Read Me - Square and Multiply Algorithm

Overview

This Java program demonstrates the Square and Multiply algorithm, a method for efficiently computing modular exponentiation. The algorithm is particularly useful in cryptography, where large numbers need to be raised to a power modulo another number.

Usage

To use this program, follow these steps:

1. Open the Main class.
2. Set the values for base, exponent, and modulus in the main method.
3. Run the program.

The program will calculate the result of base^exponent mod modulus using the Square and Multiply algorithm and display the intermediate steps, including the binary representation of the exponent and the number of multiplications performed.

Methods

toBinary(int exponent)

Converts an integer exponent to its binary representation.

squareAndMultiply(int base, String binaryExponent, int modulus)

Implements the Square and Multiply algorithm iteratively. Calculates base^exponent mod modulus efficiently.

squareAndMultiplyRecursive(int base, String binaryExponent, int modulus)

Implements the Square and Multiply algorithm recursively. Calculates base^exponent mod modulus efficiently using recursion.

print(String binaryExponent, int result)

Prints the final result of the modular exponentiation, along with the binary representation of the exponent.

Example

In the provided example in the main method, the program calculates 2^18 mod 39 using the Square and Multiply algorithm.

Note

• Ensure that the input values for base, exponent, and modulus are appropriate for your use case.
• The squareAndMultiplyRecursive method provides an alternative recursive implementation of the algorithm.

Feel free to modify the program for your specific requirements or integrate it into your projects.