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6 papers · 1 filter
Smooth Subsum Search: A heuristic for practical integer factorization
Markus Hittmeir
The two currently fastest general-purpose integer factorization algorithms are the Quadratic Sieve and the Number Field Sieve. Both techniques are used to find so-called smooth val…
Integer factorization as subset-sum problem
Markus Hittmeir
This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order…
A deterministic algorithm for finding -power divisors
David Harvey, Markus Hittmeir
Building on work of Boneh, Durfee and Howgrave-Graham, we present a deterministic algorithm that provably finds all integers such that in time …
A log-log speedup for exponent one-fifth deterministic integer factorisation
David Harvey, Markus Hittmeir
Building on techniques recently introduced by the second author, and further developed by the first author, we show that a positive integer may be rigorously and deterministica…
A time-space tradeoff for Lehman's deterministic integer factorization method
Markus Hittmeir
Fermat's well-known factorization algorithm is based on finding a representation of natural numbers as the difference of squares. In 1895, Lawrence generalized this idea and ap…
A reduction of integer factorization to modular tetration
Markus Hittmeir
Let . For the -th iterate of the exponential function , also known as tetration, we write \[ ^k a:=a^{a^{.^{.^{.^{a}}}}}. \] In this paper, we…