Cardano Autokey 1550 historical idea · modern comparison model
Cardano’s self-keying idea, compared with a modern one-letter-primer plaintext-autokey model.
The one-letter-primer widget is a modern comparison with Vigenère-style plaintext autokey, not Cardano’s exact procedure.
Why This Matters
Cardano described using plaintext as key material, but the one-letter-primer algorithm below should not be attributed to him as an exact reconstruction. Holden’s The Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital Encryption (2017), §5.3, pp. 157–159, distinguishes Cardano’s word-based scheme from Vigenère’s later use of a priming letter. This interactive isolates a simple autokey recurrence for teaching.
In this model, knowing one plaintext letter gives the next key letter and permits forward propagation. A primer of length k changes this to propagation every k positions; it does not eliminate the structural weakness. A sufficiently long correct crib can seed several such chains.
Pick a single seed letter S. The keystream is
k₀ = S kᵢ = pᵢ₋₁ for i ≥ 1
Encryption uses the standard Vigenère table: cᵢ = (pᵢ + kᵢ) mod 26. Decryption recovers p₀ from c₀ using S, then uses each just-recovered pᵢ as the key for cᵢ₊₁.
Worked example with S = Q, plaintext MEET ME AT MIDNIGHT:
Plain : M E E T M E A T M I D N I G H T Key : Q M E E T M E A T M I D N I G H Cipher: C Q I X F Q E T F U L Q V O N A
With a one-letter primer, a correct plaintext guess propagates one position at a time. Wrong guesses generate alternative chains that need evaluation against language or other evidence. Longer primers change the spacing of propagation rather than making plaintext feedback secure.
Try every possible seed letter. For each, run the cascade and look for English. The correct plaintext is among the 26 candidates; a short or unusual message may need context to distinguish it.
The lesson is that reusing message letters as raw key material does not supply independent secrecy. It should not be generalized into a rule that every data-dependent cryptographic construction is insecure: the precise construction and security definition matter.
CTR and ChaCha20 generate keystream from a secret key and nonce/counter state. Their security also depends on correct nonce use. The contrast is with this bare letter recurrence, not a claimed direct historical lineage or a universal ban on processing plaintext in authentication and encryption designs.
| Origin | Girolamo Cardano, Italy |
| Year | 1550 (De Subtilitate) |
| Key Type | Single priming letter |
| Secret choice in this model | One of 26 primer letters |
| Modern Lesson | Key reuse from the plaintext is not the same as key freshness |