To calculate the result of fast modular exponentiation:
\[ \text{Result} = (b^e) \mod m \]
Where:
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.
Let's assume the following values:
Using the formula:
\[ \text{Result} = (2^{10}) \mod 1000 = 1024 \mod 1000 = 24 \]
The result is 24.
Let's assume the following values:
Using the formula:
\[ \text{Result} = (3^{13}) \mod 50 = 1594323 \mod 50 = 23 \]
The result is 23.