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On Deterministic Reduction of Factoring Integers to Computing the Exponents of Elements in Modular Group

Pomykała J.

Fundamenta Informaticae

2017

Vol. 152, nr 3

289--295

In the paper we prove that all but at most x/A(x) positive integers n ≤ x can be completely factored in deterministic polynomial time C(x), querying the prime decomposition exponent oracle at most D(x) times. The functions A(x), C(x) and D(x) have the polynomial growth (of log x) at infinity.

Large Sieve, Miller-Rabin Compositeness Witnesses and Integer Factoring Problem

Durnoga K., Pomykała J.

Fundamenta Informaticae

2017

Vol. 156, nr 2

179--185

G. Miller in his seminal paper from the mid 1970s has proven that the problem of factoring integers reduces to computing Euler’s totient function Φ under the Extended Riemann Hypothesis. We show, unconditionally, that such a deterministic polynomial reduction exists for a large class of integers.