Modular Arithmetic

Math for CS · Axiom Academy

Clock arithmetic and congruences Modular arithmetic is the arithmetic of remainders. We use it all the time: on clock faces (12-hour clock), in days of the week, in computer hardware (binary arithmetic). (both leave remainder 5 when divided by 12) (both leave remainder 7 when divided by 10) On a 12-hour clock, time wraps around. What time is it 5 hours after 10:00? Power: If , then for any positive integer k Modular Arithmetic in Cryptography Computing Large Powers Efficiently Modular arithmetic treats numbers based on remainders mod n Addition, subtraction, multiplication all work in modular arithmetic Congruence is an equivalence relation (reflexive, symmetric, transitive) Foundation of all modern cryptography and digital security

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