Meaning of modular arithmetic | Babel Free

Definitions

Any system of arithmetic for integers which, for some given positive integer n, is equivalent to the set of integers being mapped onto the finite set {0, ... n} according to congruence modulo n, and in which addition and multiplication are defined consistently with the results of ordinary arithmetic being so mapped.

countable, uncountable

Equivalents

Examples

“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.”

CEFR level