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Prime Numbers pp 191-225 | Cite as

Exponential Factoring Algorithms

  • Richard Crandall
  • Carl Pomerance

Abstract

For almost all of the multicentury history of factoring, the only algorithms available were exponential, namely, the running time was, in the worst case, a fixed positive power of the number being factored. But in the early 1970s, subexponential factoring algorithms began to come “on line.” These methods, discussed in the next chapter, have their running time to factor n bounded by an expression of the form n°(1) One might wonder, then, why the current chapter exists in this book. We have several reasons for including it.

Keywords

Quadratic Form Discrete Logarithm Residue Class Modular Multiplication Binary Quadratic Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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