This tool calculates the result of raising a number to a power and then finding the remainder when divided by another number.

## Power Mod Calculator

Enter the values for base (a), exponent (b), and modulus (n) in the fields provided. Click the “Calculate” button to get the result of (a^b) % n.

### How It Works

The power mod calculator computes (a^b) % n using an efficient method called “modular exponentiation.” This method reduces the power calculation by breaking it into smaller multiplications and utilizing the modulus operation to prevent overflow and reduce large numbers.

### How to Use

- Enter the base value (a) in the “Base” field.
- Enter the exponent value (b) in the “Exponent” field.
- Enter the modulus value (n) in the “Modulus” field.
- Click the “Calculate” button to compute the result.
- The result will be displayed in the “Result” field.

### Limitations

This calculator assumes the inputs are non-negative integers. It also does not handle very large numbers efficiently for extremely high values of the exponent due to the limitations of JavaScript’s number handling. In such cases, consider using specialized libraries or programming languages designed for handling big integers.

## Use Cases for This Calculator

### Calculate Power Modulus

Enter the base number, exponent, and modulus value to quickly calculate the result of raising the base to the power of the exponent modulo the modulus. Great for cryptography or modular arithmetic calculations.

### Verify Primality

Use the power mod calculator to check if a number is prime by setting the base as the number to check and the exponent as one less than the number. If the result equals the number itself, it is likely prime.

### Exponential Modulus

Calculate large exponents quickly by using the power mod calculator. Simply input the base, exponent, and modulus to obtain the result without worrying about arithmetic overflow.

### Modular Exponentiation

Perform modular exponentiation efficiently by using the power mod calculator. This calculation is commonly used in computer science and cryptography for secure data transmission.

### Binary Exponentiation

Optimize exponentiation calculations with large exponents using the power mod calculator’s binary exponentiation method. It computes the result in logarithmic time, making it ideal for complex mathematical computations.

### RSA Encryption

Securely encrypt data using the RSA encryption algorithm by leveraging the power mod calculator. Set the base as the message to encrypt, the exponent as the public key, and the modulus as part of the encryption key.

### Resource-Conscious Calculations

When working with limited computational resources, the power mod calculator allows you to efficiently perform power modulus operations without the risk of memory or computational bottlenecks.

### Algorithm Testing

Test and verify the efficiency and accuracy of algorithms that involve modular arithmetic by using the power mod calculator to quickly compute results and compare them with expected outcomes.

### Secure Hashing

Implement secure hashing algorithms by utilizing the power mod calculator for modular exponentiation. This ensures data integrity and confidentiality through robust cryptographic operations.

### Cryptographic Operations

Support secure cryptographic operations by incorporating the power mod calculator into your applications. Perform key generation, encryption, and decryption operations with ease and confidence.