Micro Tools
Advertisement

Affine cipher

Encrypt and decrypt with the affine cipher. Set multipliers a and b; each letter maps through E(x) = (ax + b) mod 26.

Encrypt or decrypt

E(x) = (a*x + b) mod 26. The multiplier a must be coprime to 26.

Valid: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25.
Nothing is uploaded. Everything is computed locally in your browser.
Affine

The result appears below. Case is preserved; other characters pass through.

-
Advertisement

Math behind it

The affine cipher encrypts each letter x (A=0 through Z=25) as E(x) = (a*x + b) mod 26. The multiplier a must be coprime to 26 (one of 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25); otherwise several letters collide and decryption is impossible. Decryption uses the modular inverse of a.

Tiny key space

Only 12 valid values of a times 26 values of b gives 312 possible keys, brute-forced in milliseconds. Frequency analysis also breaks it directly since it is monoalphabetic. The affine cipher is a teaching tool for modular arithmetic, not a security mechanism.

Related tools

JSON formatterFormat and validate JSON, privately. Regex testerTest regex live with highlighting. Base64 encoderBase64 encode and decode, plus URL encoder and JWT decoder.

Affine Cipher FAQs

Why is a=13 rejected?
a must be coprime to 26 or the mapping is not reversible: with a=13, both A and N would encrypt to N. Valid a values are 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25.
What is the modular inverse?
The number a^-1 with a*a^-1 = 1 mod 26, used to decrypt. For a=5 it is 21, since 5*21 = 105 = 1 mod 26.
How many possible keys?
12 choices for a times 26 for b = 312 keys. A computer tries them all instantly, which is why the cipher is insecure.
Does it handle lowercase?
Yes, case is preserved and non-letters pass through unchanged.
Affine vs Caesar?
Caesar is the special case a=1. The affine cipher generalizes it with the multiplier, but both fall to frequency analysis.
Advertisement