Atbash & Affine Cipher Decoder Online

Atbash and affine ciphers are simple substitution ciphers. Atbash swaps each letter with its mirror (A with Z, B with Y). An affine cipher maps each letter number x to (a·x + b) mod 26. This tool reverses both.

Example

Input

Gsv jfrxp yildm ulc

Output

The quick brown fox

For the affine cipher, choose Cipher: Affine and set a = 5, b = 8: IHHWVC SWFRCP decodes to AFFINE CIPHER.

Atbash

Atbash comes from the Hebrew alphabet, where the first letter (aleph) swaps with the last (tav), and the second (bet) with the second-to-last (shin). The name spells that out: a-t-b-sh. In the Latin alphabet:

Plain	A	B	C	D	E	F	G	H	I	J	K	L	M
Atbash	Z	Y	X	W	V	U	T	S	R	Q	P	O	N

Atbash has no key and is its own inverse. It turns up in puzzles, in TV shows such as Gravity Falls, and in biblical texts (the Book of Jeremiah uses it).

Affine cipher

The affine cipher numbers letters A = 0 to Z = 25 and encrypts with E(x) = (a·x + b) mod 26. To decrypt it needs the modular inverse of a: D(y) = a⁻¹·(y − b) mod 26.

a must share no factor with 26, so it can only be 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23 or 25. With 26 values of b, that makes 312 keys (311 if you exclude the identity). Caesar is the case a = 1, and Atbash is a = 25, b = 25.

How to break them

Atbash: just apply it. There is no key.
Affine: brute force is easy with only 312 keys. With frequency analysis, two letters are enough: if ciphertext X is probably plaintext E and ciphertext Q is probably T, solving the two equations gives a and b.

How to use the decoder

Paste the ciphertext.
Choose Atbash, or choose Affine and enter a and b.
Read the plaintext. If a has no inverse mod 26, the tool tells you to pick another value.

Decode in code

Python

def atbash(s):
    return "".join(chr(155 - ord(c)) if c.isupper() else chr(219 - ord(c)) if c.islower() else c for c in s)

def affine_decrypt(s, a, b):
    inv = pow(a, -1, 26)  # modular inverse (Python 3.8+)
    return "".join(chr(inv * (ord(c) - 65 - b) % 26 + 65) if c.isupper() else c for c in s)

print(atbash("Gsv jfrxp yildm ulc"))            # The quick brown fox
print(affine_decrypt("IHHWVC SWFRCP", 5, 8))    # AFFINE CIPHER

At a glance

Atbash	`x → 25 − x`. No key, self-inverse
Affine	`x → (a·x + b) mod 26`
Valid a	1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25
Key space	312 affine keys

Frequently asked questions

Why can't a be 2 or 13?

Because 2 and 13 divide 26, those values would map two different letters to the same ciphertext letter, so the message couldn't be decrypted. a has to be coprime with 26.

Is Atbash the same as ROT13?

No. ROT13 shifts every letter by 13. Atbash reverses the alphabet. Both are self-inverse, but they produce different results: A is N in ROT13 and Z in Atbash.

How do I find the affine key?

Guess two plaintext letters from frequencies (E and T are the most common in English), set up y = a·x + b for both, and solve mod 26. Or try all 312 keys.

Last reviewed 23 October 2026 · found a mistake? contact@decoder.tools · view as markdown