How does the Affine cipher formula work?

The Affine cipher uses the encryption formula E(x) = (ax + b) mod 26 and decryption formula D(y) = a⁻¹(y - b) mod 26. Here, 'x' is the plaintext letter's numerical position, 'a' must be coprime with 26 (sharing no common factors except 1), 'b' can be any number 0-25, and 'a⁻¹' is the modular multiplicative inverse of 'a' modulo 26.

Why must 'a' be coprime with 26?

The multiplicative key 'a' must be coprime with 26 (gcd(a,26) = 1) to ensure the transformation is reversible. If 'a' shares common factors with 26, some letters would map to the same ciphertext letter, making decryption impossible. The valid values are: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25 - exactly 12 values that are coprime with 26.

How many possible Affine cipher keys are there?

There are exactly 312 possible Affine cipher keys: 12 valid values for 'a' (coprime with 26) multiplied by 26 possible values for 'b' (0-25). This makes the Affine cipher more secure than Caesar cipher (26 keys) but still vulnerable to frequency analysis and brute force attacks due to the relatively small key space.

What is a modular multiplicative inverse?

A modular multiplicative inverse of 'a' modulo 26 is a number 'a⁻¹' such that (a × a⁻¹) ≡ 1 (mod 26). For decryption, we need this inverse to reverse the multiplicative transformation. For example, if a=7, then a⁻¹=15 because (7 × 15) = 105 ≡ 1 (mod 26). Our tool automatically calculates and displays these inverses.

Is the Affine cipher secure for modern use?

No, the Affine cipher is not secure for modern cryptographic needs. With only 312 possible keys, it's vulnerable to brute force attacks. It's also susceptible to frequency analysis since it's a monoalphabetic substitution cipher. However, it's excellent for learning mathematical cryptography concepts, understanding modular arithmetic, and historical cryptographic education.

Affine Cipher: Mathematical Substitution Encryption

What is the Affine Cipher?

The affine cipher is a type of monoalphabetic substitution cipher that uses mathematical functions to encrypt and decrypt messages. Unlike the simpler Caesar cipher, the affine cipher combines both multiplication and addition operations, making it more secure while still being relatively easy to understand.

The affine cipher was developed as an extension of shift ciphers, adding a multiplicative component to increase the key space. This classical encryption method is widely used in cryptography education to teach fundamental concepts of modular arithmetic and number theory.

The Affine Cipher Formula

The affine cipher uses two keys: a (the multiplicative key) and b (the additive key). The encryption and decryption formulas are:

Encryption: E(x) = (ax + b) mod 26

Decryption: D(y) = a⁻¹(y - b) mod 26

Where:

x is the numerical value of the plaintext letter (A=0, B=1, ..., Z=25)
y is the numerical value of the ciphertext letter
a must be coprime with 26 (valid values: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, 25)
b can be any integer from 0 to 25
a⁻¹ is the modular multiplicative inverse of a

How to Use This Affine Cipher Tool

Our online affine cipher encoder makes encryption and decryption simple:

Enter your text in the input field
Select key A from the dropdown (only valid coprime values shown)
Adjust key B using the slider (0-25)
Choose mode: Encrypt or Decrypt
Copy the result with one click

The tool automatically validates your key selection and provides real-time conversion. You can also view the complete substitution alphabet generated by your chosen keys.

Features of Our Affine Cipher Tool

Real-time encryption and decryption - See results as you type
Smart key validation - Only valid A values (coprime with 26) are selectable
Substitution table display - View the complete letter mapping
Copy to clipboard - One-click result copying
Preserve case and spacing - Non-alphabetic characters pass through unchanged
Mobile responsive - Works on all devices

For automatic decryption without knowing the keys, try our Affine Cipher Decoder. To understand the mathematics behind valid keys, visit our Key Calculator.

Frequently Asked Questions

What is the affine cipher used for?

The affine cipher is primarily used for educational purposes to teach cryptography fundamentals, including modular arithmetic, multiplicative inverses, and cryptanalysis techniques. While not secure for modern applications, it provides an excellent introduction to mathematical encryption.

How many possible keys does the affine cipher have?

The affine cipher has 312 possible key combinations (12 valid values for A multiplied by 26 values for B). This is larger than the Caesar cipher's 26 keys but still small enough to be vulnerable to brute-force attacks.

Why must key A be coprime with 26?

Key A must be coprime with 26 (meaning gcd(A, 26) = 1) to ensure that each plaintext letter maps to a unique ciphertext letter. If A shares a common factor with 26, multiple letters would encrypt to the same result, making decryption impossible.

What are the valid values for key A?

The valid values for key A are: 1, 3, 5, 7, 9, 11, 15, 17, 19, 21, 23, and 25. These are all integers less than 26 that are coprime with 26.

How do I decrypt an affine cipher without knowing the keys?

You can use frequency analysis or brute-force methods to decrypt an affine cipher without the keys. Our decoder tool automatically tests all 312 key combinations and ranks results by likelihood based on English letter frequency patterns.

Is the affine cipher secure?

No, the affine cipher is not secure for modern use. With only 312 possible keys, it can be easily broken by brute-force attack or frequency analysis. It is best suited for educational purposes and understanding cryptographic concepts.

Affine Cipher - Online Encoder and Decoder

Substitution Tablea = 5, b = 8