cipher.codes

Affine

About

Affine is a monoalphabetic substitution cipher. Each letter in the alphabet is mapped to a number, then encrypted/decrypted using a math formula, and finally converted back to a letter.

Supports

✅ Perfect Decoding
✅ Uppercase letters (A-Z)
✅ Lowercase letters (a-z)
❌ Numbers (0-9)
❌ Symbols (!@#$)
❌ Emojis (😍🤬👩🏾‍💻)

Numbers, Symbols, and Emojis
Numbers, symbols, and emoji are outputted as-is by this cipher.

What is “Perfect Decoding”?
Perfect Decoding is when the decoded text exactly matches the text that was encoded.

Source

View Affine on Github

Formulas

Encoding

((coprime * letterPosition) + shift) mod 26

Decoding

(modInverseOfCoprime * (letterPosition - shift)) mod 26

Live Example

Variables

Based on the current settings for Affine:

coprime = 3
shift = 6
modInverseOfCoprime = 9

Encoding Formula

((3 * letterPosition) + 6) mod 26

Decoding Formula

(9 * (letterPosition - 6)) mod 26

Sample String

Hello World!
ABCDEFGHIJKLMNOPQRSTUVWXYZ
abcdefghijklmnopqrstuvwxyz
0123456789
!@#$
✨🦄✨

When, Encoded

Bsnnw Uwfnp!
GJMPSVYBEHKNQTWZCFILORUXAD
gjmpsvybehknqtwzcfiloruxad
0123456789
!@#$
✨🦄✨

Then, Decoded

Hello World!
ABCDEFGHIJKLMNOPQRSTUVWXYZ
abcdefghijklmnopqrstuvwxyz
0123456789
!@#$
✨🦄✨

How it works

letterPosition is the index of the letter
coprime and shift are two variables you pick!
modInverseOfCoprime is the modular multiplicative inverse of coprime

“Magic” Number 26

You’ll see a lot of references to 26, it’s not a magic number, just the
number of letters in the English alphabet.

`letterPosition`

Index of the letter in the English alphabet (0-indexed). For example,
A=0, B=1, C=2, and so on until Z=25.

`coprime`

Must be a number where the only positive integer that divides it and 26 is 1. With that limitation the only valid values are: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25

`shift`

Any integer, positive or negative

`modInverseOfCoprime`

The modular multiplicative inverse of the coprime. To be honest, I don’t fully understand the formula.

But, after extensive searching, I got a rough understanding that we need to find a number where the formula below would be correct.

(coprime * x) % 26 = 1

The value of x is the modular multiplicative inverse of coprime. The following javascript function, ~~stolen~~ converted from the examples here calculates the value for x.

function _modInverse (coprime) {
  let mod = utils.TOTAL_ALPHA
  let inverse = 1
  let y = 0

  while (coprime > 1) {
    let origMod = mod
    let origY = y
    let quotient = Math.floor(coprime / mod)
    mod = coprime % mod
    coprime = origMod
    y = inverse - quotient * y
    inverse = origY

    if (inverse < 0) {
      inverse += utils.TOTAL_ALPHA
    }
  }

  return inverse
}

`mod 26`

Both formulas for encoding and decoding have mod 26 which performs the modulo (%) operation on the output.

This is a safe-keeping action to guarantee the character is one of the 26 letters in the alphabet. Javascript doesn’t have proper support for mod so this formula is used:

export function mod (a, b) {
  return ((a % b) + b) % b
}