Integer factoring and compositeness witnesses

Integer factoring and compositeness witnesses

We describe a reduction of the problem of factorization of integers n ≤ x in polynomial-time (log x)M+O(1) to computing Euler’s totient function, with exceptions of at most xO(1/M) composite integers that cannot be factored at all, and at most x exp −cM(loglog⁡x)3(logloglog⁡x)2$\begin{array}{} \disp...

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Bibliographic Details
Main Authors: Pomykała Jacek, Radziejewski Maciej
Format: Article
Language:English
Published: De Gruyter 2020-08-01
Series:Journal of Mathematical Cryptology
Subjects:
large sieve
factoring algorithms
zn*-generating sets
dirichlet characters
smooth numbers
discrete logarithm problem for composite numbers
primality testing
euler’s totient function
rsa
11a05
11a15
11a51
11m06
11z05
computational number theory: 11y05
11y16
Online Access:https://doi.org/10.1515/jmc-2019-0023

Internet

https://doi.org/10.1515/jmc-2019-0023

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