Trithemius Progressive Cipher Polygraphia · 1518
The first published polyalphabetic cipher: a tabula recta with every letter advanced by one more shift than the last.
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Why This Matters
Johannes Trithemius (1462–1516) was a Benedictine abbot, occult scholar, and one of the most consequential cryptographers of the German Renaissance. His Steganographia (written ~1499, published 1606) disguised a cipher manual as a book of angel-summoning magic; his Polygraphia (1518) was the first printed book on cryptography in the West. The progressive cipher described here appears in Polygraphia's opening tables.
Trithemius made successive shifted alphabets visible in a tabula recta. His historical table used a smaller Latin alphabet; the 26×26 table here is a modern adaptation. Later polyalphabetic systems developed several ways to choose alphabets, rather than one simple documented lineage.
Encrypt the first letter with shift 0, the second with shift 1, the third with shift 2, and so on. The keystream is just the position counter:
Plain: S T E G A N O G R A P H I A Shift: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Cipher: S U G J E S U N Z J Z S U N
The optional starting offset simply moves the counter's origin. There is no keyword. The system is polyalphabetic in form — every letter uses a different alphabet — but the alphabet sequence is public knowledge, so it offers no real secrecy.
Because the keystream is fixed and public, the only secret is the starting position. Twenty-six guesses recover the plaintext — Caesar-grade work.
After 26 letters the shifts wrap around and a 26-period structure emerges. Splitting the ciphertext into 26 columns and frequency-analysing each one yields the offset.
Progressive substitution demonstrates that one plaintext letter can have different ciphertext representations at different positions. Similarity of that idea across later systems does not prove that every mechanical cipher descended directly from Trithemius’s table.
A publicly predictable shift sequence gives no meaningful secrecy. Modern stream ciphers instead derive a keystream from secret key material and public inputs such as a nonce. ChaCha20 is a modern example; obsolete RC4 should not be presented as an equally secure contemporary choice.
| Origin | Johannes Trithemius, abbot of Sponheim |
| Published | Polygraphia, 1518 (posthumous) |
| Key Type | Optional starting offset only |
| Significance | Introduced the tabula recta to Europe |
| Modern Lesson | A predictable keystream is barely a keystream |