Discrete Math - Modular Exponentiation
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00:35 - Introduction to Modular Exponentiation
01:15 - Principles of Powers
01:45 - Writing the Exponents
04:25 - Applying the rules of powers to find the solution
07:30 - Exercise 2
13:50 - Fast Exponentiation Algorithm
17:10 - FEMA Example 2
19:55 - Conclusions
Calculating large powers of numbers in modular arithmetic is used in cryptography and is very important. However, we know that powers of numbers, even small; numbers combined with large powers, will lead to data overflow and computing problems.
The method of Modular Exponentiation provides a step-by-step approach to calculate these numbers by using the properties of powers. The first method starts by calculating the powers of the base number starting from 1 and doubling the power in each step. The result is a series (and from one moment repeating) numbers that can be used to rebuild the original power by multiplying the numbers until the original power is reached.
In order to improve the time to resolve these problems, the fast exponentiation algorithm has been developed. Here we first write the power in binary form and apply a series of simple steps involving squares and multiplications.
Bot methods provide the same result but the time dependency is very different.
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