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Barrett reduction

In modular arithmetic, Barrett reduction is an algorithm designed to optimize the calculation of a mod n {\displaystyle a\,{\bmod {\,}}n\,} without needing a fast division algorithm. It replaces divisions with multiplications, and can be used when n {\displaystyle n} is constant and a < n 2 {\displaystyle a<n^{2}} . It was introduced in 1986 by P.D. Barrett.

Products, General idea & Single-word Barrett reduction

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General idea

IntegerFloorCeilingRoundingNTL
6 related topics

Single-word Barrett reduction

Timing attackSubtraction
2 related topics

Range of Barrett multiplication

Rounding half up
1 related topics

Barrett multiplication non-constant operands

Bit-length
1 related topics

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Overview

General idea

Single-word Barrett reduction

Range of Barrett multiplication

Barrett multiplication non-constant operands

Barrett Division

Multi-word Barrett reduction

  • RSA RSA (cryptosystem)

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Barrett reduction

Nodes24
Edges23
Triples10
Avg. degree1.92
Density0.083333
Components1

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Barrett reduction

Top relations

related to Barrett Division · 5
Barrett reduction → After, Barrett, Compute, Furthermore, This
related to Small Barrett reduction · 4
Barrett reduction → Barrett, Every, It, R-c
is a · 1
Barrett reduction → algorithm designed to optimize the calculation of a mod n

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Important terminology

displaystyle left right barrett frac one reduction lfloor mod integer multiplication rfloor algorithm division case bmod approximation check ab perform

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Barrett reductionis aalgorithm designed to optimize the calculation of a mod n0.90text
Barrett reductionrelated to Barrett DivisionBarrett0.60section
Barrett reductionrelated to Barrett DivisionFurthermore0.60section
Barrett reductionrelated to Barrett DivisionAfter0.60section
Barrett reductionrelated to Barrett DivisionCompute0.60section
Barrett reductionrelated to Barrett DivisionThis0.60section
Barrett reductionrelated to Small Barrett reductionIt0.60section
Barrett reductionrelated to Small Barrett reductionBarrett0.60section
Barrett reductionrelated to Small Barrett reductionEvery0.60section
Barrett reductionrelated to Small Barrett reductionR-c0.60section

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