Concept

Decimation + Shift

Encryption/Decryption

key = ($\alpha,\beta$)

Encryption → $y = \alpha x + \beta \mod m$

Decryption → $x = \alpha^{-1} (y - \beta) \mod m$

<aside> 💡 Condition: gcd($\alpha,m$) must equal to 1 (relatively prime)

</aside>

Example

K = (5,2)

plain = FACE

y = 5 * [5,0,2,4] + 2 mod 6

y = [ 3 , 2 , 0 , 4] → DCAE

x = $5^{-1} ([3,2,0,4] - 2)$

[5,0,2,4] → FACE

Cryptanalysis

Ciphertext only attack

Brute-Force (m = 26) → no encipherment when k = (1,0)

keys = 12 * 26 - 1 = 311

we can do freq analysis if ciphertext was large enough

Known plaintext attack