Modular Inverse Calculator
This calculator is designed to help you find the modular inverse of a given number, a critical component in various cryptography algorithms. It is intended for students, educators, and professionals in fields involving mathematical computations and cryptography.
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Data Source and Methodology
All calculations are based on the extended Euclidean algorithm, a well-established method in number theory and cryptography. For more details, refer to the Wikipedia article.
The Formula Explained
To find the modular inverse of a mod m, solve for x in the equation: \( ax \equiv 1 \mod m \)
Glossary of Terms
- Number: The integer for which you want to find the modular inverse.
- Modulus: The modulus against which the modular inverse is calculated.
- Modular Inverse: The result such that the number multiplied by the modular inverse is congruent to 1 under the modulus.
How It Works: A Step-by-Step Example
For example, to find the modular inverse of 3 mod 11:
- We need to find x such that \( 3x \equiv 1 \mod 11 \).
- Using the extended Euclidean algorithm, we find that x is 4.
- Thus, the modular inverse of 3 mod 11 is 4.
Frequently Asked Questions (FAQ)
What is a modular inverse?
A modular inverse is a number which, when multiplied by the original number, yields a product of 1 under a specified modulus.
How do I calculate a modular inverse?
To calculate a modular inverse, use the extended Euclidean algorithm.
Why is the modular inverse important in cryptography?
The modular inverse is crucial in cryptography for decryption processes, particularly in RSA encryption.
Can every number have a modular inverse?
Not every number has a modular inverse. A number has a modular inverse if it is coprime with the modulus.
What is the formula for finding a modular inverse?
The formula involves finding x in the equation \( ax \equiv 1 \mod m \), using the extended Euclidean algorithm.