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Cryptography & Ciphers

Affine Cipher Encoder

Encode English letters with an affine substitution using numeric values a and b. Check the worked example and matching decoder.

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Encode English letters with an affine substitution using numeric values a and b. Check the worked example and matching decoder.

This tool runs open-source code from CyberChef by GCHQ (Apache License 2.0). See open-source credits.

Affine Cipher Encoder replaces each letter with y = (a × x + b) mod 26, counting A = 0 through Z = 25. The multiplier a must share no factor with 26. With a = 5 and b = 8, Hello, World! becomes Rclla, Oaplx!.

The output has the same length and punctuation as the input. Only the letters A–Z and a–z change.

  • Write an affine exercise for a lesson on modular arithmetic.
  • Show that a = 1 turns the affine cipher into a Caesar shift by b.
  • Produce ciphertext for testing your own affine decoder.

Instructions

  1. Type the plaintext into Input. Upper and lower case are kept.
  2. Enter a and b. Valid values of a within 0–25 are 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, and 25.
  3. Record a and b with the ciphertext. Decode it with Affine Cipher Decoder and the same values to check the round trip.

Example

Input: Hello, World!

Settings: Affine Cipher Encoder with a = 5 and b = 8.

Result: Rclla, Oaplx!

Affine Cipher Encoder maps H (7) to 5 × 7 + 8 = 43, and 43 mod 26 = 17, which is R. The comma, space, and exclamation mark stay in place.

Limits

  • An even a, or a = 13, makes the mapping irreversible. The tool rejects those values.
  • Accented and non-Latin letters pass through unchanged.
  • With only 312 possible key pairs, anyone can try every key. The cipher gives no real secrecy.

Questions

What do a and b mean in the Affine cipher?

They define the alphabet substitution rather than a password. The multiplier a must be coprime to 26 so the mapping can be reversed. Use the same a and b in the matching decoder.

Does Affine processing change spaces and punctuation?

The operation changes letters through the 26-letter alphabet and retains their case. Nonalphabet characters pass through the transformation. Verify a short example before comparing a puzzle with a different alphabet convention.

Can the Affine tool discover unknown parameters?

This operation applies the parameters you supply; it does not search all possible keys. Readable output is evidence to inspect, not proof of the intended key. Affine substitution is for classical-cipher work, not protecting secrets.