Faster deterministic integer factorization
Edgar Costa, David Harvey

TL;DR
This paper improves the deterministic complexity bound for integer factorization, reducing the time complexity by a factor of the square root of log log N, advancing the efficiency of prime factorization algorithms.
Contribution
The authors present a novel method that improves the deterministic complexity bound for integer factorization by a factor of (log log N)^(1/2).
Findings
Complexity bound improved by a factor of (log log N)^(1/2)
Advances deterministic integer factorization efficiency
Builds on prior Pollard–Strassen approach
Abstract
The best known unconditional deterministic complexity bound for computing the prime factorization of an integer N is O(M_int(N^(1/4) log N)), where M_int(k) denotes the cost of multiplying k-bit integers. This result is due to Bostan--Gaudry--Schost, following the Pollard--Strassen approach. We show that this bound can be improved by a factor of (log log N)^(1/2).
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Cryptography and Residue Arithmetic
