Modular arithmetic

The reader now has examined, in some detail, several specific modular arithmetics, namely, #92;mathbb#123;Z#125;#95;2,#92;mathbb#123;Z#125;#95;5,#92;mathbb#123;Z#125;#95;6,#92;mathbb#123;Z#125;#95;7,#92;mathbb#123;Z#125;#95;8 and #92;mathbb#123;Z#125;#95;9.

In this section we use two historical ciphers to introduce modular arithmetic with integers. Even though the historical ciphers are no longer relevant, modular arithmetic is extremely important in modern cryptography, especially for asymmetric algorithms.

Hence for prime moduli, modular arithmetic is very similar to regular rational arithmetic with all four operations defined.