972Unsolved Historical Ciphers
1087, 638, 1193, 1083, 1531.18.536.503t, 537.788e, 2510, 1114.137 …
key not found: the codebook reaches at least 2510

The Hague → William V in exile · French numerical nomenclator · 18 June 1804

Robert Fagel to William V, 18 June 1804

William V
toWilliam V

Koninklijk Huisarchief, The Hague, Prins Willem V (old inv. nr. 337), DECODE R2238: three pages, the middle one a coded passage of 128 numerical groups between clear French sentences about the Orange compensation talks with the Batavian Republic.

The code groups were transcribed from the DECODE images and the letter was dated and placed in its negotiation. No key was found. Every key that can be reached online, in DECODE and in the digitised Royal Collections and Fagel papers, was tested and ruled out, and the passage is too short for the key to be recovered from the ciphertext alone. No decipherment is known; the key has to come from the archive.

Daniel Bourdeau · posted · updated

Method: not solved · Extent: text not obtained

Summary. DECODE records no decipherment of Robert Fagel’s letter of 18 June 1804 to the exiled Stadholder. Its coded passage is 128 numerical groups, 99 of them distinct, from 12 to 2510; dots join groups inside a word, and a few groups carry clear endings (503t, 788e, 281s), so the code is a large syllabic nomenclator for French. The clear sentences around it tie it to the final 1804 liquidation of the House of Orange’s claims, days before Fagel and d’Yvoy set out for Germany. The key was sought in every place reachable online: Euler’s 1782 Grand Chiffre of the Stadholder (DECODE R1024), direct, through its additive table from every start, and under 5,000 shifts, affine maps and digit permutations; all four KHA keys in DECODE; the eleven Fagel family keys R2842–R2852; the British Library French codes of 1798–1805; the Uppsala key R5160; and the small book cipher of the sibling letters. None can produce the letter’s groups or gives French. A text this short from a code of 2,500 values has no unique ciphertext-only solution. No key has been found. The likeliest home of the key is KHA A31-902, “Stukken betreffende de aan het hof gebruikte geheimschriften”, a packet with no scans; then A31-2307/2308 and Nationaal Archief 1.10.29 no. 1909. A request to the archive is drafted in the repository.

01 The letter

The cipher page of R2238: three lines of clear French, then rows of comma-separated figure groups, with a boxed interlinear insertion
R2238, the second page of the letter (DECODE image P3): the clear sentence ending parfaitement d’accord, then the figures, broken by the clear j’attends la réponse pour partir. Image: Koninklijk Huisarchief, The Hague, Prins Willem V (old inv. nr. 337), image P3, via DECODE R2238.

DECODE numbers the pages back to front. The first page (P2) is in clear: a letter from the Hereditary Prince of the 6th announces the Stadholder’s departure; the courier Gaebel arrived on the 9th; the Commissaires of the House kept him so that d’Yvoy could be briefed; a note went to the Batavian side, whose answer was that he hoped to speak with Damen. The second page opens in clear, “Dès lors il n’a plus fait entendre parler de lui, et l’on ne tardera pas à connaître la déclaration, sur laquelle les instructions de V. A. S. et celles du ministre du Roi sont parfaitement d’accord”, then goes into figures. The last page closes “La Haye 18 Juin 1804 … R. Fagel”.

The context is established from print. Colenbrander’s Gedenkstukken IV prints the surrounding papers: d’Yvoy’s appeal to Talleyrand of February 1804, his promise of 500,000 guilders for payments in Paris, Berlin and The Hague, Princess Wilhelmina’s letter of 14 June saying the arrangement was decided, and Fagel and d’Yvoy’s return with the signed convention on 7 August. It does not print this letter.

02 The cipher

128 groups, 99 distinct, two to four digits; 1531, 1731 and 2510 were checked at high resolution and are genuine four-digit groups. Commas separate words and dots join groups inside a word. The words &, car and que are in clear, and a boxed insertion adds a line between the rows. Small superscript marks (c, 3, 6, 9, fractions) follow some groups; their reading is uncertain. The full transcription is fagel1804/ciphertext.txt.

03 Keys tested

KeyWhat it isResult
R1024, Grand Chiffre (Euler, 1782)KHA code of 4,732 transcribed entries, 51–5000, with an optional additive tableDirect lookup is nonsense; all 187 row and 187 column starts of the table fail; so do all 5,000 cyclic shifts, affine maps, complements and digit permutations, scored with a French language model (best −10.2 per character against −8.5 for the letter’s own clear French). The table also requires a start letter at the head, which the letter lacks.
R2233, R2235, R2240The other KHA keys in DECODE (1793–1801)Small homophonic or name systems; cannot produce the groups
R2842–R2852Fagel family keys, Nationaal Archief 1.10.29Every range audited page by page; none goes above about 1055
R1035, R1891Dutch legation codebooks, 1798 and 1803Dutch-language; the plaintext is French
R8963/R8964, R8984, R8987British Library French codes, 1798–1809Numbered only to 750 or less; nonsense, also modulo 1000
R5160 (Uppsala)French nomenclator, Chiffre François, de M. de LacyNumbered 210–841 only
R2237, R2239, A32-630Sibling letters and deciphered file of 1795–97Euler/Boyer small book cipher, references to about 334; a different system

DECODE holds no second message in this code, so there is no parallel text to crib from either.

04 What would finish it

With 128 groups from a code of about 2,500 values, no statistical attack can give a unique decoding; only the codebook or a deciphered copy can. The modern KHA inventory does not match DECODE’s old number 337; the subject belongs with A31-2306–2308, the 1802–1804 compensation negotiations. The best target is A31-902, a packet of court cipher papers of the late eighteenth and early nineteenth centuries, which the Royal Collections’ catalogue backend confirms has no scans. After it come A31-2307 and A31-2308 (1804), A31-2292–2293, and Robert Fagel’s negotiation file, Nationaal Archief 1.10.29 no. 1909. A research request to the Koninklijke Verzamelingen is drafted as fagel1804/ARCHIVE_REQUEST.md.

05 Sources

Transcription, scripts and notes: fagel1804/ in the repository.