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Arbitrarily Tight Bounds On The Distribution Of Smooth Integers
 Proceedings of the Millennial Conference on Number Theory
, 2002
"... This paper presents lower bounds and upper bounds on the distribution of smooth integers; builds an algebraic framework for the bounds; shows how the bounds can be computed at extremely high speed using FFTbased powerseries exponentiation; explains how one can choose the parameters to achieve ..."
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This paper presents lower bounds and upper bounds on the distribution of smooth integers; builds an algebraic framework for the bounds; shows how the bounds can be computed at extremely high speed using FFTbased powerseries exponentiation; explains how one can choose the parameters to achieve any desired level of accuracy; and discusses several generalizations.
Anatomy of Integers and Cryptography
, 2008
"... It is wellknown that heuristic and rigorous analysis of many integer factorisation and discrete logarithm algorithms depends on our various results about the distribution of smooth numbers. Here we give a survey of some other important cryptographic algorithms which rely on our knowledge and under ..."
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It is wellknown that heuristic and rigorous analysis of many integer factorisation and discrete logarithm algorithms depends on our various results about the distribution of smooth numbers. Here we give a survey of some other important cryptographic algorithms which rely on our knowledge and understanding of the multiplicative structure of “typical ” integers and also “typical ” terms of various sequences such as shifted primes, polynomials, totients and so on. Part I
Smooth Values of Shifted Primes in Arithmetic Progressions
"... We study the problem of bounding the number of primes p ≤ x in an arithmetic progression for which the largest prime factor of p − h does not exceed y. 1 ..."
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We study the problem of bounding the number of primes p ≤ x in an arithmetic progression for which the largest prime factor of p − h does not exceed y. 1