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Computer science theory Course: Computer science theory > Unit 2 Lesson 5: Modular arithmetic

The modular inverse of 13, which we will label as 13^-1, would be a number that we could multiply by 13 such that 13 * 13^-1 mod 17 = 1. We can find a modular inverse of 13 by brute force or …

Specifically why XOR must be used when performing the one-time pad on computers. Bitwise simply means that we are dealing with individual bits, or binary numbers. In any …

If "a<p" then "a mod p = a", which means "a^p mod p = a", which means "a^p" divide by "p" will give you a remainder of "a". If "a>= p" then "a^p" divide by "p" will give you the same …

We can test whether that assumption is false, by using properties established by Euler's Theorem i.e. a^phi (n) mod n = 1 mod n, where a is coprime to n. If we can find any values of a that …

Let's explore the multiplication property of modular arithmetic: (A * B) mod C = (A mod C * B mod C) mod C

What can we do to reduce the size of terms involved and make our calculation faster? Suppose we want to calculate 2^90 mod 13, but we have a calculator that can't hold any numbers larger …

We will discuss the meaning of congruence modulo by performing a thought experiment with the regular modulo operator. Let's imagine we were calculating mod 5 for all of the integers: …

Ups. Da ist etwas schief gelaufen. Bitte versuche es noch einmal. Oh oh, es sieht so aus, als ob wir auf einen Fehler gestoßen sind. Du musst aktualisieren. Wenn dieses Problem weiterhin …