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Affine Cipher: Encrypt and Decrypt with Keys a and b

This free affine cipher tool encrypts and decrypts text with two numbers, a and b, using the formula (a × x + b) mod 26. It checks your key and shows the inverse used for decryption.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

The affine cipher is a Caesar cipher with a multiplication added. Multiplying by a spreads the letters out, and adding b shifts them. It gives 312 possible keys, still far too few to be secure, but a good step up for teaching.

Enter text, the two keys and the direction.

How to Use This Tool

  1. Type or paste your text.
  2. Enter a valid key a and a key b.
  3. Choose encrypt or decrypt.
  4. Press Run.

How the Calculation Works

Letters are numbered 0 to 25. Encryption computes (a × x + b) mod 26. Decryption computes a⁻¹ × (y − b) mod 26, where a⁻¹ is the number that gives 1 when multiplied by a modulo 26. The tool tests that a and 26 share no factor.

Worked Example

With a = 5 and b = 8, AFFINECIPHER becomes IHHWVCSWFRCP, the standard example.

Common Uses

  • Teaching modular arithmetic.
  • Puzzles.
  • Studying cipher families.
  • Homework checks.

Tips and Common Mistakes

  • Pick a from the list of 12 allowed values.
  • a = 25 and b = 25 is the Atbash cipher.
  • Try brute force over all 312 keys by hand only for short texts.

Next, you may need the Caesar cipher, Atbash cipher, Vigenère cipher, A1Z26 cipher.

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Frequently Asked Questions

A substitution cipher that maps each letter x to (a × x + b) mod 26, where a and b are the key numbers.
Only numbers with no common factor with 26: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 and 25. Otherwise two letters would map to the same one.
With x = a⁻¹ × (y − b) mod 26, where a⁻¹ is the modular inverse of a. The tool finds it for you.
Then it is a Caesar cipher with shift b.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.