International Association
for Cryptologic Research

In 2013 the function field sieve algorithm for computing discrete logarithms in finite fields of small characteristic underwent a series of dramatic improvements, culminating in the first heuristic quasi-polynomial time algorithm, due to Barbulescu, Gaudry, Joux and Thom\\\'e. In this article we present an alternative descent method which is built entirely from the on-the-fly degree two elimination method of

G\\\"olo\\u{g}lu, Granger, McGuire and Zumbr\\\"agel. This also results in a heuristic quasi-polynomial time algorithm, for which the descent does not require any relation gathering or linear algebra eliminations and interestingly, does not require any smoothness assumptions about non-uniformly distributed polynomials. These properties make the new descent method readily applicable at currently viable bitlengths and better suited to theoretical analysis.