Enter the base number, exponent, and modulus into the calculator to determine the result of fast modular exponentiation.

Fast Modular Exponentiation Formula

The following formula is used to calculate the result of fast modular exponentiation.

Result = (b^e) mod m


  • Result is the result of the fast modular exponentiationb is the base numbere is the exponentm is the modulus

To calculate the result of fast modular exponentiation, raise the base number to the power of the exponent, then take the modulus of the result by the modulus number. This method reduces the computational time by calculating the modulus at each step of the exponentiation, rather than at the end.

What is a Fast Modular Exponentiation?

Fast Modular Exponentiation is a method used in computer science to speed up the process of modular exponentiation, which involves calculating the remainder when a number is raised to a certain power and then divided by another number. This method is particularly useful in fields such as cryptography. It uses the principle of “exponentiation by squaring”, where the exponent is broken down into powers of 2. This allows the number of multiplications to be significantly reduced, thus making the calculation faster and more efficient.

How to Calculate Fast Modular Exponentiation?

The following steps outline how to calculate the Fast Modular Exponentiation using the formula: Result = (b^e) mod m.

  1. First, determine the base number (b).
  2. Next, determine the exponent (e).
  3. Next, determine the modulus (m).
  4. Use the formula: Result = (b^e) mod m to calculate the fast modular exponentiation.
  5. Finally, calculate the Result.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Base number (b) = 3

Exponent (e) = 4

Modulus (m) = 5