Die Aargauer Kantonsbibliothek hat mich um Unterstützung gebeten. Wer kann diesen verschlüsselten Brief des französischen Marschalls Nicolas de Catinat dechiffrieren?

“Ich bin auf der Suche nach einer Dechiffrierung eines Briefs von Nicolas de Catinat auf Ihren Namen gekommen”, schrieb mir Frau Dr. Ruth Wüst von der Aargauer Kantonsbibliothek in der Schweiz.

Frau Wüst ist gerade dabei, das Archiv der Familie Zurlauben (ca. 32’000 Seiten) aus der frühen Neuzeit online zu stellen. In diesem Archiv ist sie auf einen verschlüsselten Brief gestoßen, der auf den 15. September 1702 datiert ist. Geschrieben wurde er im “Camp d’Ingleshein”. Historiker vermuten, dass die Unterschrift von Nicolas de Catinat, einem hochrangigen französischen Offizier und “Marschall von Frankreich”, stammt. Als Empfänger vermutet man den Lieutenant General Beat Jakob Zurlauben. Der Brief ist auf Französisch verfasst.

Die Zurlaubens waren eine bedeutende Magistratenfamilie aus dem Schweizer Kanton Zug, die über mehr als 200 Jahre einflussreiche politische, militärische und kirchliche Positionen besetzte. Die männlichen Familienmitglieder kämpften als Söldner in den Armeen Frankreichs, Savoyens, Spaniens und des Heiligen Stuhls. Die Familie unterhielt von 1619 bis zur Französischen Revolution fast ohne Unterbrechung eine Kompanie im königlichen Garderegiment in Frankreich.

 

Drei Seiten mit einem Nomenklator verschlüsselt

Der Brief hat drei Seiten. Hier ist Seite 1:

Catinat-1

Hier ist Seite 2:

Catinat-2

Auf Seite 3 findet sich nur noch Klartext:

Catinat-3

Ein Nomenklator steckt dahinter

Wer Klausis Krypto Kolumne öfters liest, erkennt schnell, um welche Art von Verschlüsselung es sich hier handelt: um einen Nomenklator. Ein Nomenklator sieht für jeden Buchstaben des Alphabets sowie für wichtige Wörter je eine Zahl (oder eine Buchstabengruppe) vor. Ein einfaches Beispiel:

A=1, B=2, C=3, D=4, …, Z=26, HUND=99, KATZE=123, MAUS=180

Der Ausdruck HUND KATZE UND MAUS verschlüsselt sich damit in 99, 123, 21, 14, 4, 180.

Um eine Häufigkeitsanalyse zu erschweren, kann der Verschlüssler bei manchen Nomenklatoren zwischen mehreren Zahlen für denselben Buchstaben wählen. Wenn ein Nomenklator besonders viele Einträge umfasst, spricht man von einem Codebuch. Wo genau der Übergang zwischen einem Nomenklator und einem Codebuch liegt, ist nicht festgelegt, man könnte die Grenze bei etwa 1000 Einträgen ziehen.

Codebücher und Nomenklatoren waren ab dem 14. Jahrhundert bis nach dem Zweiten Weltkrieg in Gebrauch. Vor Aufkommen des Computers bildeten sie vermutlich die meistverwendete Form des Verschlüsselns überhaupt. Frühe Codebücher und Nomenklatoren lassen sich heute meist lösen (ein Beispiel ist der Mann mit der Eisernen Maske), doch ab etwa 1800 erreichte diese Technik eine Qualität, bei der auch heutige Codeknacker oft passen müssen. Ungelöste Codebuch- bzw. Nomenklator-Nachrichten sind etwa das Seidenkleid-Kryptogramm oder das van-Gelder-Kryptogramm. Auch das Ohio-Kryptogramm dürfte dazu gehören.

Leider gibt es meines Wissens momentan weltweit keinen Spezialisten für das Knacken von Codes und Nomenklatoren. Dabei gäbe es für so jemanden viel zu tun, denn in den Archiven schlummern noch unzählige Kryptogramme dieser Art.

 

Wer kann das Catinat-Kryptogramm lösen?

Der von Catinat verwendete Nomenklator sieht Zahlen zwischen 1 und 500 vor. Zweistellige Zahlen sind dabei deutlich häufiger als zu erwarten wäre. Dies könnte bedeuten, dass die Buchstaben des Alphabets mit zweistelligen Zahlen kodiert wurden, während für ganze Wörter größere Zahlen verwendet wurden (viele Nomenklatoren waren so aufgebaut, obwohl eine solche Trennung aus Sicherheitsgründen eigentlich vermieden werden sollte). Leider sind keine Wort-Zwischenräume zu erkennen, was die Sache deutlich erschwert.

Kann jemand den verschlüsselten Brief von Nicolas de Catinat lösen? Nicht nur in der Aargauer Kantonsbibliothek würde man sich freuen.

Zum Weiterlesen: Wer knackt die verschlüsselte Nachricht von Kardinal Soglia?

Kommentare (46)

  1. #1 Peter Lichtenberger
    Im hier und jetzt
    1. Mai 2016

    Ich hab’ mal die Zahlen geschwind abgetippt (Lesefehler vorbehalten 😉

    Transkription Seite 1:

    137-20-393-97-323-41-269-291-10-28-22-254-13-277
    88-43-93-30-271-106-61-296-85-40-84-229-328-109
    247-101-22-54-56-163-106-305-350-228-30-217-8-33
    50-171-188-209-214-335-314-13-198-368-130-433-101
    3-154-291-214-14-207-68-28-407-115-326-43-35-110
    204-46-159-28-1832-284-13-109-61-271-188-418-22
    85-50-84-11-14-207-82-30-396-109-335-87-106-262
    100-109-413-13-22-305-14-427-28-159-30-277-276
    204-262-88-325-64-181-20-78-97-110-327-137-13
    101-28-376-232-109-325-219-100-80-48-59-403
    77-290-159-145-126-22-66-158-325-41-269-10-66
    277-409-50-28-428-82-326-13-101-308-393-409
    335-102-106-251-30-3-3963-291-359-262-85-160
    329-136-84-43-166-50-14-184-201-226-153-129
    162-350-122-13-295-409-188-168-28-43-50-48-396
    316-56-138-30-22-20-50-84-66-100-344-202-369
    129-81-22-8-85-286-28-328-30-56-84-50-126
    188-17-14-247-35-17-200-33-84-3-8-50-275-54
    8-77-62-282-260-198-393-28-169-65-50-37-39-11
    152-129-204-298-320-64-44-345-161-84-279-56
    163-106-394-137-13-101-217-29-28-376-10-314-440
    464-399-312-408-30-344-10-106-28-308-188-121
    84-177-393-420-100-64-77-35-61-41-269-17-10-14

    Transkription Seite 2:

    84-101-22-197-296-107-106-277-37-342-87-4-324
    121-56-24-271-43-234-1366-120-33-20-441-248
    61-341-431-126-50-144-286-325-153-100-20-78-350
    110-50-327-214-87-33-291-153-198-120-413-129-336
    33-419-331-148-22-207-404-24-277-268-393-409
    284-198-8-35-28-183-284-13-20-272-331-8-272
    198-183-284-13-85-11-359-403-86-145-126-22-14
    133-427-325-64-73-82-106-28-146-63-56-331-10
    263-100-80-78-59-325-41-269-17-66-22-409-50
    28-428-82-326-13-350-308-77-251-13-291-124
    120-236-56-400-325-284-198-8-34-248-30-376
    201-14-271-43-246-407-50-84-327-200-33-24-3
    8-129-149-236-204-277-168-20-50-408-167-350
    85-129-399-431-407-62-330-254-291-277-38-83
    238-82-30-13-101-408-11-228-22-50-158-286-409
    87-126-159-291-17-171-68-28-393-281-86-153
    60-13-50-28-93-336-33-320-419-101-56-62-238
    82-30-351-228-120-400-158-409-66-277-291-325
    350-3-275-146-129-14-276-100-33-327-136-84-65
    120-126-139-106-145-270-30-44-10-11-153-50-162
    136-24-294-393-22-260-168-43-331-162-80-62
    282-260-198-393-28-129-78-396-393-291-41
    269-17-10-14-84-101-22-182-8-54-411-325-33
    140-39

    • #2 Klaus Schmeh
      1. Mai 2016

      Vielen Dank! Das macht die Untersuchung des Kryptogramms deutlich einfacher.

  2. #3 Peter Lichtenberger
    Im jetzt und hier
    1. Mai 2016

    Ich denke es ist eine Chffre ähnlich oder sogar gleich der “Grossen Chiffre”. Die kleinste Zahl ist die 3; die grösste die 440.

    Tippfehler oben: Seite 1, Zeile 6: 183 statt 1833; Seite 2, Zeile 2: 166 statt 1366

    • #4 Klaus Schmeh
      1. Mai 2016

      Wenn es sich wirklich um die “Grande Chiffre” handelt, wäre das ein Glücksfall, der das Entschlüsseln deutlich vereinfachen würde. Ich werde mal nachschauen.

  3. #5 Norbert
    1. Mai 2016

    Abo

  4. #6 Thomas
    1. Mai 2016

    Briefe an Catinat mit Dechiffriertabelle: https://www.jfbouch.fr/crypto/catinat/catinat.html
    Vielleicht passt das auch hier?

    • #7 Klaus Schmeh
      1. Mai 2016

      Danke für den Hinweis. Soweit ich sehe, passt diese Tabelle leider nicht. Die Zahl 28 kommt beispielsweise im Geheimtext vor, steht aber nicht in der Tabelle.

  5. #8 Hankook
    1. Mai 2016

    137 Hausnummer der Bibliothek vielleicht auch buch Nummer rest geht von alleine ))

  6. #9 Thomas
    2. Mai 2016

    Die Tabelle passt nicht, sie betrifft den Nomenclator, den Ludwig XIV. 1690/91 in Briefen verwendete, die Bazeries in “Le Masque de fer” (Der Mann mit der eisernen Maske) 1893 entschlüsselt. Leider gibt es Bazeries Buch, dem es gelang, vermuteten Klartext bestimmten Mustern in den Briefen zuzuordnen, nicht online. Das System der Grand chiffre ist ansatzweise hier zu sehen: https://cryptiana.web.fc2.com/code/bazeries3.htm. Danach sind Einzelbuchstaben, Silben und ganze Wörter ohne erkennbares System den Zahlen zugeordnet. Catina hat 1702 wohl dasselbe System verwendet. Wegen des Datums des Briefes ist zu vermuten, dass Catina, der sich im Lager bei Ingolsheim nahe Strassburg aufhielt, über die Eroberung der Festung Landau berichtet: Einige Tage vorher hatte die französische Besatzung der Festung unter Melac nach der Belagerung durch das kaiserliche Heer unter Ludwig von Baden kapituliert. Das sind aber wohl zu wenig Anhaltspunkte, um Bazeries Methode zu übertragen, die Chiffre hat Zahlen bis fast 500.

  7. #10 Klaus Schmeh
    2. Mai 2016

    Bart Wenmeckers über Facebook:
    The most common item in the page is symbol 28 which occurs only 11 times out of a total string of 301 so ~3.65%. There are 147 unique symbols.

  8. #11 Thomas
    3. Mai 2016

    Korrektur:
    Catina schrieb den Brief im Lager bei Ingenheim (nordwestlich von Straßburg zwischen Zabern und Hagenau)

    Nachtrag:
    Eine Fülle an zu erwartende Klartextstücken bieten die Berichte über den Verlust der Festung Landau in der Pfalz im September 1702 und die damit verbundenen militärischen Operationen im Elsass in den Memoires et correspondance… (https://books.google.de/books?id=BUT_hUwNO3UC&pg=PA142) und der minutiösen historischen Darstellung in https://books.google.de/books?id=kro5AQAAMAAJ&pg=PA283, hierin auf S. 819 insbesondere auch ein Brief Catinas an Louis XIV. vom 25. Aug. 1702. Zu vermuten sind – über Bazieres´ Einfallstor “les ennemis” hinaus – neben militärischen Begriffen (siège, forteresse, artillerie, garnison…) auch dort genannte Personen (le roi, Melac, prince Louis de Bade, Villars…) und Ortsnamen (Landau, Strasbourg, Haguenau….).
    Allerdings muss man davon ausgehen, dass die Chiffre in Catinas Brief ähnlich komplex wie die Grand chiffre von 1691 ist (Homophone, Zahlen ohne Bedeutung, Klartextwörter aus Silben und Einzelbuchstaben zusammengestückelt, ganze Wörter codiert). Die vierstelligen Zahlen in Peters Abschrift (danke!) sind glücklicherweise Schreibfehler, aber 147 Zeichen (nach Barts Zählung) im Zahlenraum bis 500 sind ja auch schon überwältigend. Die häufigsten Zahlen: 28, 50 (je 17x), 13, 22 (je 14x), 30, 84 (je 12 x), 14 (10x).

  9. #12 Ruth Wüst
    3. Mai 2016

    Ich habe Bazéries Buch bestellt und kann wahrscheinlich ab nächsten Montag relevante Seiten online stellen.

  10. #13 S. Tomokiyo
    4. Mai 2016

    I catalogued eight codes from the reign of Louis XIV
    https://cryptiana.web.fc2.com/code/louisxiv.htm
    but none of them, as far as can be known to me, seem to fit. (About items (3)(5)(7), I don’t have enough material to make a call.)

    About Bazeries, my other article
    https://cryptiana.web.fc2.com/code/bazeries2.htm
    has a link to a Google copy of Bazeries’ book
    https://books.google.co.jp/books?id=5stCAAAAYAAJ

    (Excuse me if my comments are off the point because I need to rely on machine translation.)

  11. #14 Thomas
    4. Mai 2016

    @S. Tomokiyo
    I appreciate your marvellous site about the Great cipher. Unfortunately Google books provides nothing but a snippet of “Le Masque de fer”.

    • #15 S. Tomokiyo
      5. Mai 2016

      @Thomas
      Thank you for your comments.
      That explains. I had a similar experience before. Some (telegraphic) codebooks on Google that can be viewed in the US could not be viewed here in Japan. Apparently, Google has different viewing limitations for different jurisdictions.
      Anyway, it appears you are only to wait for several days thanks to Ms Wüst.

  12. #16 imNetz
    5. Mai 2016

    netter Beitrag zur Familie Zurlauben um 1700

    https://www.e-periodica.ch/cntmng?pid=sgw-002:2008:23::329

  13. #18 Ruth Wüst
    11. Mai 2016

    I now have a copy of Bazeries, Le masque de fer on my desk. I’ll scan the annex tomorrow. It contains:
    A. Reconstitution du chiffre de Louis XIV
    B. Grand chiffre de 1691
    C. Preuve de l’exactitude de la reconstitution du chiffre

    Would this help?
    Also, I found some other books by Bazeries:
    Bazeries, Étienne.
    Les chiffres secrets dévoilés [microform] : étude historique sur les chiffres, appuyée de documents inédits tirés des différents dépôts d’archives. Paris : E. Fasquelle, 1901
    Bazeries, Étienne.
    Les chiffres secrets dévoilés.
    Paris, E. Fasquelle, 1901.
    Bazeries, Étienne.
    Les chiffres secrets dévoilés [microform] : étude historique sur les chiffres, appuyée de documents inédits tirés des différents dépôts d’archives. Paris : E. Fasquelle, 1901.
    Hermann, A. (Arthur-Joseph)
    Application du chiffre secret de M.A. Hermann aux Tables chiffrantes et déchiffrantes de M. le commandant Bazeries. 1893

    Would they also be of interest? I happen to be in Washington, DC next week and could get access to the texts at the Library of Congress.

    With regards to the article about the Zurlauben family: if anybody is interested I could send you a summary in English.

    • #19 S. Tomokiyo
      12. Mai 2016

      I would like to read an English summary of the Zurlauben article if it doesn’t bother you too much. My email is found near the bottom of my home page:
      https://cryptiana.web.fc2.com/code/crypto.htm

    • #20 S. Tomokiyo
      26. Mai 2016

      @Ruth Wüst
      Thanks to your guide to the Zurlauben article, I now see that the recipient is Beat Jakob Zurlauben II (1660-1717), a merchant/diplomat etc., rather than Beat Jakob Zurlauben (1656-1704), a lieutenant general.

  14. #21 Thomas
    11. Mai 2016

    Zu “Le masque de fer”: Man muss sehen, ob Bazeries hier etwas von seiner Methode bei der Entschlüsselung der Grand chiffre preisgibt, das sich für den Brief von 1702 verwerten lässt.
    Zu “Les chiffres secrets…”: Handelt es sich dabei nicht nur um eine Kryptographiegeschichte ohne weitere Erkenntnisse über die Grand chiffre?
    Zu “Application du chiffre..”: Hier geht es wohl nicht um die Grand chiffre, sondern um den von Bazieres selbst entwickelten Zahlencode, siehe https://cryptiana.web.fc2.com/code/telegraph2.htm

    • #22 S. Tomokiyo
      12. Mai 2016

      “Le masque de fer” deals with codebreaking in the annex “A. Reconstitution du chiffre de Louis XIV” (p.257-268), in particular p.262-264, but I fear it does not help much for the 1702 cryptogram.
      “Les chiffres secrets …” mentions codebreaking but mainly deals with cipher (e.g., Vigenere) as opposed to code. Pages 142-145 deals with code (my summary at https://cryptiana.web.fc2.com/code/codebreaking.htm#SEC3D ) and pages 275-277 print a Napoleonic small cipher but neither seems helpful.

  15. #23 S. Tomokiyo
    12. Mai 2016

    I added a section on my webpage
    https://cryptiana.web.fc2.com/code/louisxiv.htm#SEC9
    with historical backgrounds (with a map) and some observations on the 1702 code. I limit myself to the latter here.

    (1) When one compares the cryptogram in “Le masque de fer” on p.292 ff. with the 1702 cryptogram, the latter has significantly more sequences of two-digit figures. This seems to indicate that the 1702 code is much simpler than the one broken by Bazeries and may be something similar to Item (4) (“Louis XIV’s Code/Cipher (1690, 1693)”) of my catalog. In particular, it seems probable that low numbers (e.g., 1-80) represent single letters.
    I have seen participants in this blog are adept in algorithmic tools such as hill climbing and simulated annealing. I wonder running such tools with a constraint like “1-80 (or 1-100) must be single letters a-z (possibly in this order)” may not reveal something.

    (2) Some observations for paper-and-pencil codebreakers.
    The most frequent numbers are 28, 50 (17 times), 13, 22 (14 times), 30, 84 (12 times), and 14 (10 times), as already pointed out by Thomas.
    The most frequent two-group sequences are: “41 269” (5 times), “13 101” (4 times), “50 28”, “50 84”, “82 30”, “101 22”, “183 284”, “269 17”, “284 13” (3 times each). Of these, all instances of “269” are in the sequence “41 269”.
    I guess “50 28”, “50 84”, “82 30” are bigrams that are frequent but not those bigrams (e.g., “la”, “le”, “li”, “lo”, “lu”) given their own code numbers. For what it is worth, in the case of a cryptogram of Item (4), such bigrams were “au”, “er”, “ez”, “ur”, “us”.

  16. #24 Thomas
    12. Mai 2016

    Your new section – congrats, great job. A minor detail: We can´t yet be sure if Catina´s camp (“Inglesheim”) was in Ingenheim (between Saverne and Haguenau), or in Ingolsheim (not far from Landau, south of Wissembourg). I think it wasn´t in Lingolsheim (west of Strassbourg) because of the “L”, even though Vault mentioned a camp near Eckbolsheim on Sept. 14. My conclusion: It was somewhere in Alsace 😉

    Now you fired the first shots by pencil and paper, let me add:

    We find the two group sequence 41-269 in line 11, line 23, line 32 and line 45/46. In lines 11 an 32 it is part of two almost identical longer sequences:

    line 11, 12:
    -325-41-269-10-66-277-409-50-28-428-82-326-13-101-308-
    line 32, 33:
    -325-41-269-17-66-22-409-50-28-428-82-326-13-350-
    308-
    Therefore I guess there are homophones: 10=17; 22=277; 101=350.

    In line 23/24 it has:
    -41-269-17-10-14-84-101-22-
    and in line 46/47:
    -41-269-17-10-14-84-101-22-

    Let´s have a look at 13-101 and 13-305:

    line 9: -137-13-101-28-376-
    line 21: -137-13-101-217-29-28-376-
    (217 and 29 = nulles?)
    line 12: -326-13-101-308
    line 33: -326-13-350-308
    line 38: -30-13-101-408

    Maybe 13-101 and 13-350 are “en-ne” in Bazeries´ “ennemis”?

  17. #25 Klaus Schmeh
    15. Mai 2016

    Hinweis von Frau Dr. Wüst:
    Ich habe jetzt den Appendix von Bazeries Buch eingescannt. Dort ist die Grand Chiffre von 1691 abgedruckt.
    https://scienceblogs.de/klausis-krypto-kolumne/files/2016/05/Bazeries-Appendix.pdf

  18. #26 Thomas
    16. Mai 2016

    @Ruth Wüst
    Danke für den “annexe”. Im “appendice” sollen auf den S. 207 – 220/221 noch “Lettres de Catinat…” abgedruckt sein. Könnten Sie auch diese noch einscannen?

    Wie S. Tomokiyo beobachtet hat, ist die Chiffre im Brief von 1702 weniger komplex als die grand chiffre Ludwigs XIV., eher handelt es sich um eine petit chiffre, wie sie in “Le Masque de fer” auf S. 272 erwähnt ist.

    • #27 S. Tomokiyo
      17. Mai 2016

      Perhaps you are aware that the small cipher mentioned on p.272 of “Le Masque de fer” is Item (7) of my catalog, where you can see the letter in code but I have not seen its plaintext version. (By the way, I made several corrections in my page, thanks to you!)

  19. #28 S. Tomokiyo
    16. Mai 2016

    One would see that the identifications (10=17; 22=277; 101=350) update the statistics as follows but I couldn’t get any further.
    Frequent groups:
    22/277 (22x), 28, 50 (17x), 101/350 (15x), 10/17, 13 (14x), 30, 84 (12x), 14, 393 (10x)
    Frequent two-group sequences:
    “13 101/350”, “41 269” (5x)
    “269 10/17” (4x)
    “10/17 14”, “101/350 22/277”, “183 284”, “284 13”, “50 28”, “50 84”, “66 22/277”, “82 30” (3x)

    Frequent double letters in French (as “10 17” is likely to be) are LL, TT, SS, CC, MM.

  20. #29 Klaus Schmeh
    17. Mai 2016

    Here are a few more letters from Catinat, as provided by Ms. Wüst: https://scienceblogs.de/klausis-krypto-kolumne/files/2016/05/Bazeries-More-Letters.pdf

  21. #30 Norbert
    26. Mai 2016

    Some more corrections to Peter Lichternberger’s transcript:
    (page / line / group no.)

    1/01/12: 257 (instead of 254)
    1/02/10:  50 (instead of 40)
    1/10/10:  78 (instead of 48)
    1/13/02: 107 (instead of 102)
    1/13/07: 393 (instead of 3963)
    1/14/11: 152 (instead of 153)
    1/15/12:  78 (instead of 48)
    1/16/01: 326 (instead of 316)
    1/18/14: probably 57 instead of 54
    (not sure though - there is another appearance of 54, which speaks in its favour)
    1/20/10: 184 (instead of 84)
    1/23/02: 277 (instead of 177)
    2/10/09: strange "5" in 251, could also be 231
    (251 still appearing more probable to me)
    2/11/09:  35 (instead of 34)
    2/14/08: 257 (instead of 254)
    2/20/11: 152 (instead of 153)
    2/21/03: 295 (instead of 294)

  22. #31 Norbert
    26. Mai 2016

    According to Edmond Lerville (“Les cahier secrets de la cryptographie”, p.72), the codebooks for the “Grand” and the “Petit Chiffre” were changed about every three years. The Grand Chiffre consisted of approximately 590 codewords, compared to about 370 in the Petit Chiffre (ibid., p.73). This should yield a remarkable difference of Friedman’s “Index of Coincidence”. I put this to the test, let my pc compute the IC of all Catinat letters that Thomas referred to in comment #6, and compared these to the IC of our cryptogram.


    Louvois 1691/07/08: IC = 0.00490
    Louvois 1691/07/09: IC = 0.00492
    Louis   1691/08/19: IC = 0.00486
    Louis   1691/08/24: IC = 0.00489
    Louis   1691/08/29: IC = 0.00412
    Louis   1691/09/06: IC = 0.00431
    Louis   1691/09/14: IC = 0.00515

    Catinat 1702/09/15: IC = 0.00884

    Not really suprising, the results confirm S. Tomiyoko’s statement that the code used in this letter is significantly less complex than the Grand Chiffre from 1691. I wondered if a “Petit Chiffre” sample might also be available, and guessed that the letter from Feuquières (“De Pignerol, ce.25 janvier 1691”), found on S. Tomiyoko’s site here, might be such a Petit Chiffre example (in fact, I even assume Edmond Lerville is referring to exactly that letter when he states that the Petit Chiffre uses appr. 370 different figures). Here is the IC for that one:

    Feuquières 1691-01-25: IC = 0.00882

    This is a stunning accordance with our cryptogram! So I think it is most likely that both Feuquières (1691) and Catinat (1702) are using the same system (most probably a Rossignol one, most probably a “Petit Chiffre”). The relevant codebooks, however, are likely to be completely different …

  23. #32 Thomas
    26. Mai 2016

    @Norbert
    Interesting! That means the ICs of Catinat´s and Feuquières´ letters almost reach French plaintext IC (2,02, Wiki). But does it make sense to determine the IC if the key is a nomenclator with bigrams, nulls and codes? Or do your results prove that Catinat´s key is completely different, i.e. only a substitution with a few homophones?

    Obwohl dies eigentlich zum Rabenhaupt-Thread gehört: Eine Untersuchung des IC bei einem Nomenclator findet man auch in https://crypto-world.info/casop15/crypto1112_13.pdf, dort im Abschnitt D, zum Rabenhaupt-Brief. Angesichts der vielen (zu vermutenden) Nomenklatoren in diesem Blog wäre es ja interessant herauszufinden, ob und welche Rückschlüsse ein bestimmter IC hier zulässt.
    Ich gebe nur einmal die englische Google-Übersetzung des Abschnitts aus der crypto-world wieder:
    “We have created a plaintext statistics based on the unencrypted part of the letter and the accompanying worksheet. One of the important characteristics used in the analysis of encrypted text is called. Index of coincidence (IC). These are statistics that expresses the probability that at a randomly selected texts we agree characters in the same place between the two texts. Accidental text with a 26-character alphabet is the probability of close to 3.7%. On the contrary, the real language, this probability is significantly higher. Rabenhauptová the plaintext letter is this figure to 7.5%. Clearly, the substitution cipher IC maintained by maintaining the probability of each character. Similarly, if you choose the right group of characters from one row of the table homophones, and we have a sufficient number of characters encrypted text, we get close IC IC plaintext. On the other hand, if we choose the wrong group (e.g. the symbols used as bigrams), the IC is likely to be significantly different (lower). After a little experimentation, we can see that the letters in encrypted text have similar statistics (IC allocation of frequencies) as plaintext letters corresponding substitution cipher (see. Fig. 6). Therefore probably one row of the table represents the letter of homophones. Some disagreements statistics can also be caused by duplication of some characters (already mentioned “NN” extreme example is shown in Figure 7).”

  24. #33 S. Tomokiyo
    28. Mai 2016

    It is remarkable that IC can tell the identity of two codes from encoded text alone. I wonder whether the cryptogram here in the 1690/1693 code of my Item (4) has a similar IC.
    This is because I have been reviewing the 1702 cryptogram on the basis of this 1690/1693 code (but with no luck). The 1690 cryptogram shows the letters/syllables represented by the most frequent code groups are: s (48 x), de (43 x), u (33 x), re (30 x), la (28 x), n (28 x), r (27 x), e (25 x), a (25 x), a (23 x), s (23 x), pa (22 x), r (21 x), en (20 x) (s and a have homophones). The rank of “e” lower than “s” is because syllables such as “be”, “ce”, “de”, … have their own code groups.

  25. #34 S. Tomokiyo
    29. Mai 2016

    I examined what precedes/follows the most frequent groups 50 and 28 (as in a contact chart).
    Of the 18 instances of “50”, ten are followed by a two-figure group, including 3 instances of “50 28” and four instances of “50 84.” Of the letter, two are part of “85 50 84.” The groups after “28” do not show such a bias.
    Ten out of 18 instances of “50” and seven out of 17 instances of “28” follow a two-figure group.
    The succession of these most frequenty groups “50 28” is part of the two long, seemingly indentical sequences noted by Thomas. The above difference in the following group suggests “50 28” is not double letters (i.e., it may be “us”, “es” etc. but not “ss”, “ee”, “uu” (i.e., “ve”), etc.).

    I uploaded in my site some base statistics for my reference:
    (1) Frequency
    https://cryptiana.web.fc2.com/code/catinat1702_1.txt
    (2) Two-code group frequency
    https://cryptiana.web.fc2.com/code/catinat1702_2.txt
    (3) Two-code group frequency sorted by the second group
    https://cryptiana.web.fc2.com/code/catinat1702_3.txt

  26. #35 Norbert
    30. Mai 2016

    @ S. Tomokiyo
    Louis XIV to French Ambassador in Constantinople
    1st letter 1690/07/31: IC = 0.01185
    2nd letter 1690/08/09: IC = 0.01278

    My conclusion is that the code of the Constantinople letters is significantly simpler than the Catinat 1702 code.

    Maybe interesting: The IC of the Constantinople letters remains about the same, when we take both letters combined into consideration (0.01224). This is no surprise, because they are already (partially) decoded, and we know that the used codebook is the same.

    In the case of Feuquières 1691 (IC=0.00882) and our cryptogram (IC=0.00884) the “combined IC” is completely different (0.00587), cleary indicating that the system in general should be very similar (or identical), but the actual codes have changed between 1691 and 1702.

    I have a suggestion for these groups:
    page 1, line  1:    041 269 291 010
    page 1, line 11:    041 269 010 066
    page 1, line 23:    041 269 017 010
    page 2, line  9:    041 269 017 066
    page 2, line 22/23: 041 269 017 010

    My proposal: 10, 17, 66 and 291 all stand for “e”. Both 41 and 269 have no other occurrence than these, so without context it is a hard guess, but imo “l’ armée” (l-arm-e-e) looks promising.

    One question: Since the letter has no plaintext leading-in, should we expect any form of address in the first groups? And if yes, how would Catinat address Zurlauben: “Monsieur”?

    • #36 S. Tomokiyo
      30. Mai 2016

      Thank you for your analysis. I’m impressed with what IC can tell.
      Now it seems established that the 1702 code is similar (or identical) in scheme with the Feuquiere code of 1691, though not in the specific assignment; is less complex than the code identified by Bazeries; and is more complex than the code of the Constantinople letters.
      I hope someone finds Catinat’s other letters to Zurlauben in plaintext that allow us to identify a typical beginning in his letters. (Vault prints some letters to Catinat (p.807, 853, etc.) but I’ve seen no letters to/from Zurlauben.)

    • #37 S. Tomokiyo
      Yokohama
      31. Mai 2016

      Now I’m not so sure as I was this morning.
      The most striking difference between the code broken by Bazeries (pdf) and the code of the Constantinople letters (my Item (4)) is that the latter has a significant regularity in the arrangement of entries. But, in my understanding, such a difference is not reflected by IC.
      As an example, a text enciphered with an alphabetically ordered substitution table (i.e., Caesar) and a text enciphered with a mixed alphabet (and even a plaintext) result in the same IC (see here). On the other hand, more homophones certainly lowers IC. After all, IC is a measure of how much the frequency distribution of the letters (symbols) in a text (encoded/enciphered or not) diverges from the uniform distribution (here) and it does not tell, e.g., whether a cryptogram is encoded with a one-part code or a two-part code.
      Having said this, it remains remarkable that IC gives almost the same IC for the 1691 Feuquieres cryptogram and the 1702 cryptogram despite the significant difference in size.
      IC is surely a powerful tool but we have to consider what kind of complexity is indicated by IC.

  27. #38 S. Tomokiyo
    7. Juni 2016

    In the hope that anything is better than nothing, below are links to my preliminary contact analysis. It revealed nothing promising (for me).
    https://cryptiana.web.fc2.com/code/catinat1702_4.txt
    https://cryptiana.web.fc2.com/code/catinat1702_5.htm

  28. #39 Thomas
    8. Juni 2016

    Thanks for your contact analysis. It should be difficult to identify the vowels e and a, because they are part of frequent words (esp. articles) which I presume are substituted as a whole by code. The most frequent consonants in French are s, n, r, t. Thereof s, n and t are parts of digraphs which are rarely reversed: “nt” and “ns”. Maybe we can identify them by means of contact statistics? Other frequent but rarely reversed digraphs are “qu” and “ou” (but maybe they are also substituted by a single number).

  29. #40 S. Tomokiyo
    8. Juni 2016

    Yes, we must remember that the usual letter frequency is hidden by inclusion of those letters in syllables having their own code. My pet theory (i.e., modeled after my Item (4) albeit being more complex in some way) shows that “le” (195), “la” (185) (and actually seemingly every combinations of “consonant+vowel”) have their own code numbers. As you predict, “qu” (actually “qu+vowel”) has encoded as a whole (327, 337, …).
    Remarkably, “nt” (76, 77) and possibly “ns” (268???) are so frequent that they are given their own code numbers, while “ou” is not encoded in its own and the Constantinople letters encode it as “42 59” and “41 60”.
    Having said this, it is difficult to identify two-groups sequences that are rarely reversed because almost all sequences are rarely reversed. For example, when we compare “50 14, 50 28, 50 37, 50 78, 50 84, 50 126, 50 144, 50 158, 50 162, 50 171, 50 275, 50 327, 50 408” with “8 50, 13 50, 20 50, 22 50, 33 50, 43 50, 65 50, 84 50*, 85 50, 110 50, 126 50, 152 50, 166 50, 407 50, 409 50”, only “50 84” appears in both. (At least, we may say the combination “50 84” is not “ou” but even this is not certain.)

    By the way, when I uploaded the contact analysis, I also added some statistics to my Item (4) as a guide to frequencies in texts encoded in this code. I (only wishfully) guess that 393 is “de” and 291 or 409 is “la” in our 1702 code.
    Further, I just made some additions to the contact analysis. (I tried to find homophones for 50 and 28. 50 and 33 may be but I cannot say it definitely.)

  30. #41 Norbert
    9. Juni 2016

    I searched the Grand Chiffre letters decrypted by Bazeries for code pairs that appear in straight and reversed order, i.e. “xy” and “yx” (after eliminating the homophones). Here are the plaintext equivalents of the most frequent hits (with count of appearance):

    re|r: 258          s|si: 35
    de|s: 133          ro|p: 35
    e|e: 106           n|co: 30
    mi|ne: 100         i|ne: 30
    la|p: 94           re|de: 30
    re|z: 86           vous|de: 30
    de|la: 64          re|ti: 29
    r|de: 61           r|les: 28
    se|s: 57           a|y: 27
    troupe|s: 57       a|s: 27
    r|le: 53           me|s: 26
    te|p: 49           t|t: 25
    g|ne: 48           de|se: 23
    s|ne: 44           r|ue: 23
    r|te: 41           n|ue: 21
    en|ne: 38          r|ne: 20
    te|s: 37           r|se: 19

    … followed by many others. This of course, is no proof but I think it could be worth trying the most frequent hits in our cryptogram for 50/84 and maybe also 393/28, 159/28, 22/66, 50/126 and 291/277.

    On the other hand, “84 50” does appear only once, as opposed to “50 84” (four times). This could have occurred by mere chance, so the above statistic might be of no relevance … Nevertheless, to me it seems that 50/84 are not very likely to be both single letters (no guarantee).

    Some more statistical comparisons with the Grand Chiffre letters suggest that 28 might stand for “s”, but this is even more uncertain than the above said.

  31. #42 S. Tomokiyo
    9. Juni 2016

    Let me quickly add “50/84, 393/28, 159/28, 22/66, 50/126, 291/277” is the exhaustive list of sequences that occur in both “xy” and “yx” in our 1702 cryptogram. Except for “393 28” (2x) and “50 84” (4x), each of them occurs only once.

  32. #43 S. Tomokiyo
    19. Juni 2016

    I found three French codes from 1702 but unfortunately they do not fit our cryptogram.
    Two (Item (8B) of my updated site) were used in what seem to be letters of April 1702 from Versailles to a French minister at Wolfenbüuttel. They are both very similar to Item (4), though enlarged to 540/560 entries.
    The other (Item (10B)) was used between Guelders and Rheinberg in November 1702. This is more like the code broken by Bazeries and employs two-part principles (i.e., random arrangement of entries), though it had less than 400 entries.

  33. #44 Thomas
    22. Juni 2016

    @ S. Tomokiyo
    In the codes 4 and 8B on your website the single plaintext letters are substituted in alphabetical order by numbers up to 99. I wonder if frequency bar charts of the numbers 1 – 99 in codes 4, 8 B and Catinat (1702) would show similar, maybe shifted, patterns. Have you tested that yet?

    • #45 S. Tomokiyo
      23. Juni 2016

      That was my first hypothesis (see my comments (1) on 12 May, #23) but there is some evidence against it.
      Frequency distribution (data) did not seem to be consistent with a shifted regular alphabet, though I confess I did not go so far as to produce frequency bar charts but only compared distances between the most frequent letters. Possible homophones (e.g., 10 and 17) are also against the regular alphabet hypothesis. Although I still think the code of our cryptogram is similar to the Codes (4) and (8B) in that low numbers are single letters (and possibly “nt”, “ns”, etc.), I feel the regular alphabet has to be discarded.
      Having said this, I may try frequency bar charts to see if anything definite can be said. (I may take some weeks because of another project I’m now finishing.)

  34. #46 S. Tomokiyo
    28. Juni 2016

    I posted frequency histograms for the 4/5 April letters (my Item (8B)) and Catinat’s cryptogram of 15 September 1702 at
    https://cryptiana.web.fc2.com/code/catinat1702_6.bmp
    (I couldn’t get the x-axis labelling right with OpenOffice Calc. Sorry for the mess.)
    It may not help but it’s interesting to observe that the codes used on 4 April and 5 April are very similar but can give so dissimilar histograms depending on the user.