Understanding Affine Cipher Keys
The affine cipher calculator helps you understand and work with the mathematical keys used in affine encryption. The cipher uses two keys: A (multiplicative) and B (additive), but not all values are valid for key A.
Why Key A Must Be Coprime with 26
For the affine cipher to work correctly, key A must be coprime with 26. Two numbers are coprime when their greatest common divisor (GCD) equals 1.
Why is this necessary?
If A and 26 share a common factor, multiple plaintext letters would encrypt to the same ciphertext letter. For example, if A=2:
- A(0): (2×0) mod 26 = 0
- N(13): (2×13) mod 26 = 0
Both A and N would encrypt to the same letter, making decryption impossible!
Valid Key A Values
Only 12 values are valid for key A in the affine cipher:
| A Value | Modular Inverse (A⁻¹) | Verification (A × A⁻¹ mod 26) |
|---|---|---|
| 1 | 1 | 1 × 1 = 1 |
| 3 | 9 | 3 × 9 = 27 → 1 |
| 5 | 21 | 5 × 21 = 105 → 1 |
| 7 | 15 | 7 × 15 = 105 → 1 |
| 9 | 3 | 9 × 3 = 27 → 1 |
| 11 | 19 | 11 × 19 = 209 → 1 |
| 15 | 7 | 15 × 7 = 105 → 1 |
| 17 | 23 | 17 × 23 = 391 → 1 |
| 19 | 11 | 19 × 11 = 209 → 1 |
| 21 | 5 | 21 × 5 = 105 → 1 |
| 23 | 17 | 23 × 17 = 391 → 1 |
| 25 | 25 | 25 × 25 = 625 → 1 |
Invalid values (share factors with 26): 2, 4, 6, 8, 10, 12, 13, 14, 16, 18, 20, 22, 24
Modular Multiplicative Inverse
The modular inverse of A is the number A⁻¹ that satisfies:
(A × A⁻¹) mod 26 = 1
This inverse is essential for decryption. Without it, you cannot reverse the multiplication step.
How to calculate:
- Trial method: Test each number from 1 to 25 until you find one where (A × x) mod 26 = 1
- Extended Euclidean Algorithm: A more efficient mathematical approach
Our calculator tool computes modular inverses automatically. Simply enter your A value to see its inverse.
Using the Key Calculator
Our affine cipher key calculator provides:
- Valid Key Table - View all 12 valid A values with their inverses
- Inverse Calculator - Enter any A value to compute its modular inverse
- GCD Checker - Verify if two numbers are coprime
- Random Key Generator - Generate valid random key pairs
- Substitution Table - See the complete letter mapping for any key pair
Use these tools to better understand the mathematics behind the Affine Cipher and verify your manual calculations.
Frequently Asked Questions
How do I know if a number is coprime with 26?
Calculate the GCD (greatest common divisor) of your number and 26. If GCD = 1, they are coprime. Since 26 = 2 × 13, any number divisible by 2 or 13 is NOT coprime with 26.
What is the total number of possible affine cipher keys?
There are 312 possible key combinations: 12 valid A values × 26 B values. This is why the affine cipher is vulnerable to brute-force attacks using our decoder.
Can B be any value?
Yes, key B can be any integer from 0 to 25. Unlike key A, there are no restrictions on B because it only affects the additive shift, not the multiplicative mapping.
How does affine cipher compare to other ciphers?
The affine cipher is more secure than the Caesar cipher (26 keys) but less secure than polyalphabetic ciphers like Vigenere. It serves as an excellent educational bridge between simple substitution and more complex encryption methods.