Ahmad Samer Wazan's blog

Modular arithmetic is very important to cryptography. It is arithmetic that allows us to achieve a set of operations over a set of numbers that wrap around a circle.   While modular addition, subtraction, and multiplication are easy to understand, the modular division is somehow tricky. The main reason is that the modular division doesn't have always a solution, and sometimes it gives multiple solutions! To explain it clearly, I present two approaches to calculating the modular division. The first approach uses the modular multiplication table, while the second approach uses the successive subtraction method. Both approaches allow us to see whether there are zero, one, or multiple solutions to the modular division. However, none of these approaches are efficient to calculate the modular division of big numbers.  The objective of this article is to explain when the modular division can have zero, one or multiple solutions.  The article shows also that when multiple solutions to the

We tend to believe that having a big keyspace is necessary to ensure the secrecy of our information. While this belief is correct for most of our communications, there will be cases when we can obtain perfect secure ciphers whose key spaces are small.  We need to check Shannon’s definition of Perfect Secrecy to see how it is possible. Claude Shannon has many contributions. One of his main contributions was the transformation of cryptography from an art into a rigorous science using probability theory.  In his work, entitled "Communication Theory of Secrecy Systems" 1 ,  Shannon defined the concept of Perfect Secrecy and   proved that the Vernam Cipher is perfectly secure.  Shannon stated that " “Perfect Secrecy” is defined by requiring of a system that after a cryptogram is intercepted by the enemy the a posteriori probabilities of this cryptogram representing various messages be identically the same as the a priori probabilities of the same messages before the intercept