Fra Giovanni di Lucca to the Emperor (1644)

Summary. S. Tomokiyo’s page of unsolved ciphers carries this item with the remark that it “can be deciphered to read Al principe di trenti…” and that “someone versed in Italian would be able to complete the decryption”. Nobody had, and the reason is visible in the crib itself: principe is written 26 21 17 17 6 15 26 1, so the figure 17 must be i and n in the same word, which no substitution allows. It is a polyphonic alphabet: 17 stands for i or n, 19 for t or s, and the other twenty-two figures for one letter each, with two figures for each of a, e, o, u. Fixing the eight letters the crib gives without contradiction and annealing the other sixteen against an Italian 5-gram model, every seed returns the same reading; the same procedure on five shufflings of the ciphertext returns nothing. A Viterbi pass over the two alternatives then chooses i or n, t or s at each occurrence. The paragraph relays an offer to Ferdinand III, in the spring of Rákóczi’s invasion of Hungary: to keep the Turk from helping the Prince of Transylvania, to raise the Prince of Moldavia against him, to supply two thousand Cossacks, and to press the Emperor to make no peace until he is humbled or beaten. Status: read. Three spellings and the speaker’s name wait on the manuscript images, which need a DECODE login.

01 The document

Tomokiyo transcribed the cipher paragraph in his article on variable-length figure codes in the Austrian archives (DECODE R2159, R1408, R2179 and a Starhemberg letter of 1758). His note on this one: from Fra Giovanni di Lucca to the Emperor, 30 May 1644, in Italian; “the number groups may consist of one or two digits, but there is no difficulty in identifying individual groups because the groups are delimited by dots.” DECODE’s public record says Non-decrypted, cipher type Unknown, symbol set numerical, two pages, partly encrypted, with a placeholder date range of 1686–1877. The images are not public. Everything below rests on the transcription.

3 11 26 21 17 17 6 15 26 1 8 17 19 21 9 14 19
15 25 3 14 15 3 11 13 15 12 26 1 8 17 21 18 6 13 14 18 2 14 12 13 8 18 6 10 1 15 11 22 25
21 6 18 14 13 14 11 17 8 15 9 3 15 23 22 13 1 5 9 21 18 21 15 25 13 11 19 3 32 7 6 18
14 22 21 9 8 17 11 25 15 19 7 19 3 21 9 4 15 19 13 2 14 18 17 11 26 21 17 17 6 15
26 1 8 15 4 18 2 13 8 3 14 17 9 7 22 11 17 8 3 21 13 8 23 12 17 11 15 3 6 18 19
9 6 10 15 7 22 12 3 17 8 1 21 13 9 25 18 17 6 13 17 23 17 3 19 25 9 11 7 22
1 21 3 9 11 15 12 26 7 21 9 22 13 21 7 6 10 7 17 18 17 5 3 6 15 9 26 9 6 7
5 17 14 6 10 7 17 18 17 11 10 9 4 17 10 25 12 17 11 15 9 19 13 18 23 15 17
22 18

231 groups, 24 distinct figures (1–15, 17–19, 21–23, 25, 26, 32), index of coincidence 0.050. There is exactly one doubled pair in the whole text, 17 17, and it occurs twice in the same word. Italian prose doubles a consonant at three to four positions in a hundred, so a plain letter-for-letter substitution is excluded before anything is tried: the doubles are being split between homophones, or a figure is doing two jobs.

02 Solving

Unconstrained annealing fails. A homophonic annealer with a 5-gram Italian model (Villari’s Machiavelli e i suoi tempi, I promessi sposi, La Mandragola; 4.1 million letters, v written u) was run from sixteen seeds. All sixteen converged on the same optimum, estreesitenetrentiuenieseist…, which is not Italian. The solver reads a matched 231-letter Italian control in one seed of three, so this is a flat landscape, not a proof.
The crib is inconsistent with a substitution. Al principe di = 3 11 | 26 21 17 17 6 15 26 1 | 8 17. From di, and from il = 17 11 later in the text, 17 is i; in principe the second 17 must be n. Eight letters survive without contradiction: 3 a, 11 l, 8 d, 17 i, 26 p, 21 r, 1 e, 19 t.
Crib-fixed annealing. With those eight fixed and the other sixteen figures free, six seeds converge on one reading at −2.50 nats per 5-gram: alpriicipeditrantiuanialoimpediroconoinmodocheilturcononlidiaaiutoefaroriuoltase… — lo impedirò … che il Turco non li dia aiuto e farò rivoltare… Word after word is Italian, to the last group.
Two figures carry two letters. Holding the rest, 17 reads n in principe (twice), manderò, con una, non, vinto, and i in di, il, impedirò, li, lui, dumilia, finché; 19 reads t in Transilvania, rivoltare, sua, humiliato, vinto, and s in Transilvania, se sarà bisogno, Cosachi. No third value is needed for either. A Viterbi decode over the two alternatives with the same model makes each choice mechanically and agrees with the hand reading except at two places noted below.
Control. The crib-fixed procedure on five shufflings of the same ciphertext — same figures, same counts, same eight letters fixed — reaches −3.40 to −3.68 per 5-gram against −2.50 for the letter, about 200 nats over 227 5-grams. Worth saying plainly: the unconstrained false optimum in step 1 scored the same as the true reading, so the model does not pick the solution by itself. The eight crib letters do, and the shuffles show that eight fixed letters on this text do not manufacture Italian on their own.

03 The key

1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	17	18	19	21	22	23	25	26	32
e	g	a	b	f	c	e	d	a	h	l	m	o	n	i	i / n	o	t / s	r	t	u	u	p	r
7	3	16	3	3	13	10	10	12	6	13	6	13	10	18	24	14	9	14	8	4	7	7	1

Third row: occurrences. Figures 16, 20, 24 and 27–31 do not occur; q, z and consonantal v are absent from the text. The arrangement shows no alphabetical order. b, g and the second r rest on one to three occurrences each, in words no other letter fits (bisogno, Bogdania, habbi; ogni, bisogno, Bogdania; rivoltare).

An alternative to polyphony. Every “17 = n” could be a 14 transcribed as 17 (a 4 and a 7 are close in seventeenth-century hands), and “19 = s” could be a misread figure for an s otherwise unused. Either would make this an ordinary homophonic alphabet. The images would settle it; the reading is unchanged either way.

04 Reading

Al principe di Transil[u]ania lo impedirò con ogn[i] modo che il Turco non li dia aiuto, e farò rivoltare contra di lui, se sarà bisogno, il principe di Bog[o]dania, et li darò dumilia Cosachi, et manderò a voi con una sua lettera all’Imperatore che non faccia pace fin che [io] l’habbi humiliato o vinto.

As to the Prince of Transylvania: I shall by every means prevent the Turk from giving him help, and if need be I shall make the Prince of Moldavia rise against him and give him two thousand Cossacks, and I shall send [him] to you with a letter of his to the Emperor, that he make no peace until I have humbled or defeated him.

Transiuania (19 21 9 14 19 15 25 3 14 15 3) has no l, and ogn modo lacks the i of ogni: the writer’s spelling or a dropped group, in each case.
Bogodania (4 18 2 13 8 3 14 17 9): Bogdania is the ordinary Italian and Turkish name of Moldavia (Boğdan). The extra 13 is the writer’s or the transcriber’s. The Viterbi pass prefers Bogodanna on statistics; the place-name fixes 17 = i here.
19 25 9 before lettera is sua (Viterbi) or tua; sua is the grammatical reading.
17 18 17 11 10 9 4 17 is io il habi or no il habi (non l’habbi); the sense is the same.

05 Context

In February 1644 György Rákóczi I, Prince of Transylvania, invaded Habsburg Hungary in alliance with Sweden and France and with the Porte’s leave. Through the spring Ferdinand III’s diplomacy worked to have the Ottoman support withdrawn and to find pressure on Rákóczi’s eastern flank. The paragraph is a first-person offer, carried by the friar, from someone who claims to be able to work on the Porte, to set the Prince of Moldavia (Vasile Lupu) against Rákóczi, and to dispose of two thousand Cossacks. Who is speaking is not in the cipher. That combination of levers points to Poland — the King, Władysław IV, who was Ferdinand III’s brother-in-law, or the Grand Hetman Stanisław Koniecpolski, who kept his own relations with Moldavia and the Tatars and had beaten the Tatars at Ochmatów that January — but that is an inference from the content, not a reading.

Fra Giovanni di Lucca (Giovanni Giuliani da Lucca), Dominican, is known from his Relatione and Itinerario as a missionary of the 1620s and 1630s to the Tatars, Circassians, Abkhazians, Mingrelians and Georgians, and from later work in Moldavia (Cristian Luca, 2004, not consulted here). A Dominican who moved between Moldavia, the Cossack lands and Vienna is the sort of courier such an offer would use. Whether the cleartext of ff. 18–19 names the principal, the manuscript would show; Tomokiyo’s article quotes only the cipher.

06 Method and files

Ciphertext from Tomokiyo’s article; counts, doubles and index of coincidence checked (lucca/ct.txt).
Italian 5-gram model with absolute discounting and interpolation, Roman-numeral page references stripped (lucca/lm.py).
Homophonic annealer, unconstrained (lucca/solve.py), then with the eight consistent crib letters fixed (lucca/crib_anneal.py).
Polyphonic Viterbi over {i, n} for 17 and {t, s} for 19 (lucca/decode.py).
Shuffled-ciphertext control of the crib-fixed procedure (lucca/control.py).

Checked: transcription counts, crib consistency, convergence across seeds, five shuffled controls, word-level Italian. Not checked: the manuscript images, the cleartext frame, the identity of the speaker. The historical attribution in §05 is an inference and should be verified before it is repeated.

07 Sources

S. Tomokiyo, “Variable-Length Numerical Code in Austrian Archives” (cryptiana), and “Unsolved Historical Ciphers” (cryptiana), German section.
DECODE record R2159, ÖStA HHStA Staatskanzlei Interiora, Chiffrenschlüssel Kt. 20 Fasc. 27 ff. 18–19.
Fra Giovanni di Lucca, Relatione … delli Tartari, Percopiti, Nogai, Circassi, Abazza, Mengrilli e Giorgiani and Itinerario (manuscripts, catalogued at the National Library of Russia); Cristian Luca, “Note sull’attività missionaria del domenicano Giovanni Giuliani da Lucca”, in Prinos lui Petre Diaconu la 80 de ani (Brăila, 2004), pp. 685–692.
On the 1644 campaign: the Transylvanian invasion of Hungary, 1644–45, and Koniecpolski at Ochmatów, January 1644 (standard accounts).

Analysis scripts and the ciphertext are in the repository (lucca/).