modular arithmetic

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modular arithmetic

(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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Keywords: information security, cryptography, modular arithmetic, primality test, number theory
This method can be found in The Book of Common Prayer and involves Golden Numbers and Sunday Letters, both of these are calculated by using Modular Arithmetic.
The modular arithmetic unit embedded in this chip operates on integers of up to 1024 bits wide and reads operands from the data register file, operates on them, and writes the results back to the data register file.
Most of the students were familiar with modular arithmetic and could understand the working principle involved.
The ST19NR66 includes a 1088-bit Modular Arithmetic Processor (MAP) for public-key cryptography, an enhanced DES (eDES) engine, and AES-128 (Advanced Encryption Services) software-library capability.
Number theory offers a way to rid calculations of these intrinsic errors by combining a special procedure called modular arithmetic with a set of numbers known as Fermat numbers.
The technology, known as Real Privacy Management (RPM), uses unique, modular arithmetic to mutually authenticate and secure each device on a network while securing every single bit of transmittable data in real-time without creating additional overhead.
The mathematics, though esoteric, turns out not to be too difficult to learn and use; readers are expected at the very least however, to be familiar with modular arithmetic, that is, the number systems formed by the remainders of the integers after division by the selected modulus--for example, how you can add four hours to 10:00 and get 2:00.
He pairs music and math concepts such as scales and modular arithmetic, octave identification and equivalence relation, intervals and logarithms, equal temperament and exponents, overtones and integers, tone and trigonometry, and tuning and rationality.
However, the processors typically used as system processors in these applications lack the dedicated modular arithmetic instructions required for optimal implementation of these algorithms, resulting in a throughput penalty that is typically several Mbytes/s.
Similarly, in modular arithmetic what counts is not the numerical valve itself but the remainder after division by the modulus (17 in the example).
These auxiliary functions include: Modular Arithmetic functions, Random Number Generator (RNG), SHA-1 Hash algorithm and the Message Digest algorithm MD5.

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