Add to ORKGThis paper deals with products of moderate-size primes, familiarly known as smooth numbers. Smooth numbers play an crucial role in information theory, signal processing and cryptography. We present various properties of smooth numbers relating to their enumeration, distribution and occurrence in various integer sequences. We then turn our attention to cryptographic applications in which smooth numbers play a pivotal role.59 page(s
We prove a result on the multiplicative structure of integers which, in principle, may have applicat...
An RSA modulus is a product M = pl of two primes p and l. We show that for almost all RSA moduli M, ...
With the increasing amount of information transmitted over networks, there is a need to be able to k...
A smooth number is a number with only small prime factors. In particular, a posi-tive integer is y-s...
We give a new approach for finding large twin smooth integers. Those twins whose sum is a prime are ...
© 2017, Allerton Press, Inc. A natural number n is called y-smooth (y-powersmooth, respectively) for...
We establish upper bounds for the number of smooth values of the Euler function. In particular, alth...
We study the function Θ(x, y, z) that counts the number of positive integers n ≤ x which have a divi...
We study the function O(x, y, z) that counts the number of positive integers n ≤ x which have a divi...
Abstract. Let P (n) denote the largest prime divisor of n, and let Ψ(x, y) be the number of integers...
We study the function Θ(x, y, z) that counts the number of positive integers n ≤ x which have a divi...
The book introduces new ways of using analytic number theory in cryptography and related areas, such...
International audienceAbstract Let b ⩾ 2 be an integer. Among other results we establish, in a quant...
textThis report explores the historical development of three areas of study regarding prime numbers....
We estimate multiplicative character sums over the integers with a fixed sum of binary digits and ap...
We prove a result on the multiplicative structure of integers which, in principle, may have applicat...
An RSA modulus is a product M = pl of two primes p and l. We show that for almost all RSA moduli M, ...
With the increasing amount of information transmitted over networks, there is a need to be able to k...
A smooth number is a number with only small prime factors. In particular, a posi-tive integer is y-s...
We give a new approach for finding large twin smooth integers. Those twins whose sum is a prime are ...
© 2017, Allerton Press, Inc. A natural number n is called y-smooth (y-powersmooth, respectively) for...
We establish upper bounds for the number of smooth values of the Euler function. In particular, alth...
We study the function Θ(x, y, z) that counts the number of positive integers n ≤ x which have a divi...
We study the function O(x, y, z) that counts the number of positive integers n ≤ x which have a divi...
Abstract. Let P (n) denote the largest prime divisor of n, and let Ψ(x, y) be the number of integers...
We study the function Θ(x, y, z) that counts the number of positive integers n ≤ x which have a divi...
The book introduces new ways of using analytic number theory in cryptography and related areas, such...
International audienceAbstract Let b ⩾ 2 be an integer. Among other results we establish, in a quant...
textThis report explores the historical development of three areas of study regarding prime numbers....
We estimate multiplicative character sums over the integers with a fixed sum of binary digits and ap...
We prove a result on the multiplicative structure of integers which, in principle, may have applicat...
An RSA modulus is a product M = pl of two primes p and l. We show that for almost all RSA moduli M, ...
With the increasing amount of information transmitted over networks, there is a need to be able to k...