Cryptography and Network Security

In integer arithmetic, we use a set and few operations. We are familiar with this set and corresponding, but they are reviewed here to create a background for modular arithmetic. ( i ) Set of Integers : The set of integers, denoted by 'Z', contains all integral number ( with no fractions ) from negative infinity to positive infinity. Which is shown as follows Z = { -∞, ........, -2, -1, 0, 1, 2, ............., +∞ }. ( ii ) Binary operations : In cryptography, we are interested in three binary operations applied to the set of integers. The binary operation takes two integers and create one output. Three common binary operations defined for  integers are addition, subtraction and multiplication. Each of these operations takes two input ( a, b ) and creates one output ( c ) as shown in the following figure. The following shows the results of the three binary operations on two integers because each input can be either positive or negative, we can ...