The Ciphers of Trithemius

Johannes Trithemius (1462–1516), abbot of Sponheim and later of the Schottenkloster in Würzburg, stands at the head of printed cryptography. His Polygraphiae libri VI — "Six Books of Polygraphy" — is his open cryptographic manual, the first printed book on the subject in the West: completed late in his life, dedicated to Emperor Maximilian I, and printed in 1518, two years after his death. Its notorious companion, the Steganographia (composed around 1499–1500), circulated only in manuscript during his lifetime and earned him lasting accusations of necromancy, because its cipher instructions are dressed as conjurations of angels and spirits. Both systems — and the explanatory keys Trithemius supplied for them — are in this corpus.

The "Ave Maria" cipher: a prayer that is also a message

The heart of the Polygraphia is verbal substitution, often called the "Ave Maria" cipher. Each of its books presents a different modus of enciphering, but the basic mechanism is constant. The plaintext is broken into individual letters, and each letter is replaced by a Latin word drawn from a substitution column — an alphabetum of cipher words. In the multi-column modi the substitution rotates with the letter's position: position 1 uses column 1, position 2 uses column 2, and so on, returning to column 1 once the columns are exhausted. The columns are built so that any plaintext produces a grammatical Latin sentence — invariably a devotional invocation. The ciphertext is thus undetectable: it reads as ordinary monastic prayer.

The corpus's own worked example takes the eight-letter plaintext ABCDEFGH through the eight columns of Modus Primus (the first cipher of the Clavis Polygraphiae): A in column 1 becomes facti, B in column 2 certe, C in column 3 timendum, D in column 4 continue, E in column 5 sempiternum, F in column 6 fabricatorem, G in column 7 supercaelestium, and H in column 8 compassionem. The resulting ciphertext reads:

Facti certe timendum continue sempiternum fabricatorem supercaelestium compassionem.

To an eavesdropper this is a pious Latin sentence; only the recipient who knows to take each word back through its enciphering column recovers ABCDEFGH.

The cipher words above are given in their intended forms, to show the mechanism clearly. The OCR'd source cells themselves carry scannos — certe appears as Lerte, fabricatorem as fabricatosem, supercaelestium as supercelestvm — and those damaged forms are preserved as they appear in the rendered chunk tables and the facsimile beside them, per the editorial principle below.

The published tables let you watch this machinery at full width. One chunk of the Clavis Polygraphiae (full_chunk_0085) parses twenty-two substitution columns against Trithemius's 24-letter alphabet (a b c d e f g h i k l m n o p q r s t v x y z w, omitting j and u). Reading across the row for the letter b, the first columns give ebales, abadan, abzym, abenoz, abadiel, abnason — six different ways of saying "b", each pulled from a different prayer-vocabulary.

Rotating alphabets: the tabula recta and the Orchema numerale

The Polygraphia's sixth book moves from words to tables. Its alphabet-rotation expansion figures (tabula recta / auersa / aucta) derive new cipher alphabets from a base alphabet by transposition — in the rendered Prima figura expansionis tabulae rectae, each row is the alphabet stepped one place from the row above. This rotating-alphabet family is the ancestor of what later cryptographers know as the Vigenère table. Alongside it sits the Orchema numerale, a numerical-substitution matrix indexed by Latin letters with Trithemius's own note describing its diagonal use.

An honest note about what you will see. In the printed book these are worked example figures, set as paired plaintext/cipher columns — not one mechanical master grid. The OCR that underlies this corpus frequently linearised those paired columns into identical rows, a layout that cannot be recovered from the text alone. Rather than fabricate grids, this corpus omits the misleading transcription in 31 of the 54 cipher-grid chunks and shows the source facsimile instead; where the OCR did preserve the rows, they are transcribed as tables with illegible cells marked — and OCR noise left visible. In every case the facsimile shown beside the rendering is authoritative for the cipher.

The Steganographia: ciphers dressed as conjurations

The Steganographia works differently, and its mechanism is documented in Trithemius's own key, the Clavis generalis triplex — the "Threefold General Key to the Steganographic Books." Unlike the Polygraphia scheme (plaintext letter → Latin word), the Clavis convention is letter-pair substitution: each plaintext letter maps to a single ciphertext letter. The source records each alphabet as comma-separated pairs of the form Ax,bz,ca,db… — read as A→x, b→z, c→a, d→b, …. The cipher letters are then padded out into an innocent-looking Latin prose Exemplum that reads as ordinary devotional writing.

The rendered chunks show the full anatomy of one concealment: the Alphabetum (the substitution table); the Intentio Mysterij, the secret message in early-modern German — in one example, "Ich bittedich komm von stund an zu mir/ es thut sehr noth" ("I beg you, come to me at once; the need is great"); the Literae significantes, the bare ciphertext letters; and the Exemplum, the Latin cover prose that carries them, opening "Creator genyri humani apice Deus…" (OCR scannos preserved as they appear in the scan).

What of the angels? The Steganographia's instructions are framed as conjurations of spirits — Pamersiel, Padiel, Camuel, Aseliel and dozens more — and strings like Camuel aperoys, melym mevomanial, casmoyn cralty bufaco aeli lumar photirion theor besamys are not Latin and not nonsense: they are constructed cipher cover-text. Trithemius framed his cipher schemes in spirit-conjuration language for cover, and the Clavis is the antidote he supplied, demonstrating that the "spirit names" resolve into a cryptographic system, not a magical one. This corpus accordingly preserves the magical surface verbatim — spirit names unanglicized, conjuration formulae quoted rather than translated — without glossing over the cryptographic substrate or treating the angels as the real subject. That framing nonetheless cost the book dearly: printed posthumously in 1606, the Steganographia was placed on the Index Librorum Prohibitorum.

Solved: the Clavis ciphers decoded

The breakthrough was identifying that the Clavis cipher is not a uniform Caesar shift (which is why brute-force over all 24 shifts scored no better than chance). Each modus prints its own explicit, irregular substitution alphabet, and the ciphertext is decoded by inverting that alphabet letter by letter. The alphabets are roughly −N on Trithemius's 24-letter alphabet, but irregular enough that the printed Alphabetum itself — not a shift rule — is the key. A hand-check on the opening of Modus II confirms it: the cipher stream gafzgbc… maps g→i, a→c, f→h, z→b → "Ich b[…ittedich]" ("I beg you…").

The simple modi (five worked examples) are solved — their German plaintext recovered and recognisable:

The decodes are letter-for-letter through the printed alphabet — no guessing. Each recovered plaintext is an ordinary early-modern German sentence (a request to come at once, a report of Saxon musters, a note about keeping books secret), confirming that the Steganographia's "spirit names" and "angelic conjurations" are cover for mundane correspondence, exactly as Trithemius's Clavis was designed to demonstrate. The full char-aligned decodes — with each cipher letter mapped to its plaintext letter, match shown green and OCR-drift shown red, beside the facsimile crop of the cipher line — are in the cipher solutions page.

Honest scope of the solve

Two limits remain, and they are stated plainly:

• The residual gap is OCR, not the cipher. The cipher lines are tiny, period-separated Fraktur letters in 1608 print — at the ceiling of current vision OCR — so a few letters per line drift. The German is recovered and recognisable (62–77% character match on the simple modi, 70–92% on the high modi), but not a perfect transcription. The high-modus cipher lines in particular were beyond vision OCR and were recovered by human eye-reading of zoomed facsimile crops against a Fraktur reference key — the one step in the pipeline a machine could not do.
• The full range of modi present in the facsimile is solved — simple (II–XI) and high (XXXII–XXXIX) alike. The high modi use the same explicit-alphabet inversion as the simple ones; their "alternating words / null rhythm" rule-language describes only how the cipher stream was extracted from the cover letter, not a different decryption. Six high modi now decode end-to-end:

Each is an ordinary early-modern German sentence — a warning of a planned stabbing (XXXVII), a character reference for a drinker (XXXIII), a report of an absent abbot (XXXV), a slander warning (XXXVIII), a signal by a woodsman's whistle (XXXII), a counsel to stay away (XXXIX). The "angelic" frame dissolves entirely: these are mundane letters about money, drink, and danger, hidden in Latin cover prose. The high-modus decodes were cracked by inverting each modus's printed Alphabetum table against a human-transcribed cipher line — the dense Fraktur Literae stream being the one input vision OCR could not supply.

For the published translations of these works, the cryptographic substitutions are still passed through as written — the cipher streams in the body text are transcribed, not decoded inline. The executable cipher edition now traces Modus II from the printed page through a committed transcription and explicit-alphabet inversion. It keeps the imperfect computed output separate from the printed Intentio, labels evidence, repair, and inference, and supplies JSON and TSV downloads so the result can be recomputed without the website. For the comprehensive modern English edition of the Steganographia and its angelological framing, see Skinner & Clark (2024); for the foundational cryptanalysis, Ernst (1996) and Reeds (1998), who independently solved Book III.

Explore the cipher materials in this corpus

• Executable cipher edition — Modus II, step by step — a reproducible worked example with facsimile evidence, explicit editorial status, keyboard-operable navigation, substitution table, plain-text account, and downloadable data.
• Substitution tables (Polygraphia VI, cipher-key renderings) — the "Ave Maria" alphabets, rendered alphabet-down / columns-across beside the source facsimile.
• Rotation figures and the Orchema numerale (cipher-grid renderings) — the tabula recta family, with facsimiles wherever the OCR collapsed the figure.
• Worked steganographic examples (Clavis Steganographiae) — freshly translated passages from the triple key; the letter-pair claves themselves are on the cipher-key page.
• The parallel viewers — e.g. Polygraphia VI and Clavis triplex — keep the Latin OCR beside the English throughout.