Affine cipher decoder
Turn affine cipher text back into plain text when you know both keys, for puzzles and homework. It is a puzzle cipher that protects nothing.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter encoded text, multiplier a and shift b.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Original = a⁻¹ × (y - b) mod 26, where a⁻¹ is the inverse of a, so a × a⁻¹ mod 26 = 1.
Example
Inputs: Multiplier a = 5, Shift b = 8. Result: Decoded text: AFFINE CIPHER; Inverse of a: 21.
IHHWVC SWFRCP
AFFINE CIPHER
Limits and caveats
- This is a puzzle and teaching cipher that is easy to break, so never use it to protect passwords or sensitive data.
- You need the same a and b values used to encode.
Questions about this tool
How do I find the inverse of a by hand?
Try 1 to 25 until one gives remainder 1 when multiplied by a and divided by 26. The inverse of 5 is 21, since 105 = 4 × 26 + 1.
What if a = 1?
The cipher becomes a plain Caesar cipher with shift b.
Do spaces stay in place?
Yes. Only Latin letters change; spaces and symbols stay as they are.