If the number \(b\) could be used to divide another number \(a\) without any remainder, then \(b\) is said to be a divisor (or a factor as it implies to be multipliable by \(b\)) to \(a\), which can be denoted as \(b | a\).
Divisor
- TAC3121 Chapter 2: Finite Fields and Computational Number Theory
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Kasiski Method
Kasiski Method is a #Cryptanalytic Attack, developed by Baddage and Kasiski, attempts to break #Polyalphabetic Cipher by deducing the length of the keyword. The repetition in the ciphertext, especially in Vigenère Cipher gives clues to the key length by examining the period apart between multiple identical ciphertext patterns and find out the common factor# of the distances (excluding 1 as a possible key length). After that, we could easily do a Frequency Analysis on the ciphertext.
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Greatest Common Divisor (GCD)
To find \(GCD(a, b)\), one could use Euclidean Algorithm# using the theorem \(GCD(a, b) = GCD(b, a \mod b); a > b\) to find the largest #Divisor that could divide both \(a\) and \(b\). If the GCD between the two numbers is 1, then we could say that \(a\) and \(b\) are relatively prime to each other and a multiplicative inverse# could be found. There are several rules to know: