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Deterministic Integer Factorization Algorithms
N. A. Carella
arXiv (Cornell University)5 Aug 2013Open access
Deterministic Integer Factorization Algorithms
N. A. Carella · arXiv (Cornell University) · 5 Aug 2013
Abstract
A new integer deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/6+\varepsilon})$ arithmetic operations, is presented in this note. Equivalently, given the least $(\log N)/6$ bits of a factor of the balanced integer $N = pq$, where $p$ and $q$ are primes, the algorithm factors the integer in polynomial time $O(\log(N)^c)$, with $c \geq 0$ constant, and $\varepsilon > 0$ an arbitrarily small number. It improves the current deterministic factorization algorithm, rated at arithmetic operations to $O(N^{1/5+\varepsilon})$ arithmetic operations.
Identifiers
- NobleID
- NI7P28W33R33S90
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- Published
- 5 Aug 2013
- Publisher
- Cornell University
- Language
- EN