A log-log speedup for exponent one-fifth deterministic integer factorisation

Source abstract

Building on techniques recently introduced by the second author, and further developed by the first author, we show that a positive integer N N may be rigorously and deterministically factored into primes in at most $$O ( N 1 / 5 log 16 / 5 ⁡ N ( log ⁡ log ⁡ N ) 3 / 5 ) O\left ( \frac {N^{1/5} \log ^{16/5} N}{(\log \log N)^{3/5}}\right )$$ bit operations. This improves on the previous best known result by a factor of ( log ⁡ log ⁡ N ) 3 / 5 (\log \log N)^{3/5} .