# modular arithmetic

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## modular arithmetic

(mathematics)
(Or "clock arithmetic") A kind of integer arithmetic that reduces all numbers to one of a fixed set [0..N-1] (this would be "modulo N arithmetic") by effectively repeatedly adding or subtracting N (the "modulus") until the result is within this range.

The original mathematical usage considers only __equivalence__ modulo N. The numbers being compared can take any values, what matters is whether they differ by a multiple of N. Computing usage however, considers modulo to be an operator that returns the remainder after integer division of its first argument by its second.

Ordinary "clock arithmetic" is like modular arithmetic except that the range is [1..12] whereas modulo 12 would be [0..11].
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Such advanced algorithms comprise of modular arithmetic, modular exponentiation, prime number theory, Chinese Reminder Theorem, and Fermat's Little Theorem and Euler's Theorem.
Key words: Modular Arithmetic, Congruence, Divisibility, b-adic expension.
Moving up a level in difficulty, the Diffie-Hellman-Merkle (DHM) method also uses modular arithmetic but involves discrete logarithms instead of factoring.
The great news about modular arithmetic is that we can reduce each of the four numbers modulo 7 before we add them.
The same drills were prepared in paper and electronic formats for the third teacher-assisted session devoted to modular arithmetic.
We explored students' thinking on tasks designed to probe their different ways of understanding and representing modular arithmetic problems.
The algebra topics covered in the book are: modular arithmetic, rings and fields, groups and permutations, group homomorphisms and subgroups, polynomial rings and algebraic geometry (mainly elliptic curves).
A modular arithmetic task was used because it has been found in previous literature (Beilock & Carr, 2005) to be robust to the effects of mathematical training and because the task is easy enough to solve without a calculator or pen and paper.
Since ancient time, number theory has been an important study subject and modular arithmetic has also been widely used in cryptography.
On the other hand the authors outline the basics of complex numbers and modular arithmetic.
In the early 1800s, while creating a branch of Mathematics called Modular Arithmetic, the great mathematician Carl Fredrich Gauss produced a method to find the date of Easter Sunday.
Both processors accelerate a variety of IPSec and SSL/TLS protocols, including DES, Triple DES, AES (with 128, 192, and 256-bit key lengths), and ARC4 encryption; MD5, SHA-1 hashing and authentication; RSA, DSA, SSL, IKE, and Diffie-Hellman public key support; 3,072-bit modular arithmetic and exponentiation, plus true Random Number Generation (RNG).

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