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Perform modular arithmetic operations
Execution
Fill in the form, run the tool, and review the result in one place.
Samples
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Tool usage guide
The Modular Calculator is a precise utility designed to perform modular arithmetic operations, including addition, subtraction, multiplication, division, exponentiation, and finding modular inverses.
Background
Working on an RSA encryption assignment requiring the calculation of (a^b) mod m.
Problem
Manually calculating large powers and finding the remainder is prone to human error.
How to use
Select 'Power' as the operation, enter the base, exponent, and modulus values.
operation: power, a: 7, b: 13, modulus: 17Outcome
The tool returns the result of 7^13 mod 17, which is 11.
Background
Developing a custom hashing algorithm that requires finding the modular multiplicative inverse.
Problem
Need to quickly verify the inverse of a number within a specific prime modulus.
How to use
Select 'Modular Inverse' from the operation list and input the number and modulus.
operation: inverse, a: 3, b: 0, modulus: 11Modular arithmetic is a system of arithmetic for integers where numbers 'wrap around' upon reaching a certain value, known as the modulus.
Yes, the calculator handles negative inputs and provides the correct positive remainder within the specified modulus.
A modular inverse of 'a' modulo 'm' is an integer 'x' such that (a * x) % m = 1.
The tool supports standard integer inputs; however, extremely large numbers may be limited by your browser's processing capacity.
Division by zero is undefined in modular arithmetic; the tool will return an error if you attempt this operation.
Outcome
The tool calculates the inverse of 3 modulo 11, which is 4.