Search for a tool
Modular Multiplicative Inverse

Tool to compute the modular inverse of a number. The modular multiplicative inverse of an integer N modulo m is an integer n such as the inverse of N modulo m equals n.

Results

Modular Multiplicative Inverse -

Tag(s) : Mathematics, Arithmetics

dCode and you

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!
You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Modular Multiplicative Inverse tool. Thank you.

Modular Multiplicative Inverse

Modular Inverse Calculator

Tool to compute the modular inverse of a number. The modular multiplicative inverse of an integer N modulo m is an integer n such as the inverse of N modulo m equals n.

What is the modular Inverse?

The value of the inverse modular of $$a$$ by the modulus $$n$$ is the value $$u$$ such as $$u \equiv a^{-1} \pmod n \\ a u \equiv 1 \pmod n$$

How to calculate a modular inverse?

To calculate the value of the modulo inverse, use the extended euclide algorithm which find solutions to the identity of Bezout $$au + bv = \text{G.C.D.}(a, b)$$. As here $$\text{G.C.D.}(a, b) = 1$$, only the value of $$u$$ is needed.

Example: $$3^-1 \equiv 4 \mod 11$$ because $$4 \times 3 = 12$$ and $$12 \equiv 1 \mod 11$$

dCode uses the Extended Euclidean algorithm for its inverse modulo calculator and arbitrary precision functions to get results with big integers.

How to calculate v?

Use the Bezout identity, also available on dCode.

What does invmod mean?

The keyword invmod is the abbreviation of inverse modular.

What is a multiplicative inverse?

A multiplicative inverse is the other name of a modular inverse.