The Role of Smooth Numbers in Number Theoretic Algorithms

Carl Pomerance
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Carl Pomerance: The University of Georgia

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 411-422 from Springer

Abstract: Abstract A smooth number is a number with only small prime factors. In particular, a positive integer is y-smooth if it has no prime factor exceeding y. Smooth numbers are a useful tool in number theory because they not only have a simple multiplicative structure, but are also fairly numerous. These twin properties of smooth numbers are the main reason they play a key role in almost every moder integer factorization algorithm. Smooth numbers play a similar essential role in discrete logarithm algorithms (methods to represent some group element as a power of another), and a lesser, but still important, role in primality tests.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_34

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