Prime Numbers pp 407-496 | Cite as

Fast Algorithms for Large-Integer Arithmetic

  • Richard Crandall
  • Carl Pomerance


In this chapter we explore the galaxy of “fast” algorithms that admit of applications in prime number and factorization computations. In modern times, it is of paramount importance to be able to manipulate multiple-precision integers, meaning integers that in practice, on prevailing machinery, have to be broken up into pieces, with machine operations to involve those pieces, with a view to eventual reassembly of desired results. Although multiple-precision addition and subtraction of, integers is quite common in numerical studies, we assume that notions of these very simple fundamental operations are understood, and start with multiplication, which is perhaps the simplest arithmetic algorithm whose classical form admits of genuine enhancements.


Fast Fourier Transform Discrete Fourier Transform Fast Algorithm Elliptic Multiplication Fast Fourier Transform Algorithm 
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Copyright information

© Springer-Verlag, New York, Inc. 2001

Authors and Affiliations

  • Richard Crandall
    • 1
  • Carl Pomerance
    • 2
  1. 1.Center for Advanced ComputationPortlandUSA
  2. 2.Department of MathematicsDartmouth UniversityHanoverUSA

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