Open AccessDiscrete logarithms in quasi-polynomial time in finite fields of fixed characteristic
Author(s) -
Thorsten Kleinjung,
Benjamin Wesolowski
Publication year - 2021
Publication title -
journal of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 8.574
H-Index - 111
eISSN - 1088-6834
pISSN - 0894-0347
DOI - 10.1090/jams/985
Subject(s) - algorithm , artificial intelligence , computer science
We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, we prove that it can be solved in the field of cardinality p n p^n in expected time ( p n ) 2 log 2 ( n ) + O ( 1 ) (pn)^{2\log _2(n) + O(1)} .