Pharaoh and the purpose of
its construction was not on this plane.
2. The basic model of the Pyramid cipher was established.
The basic model of the code of a pyramid is formed of 365 small pyramids
which consist at 14 steps of model of the code.
Thanks,
Petros M.Petrosyan
gud cipher
Here is the real description of the Petersen cipher which is no doubt what the signature is all about. I am working on it and actually will have a copy of the Petersen publication in a day or two. Meanwhile:
It uses a two dimensional coordinate representation of the letters, randomized by permuting the row and column indices according to some numerical double key, which is based on a key-word or key-sentence (‘Le jour et la nuit’ in Petersen’s example). Thus each letter is represented by two coordinates, and the message to be encoded is first replaced by the sequence of the coordinates of the letters. Conceptually, this fractionating of the indices, and then destroying the basic difference between the 1st and the 2nd coordinate, is the main idea of the cipher. The obtained sequence of numbers is rearranged diagonally in a 2-dimensional array. To destroy the diagonal pattern, the columns are permuted according to a further numerical key, also obtained from the same key-sentence. In the resulting permuted array, the columns are read two and two, from top to bottom, giving the coordinates of the letters of the enciphered message. To decode the message the operations should be performed in inverse order, and Petersen says that for 100 letters this can be done in 12 minutes, or 8 minutes using a special apparatus with movable slips, or 5 minutes for trained army personnel.
My best guess without further work is that the first two-digit number is the transposition (or permutation) of the indices and the second is the letter coordinates. hence two sets of coordinates – two letters – J.P.
Fascinating – please let us all know what you find when your copy of Petersen’s publication arrives! 🙂
Follow up on Peterson pamphlet. I underestimated Harvard’s backlog but will have it in a couple of weeks. It is in French as I understand it. Also I am having it copied and sent on a personal/scholarly use basis although I don’t think that would stop me from getting it translated and publishing the essence of the document. Coming soon.
I am still waiting on the Petersen pamphlet but have found that there is a detailed account of it in “Mr. Babbage’s Secret” written by Ole Immanuel Franksen. As the book is in English whereas the actual pamphlet is in French, Franksen’s book may actually be more helpful.
Unfortunately I am living on peanuts these days and cannot afford the book just for a few pages. (Nor can I find one to “borrow”.) If anyone has the book and is willing to copy the few pages on Petersen’s cipher system, I would appreciate a copy. I will, of course find a way to share the pamphlet on a one to one basis so as not to offend the restriction of personal/scholarly use.
My public email is [email protected].
Thanks
I’ve just ordered a copy for myself (looks like my kind of a book!), though thankfully not at the $10000 price it (mistakenly?) appears at on the Amazon US site, will see what I can do for you… 🙂
I have received a copy of the Petersen pamphlet from Bjarne Toft, not Harvard U. so there is no restriction on its use. The paper is in French but does contain a detailed description of Petersen’s system, which should enable a solution to the signature puzzle. Further details shortly.
OK. Research all done. Petersen crypto pamphlet read. Relevant pages of Franksen book on Petersen’s code read. 1st Near and Far article (in Danish) sort of read. Conclusion: No help at all. I can say:
– It is not likely a book code.
– It is not based on Petersen’s cipher because it is too short.
– Petersen signed his name “Julius Petersen” in later years.
– I believe the articles are a progressive series on the basics of cryptology and very likely in those articles he gives hints as to what system he used for the numbered signature. Unfortunately, although they are available, translating them is not within my abilities.
– Given that the “signature” heads these lessons on or analysis of cryptology, some simple matrix or other crypto system available at the time was used.
– Both the pamphlet and the articles were written in 1875 so while his complete cipher system does not appear to have been used, his techniques, i.e. permuting by shifting columns and entering plaintext diagonally may be relevant.
Best I can do for now. The numbers re-arranged are:
4694
5735
Note that (4,5), (6,7), and (4,5) are consecutive. 73 is 4 more than 69. The numbers consecutive are 3,4,5,6,7,9.
Back to work.
As you point out, all the consecutive digits are perhaps overly coincidental:
46, 9, 457, 3, 5
However, I think it will take a visit from the Cryptographic Muses to suggest where to take this… it’s a toughy. 🙁
Did Petersen leave his papers to a University archive? If so, has Bjarne Toft looked through them?
This is all we know about his papers:
“Only very few of Julius Petersen’s belongings are preserved to this day. Of books we have found only three, including a copy of the 1866 edition of Methods and Theories with numerous annotations in Petersen’s handwriting.‘15 They had been given around 1930 by Petersen’s brother, Valdemar Petersen in Odense, to a 14 year old boy, Poul H. Rasmussen, who was interested in mathematics, and who grew up to become an engineer (without losing his interest in mathematics). It is perhaps fitting that of all the books in Petersen’s private library among the few to survive should be the one he loved best.
Until about 1980 a collection of books and manuscripts that had belonged to Petersen remained intact in Aarhus, but then disappeared. Only special items,
like his doctoral diploma (1871) and the letter of appointment from the Polytechnical School (1871), signed by the King, were preserved, due to Mrs. Ase Wiuff Borreglrd-Otzen, Copenhagen. Petersen’s silverware and his early Bing & Grondahl porcelain of course still exist, but scattered among many people. ” (From a bio by Bjarne Toft and others – Discrete Mathematics 100 (1992) 9-82 North-Holland ,)
escher7: oh well, it was worth a try. 😉
It can’t refer to the issue of Naer og Fjern, can it? The same signature appears at the end of each article?
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(46 – (9*4) – 0) / 1 = 10 (J)
(57 – (3*5) – 10) / 2 = 16 (P)