PwrDem

Modular Exponentiation Demonstration

Demonstrates how to compute $a^k \pmod{m}$ using different algorithms

Algorithm Type:Square-and-Multiply MethodRight-to-Left Binary MethodLeft-to-Right Binary Method

Base $a$:

Exponent $k$:

Modulus $m$:

Understanding Modular Exponentiation

This algorithm calculates $a^k \pmod{m}$ using various methods. The binary methods express the exponent $k$ in binary form and process the bits either left-to-right or right-to-left. The square-and-multiply method repeatedly squares and conditionally multiplies based on the binary representation of the exponent.

1. 1Convert exponent $k$ into binary form (for binary methods).
2. 2Initialize the result appropriately for the chosen method.
3. 3Process the binary representation of $k$:
4. 4- Square-and-multiply: use repeated squaring with conditional multiplication
5. 5- Right-to-left: scan from least significant to most significant bit
6. 6- Left-to-right: scan from most significant to least significant bit
7. 7Apply modular arithmetic at each step to keep numbers manageable.
8. 8The final result is $a^k \bmod m$.