**A new perspective on the powers of two descent for discrete logarithms in finite fields**

*Thorsten Kleinjung and Benjamin Wesolowski*

**Abstract: **A new proof is given for the correctness of the powers of two descent method for computing discrete logarithms. The result is slightly stronger than the original work, but more importantly we provide a unified geometric argument, eliminating the need to analyse all possible subgroups of $\mathrm{PGL}_2(\mathbb{F}_q)$. Our approach sheds new light on the role of $\mathrm{PGL}_2$, in the hope to eventually lead to a complete proof that discrete logarithms can be computed in quasi-polynomial time in finite fields of fixed characteristic.

**Category / Keywords: **foundations / discrete logarithm problem

**Original Publication**** (with minor differences): **ANTS-XIII, Thirteenth Algorithmic Number Theory Symposium

**Date: **received 4 Jul 2018

**Contact author: **benjamin wesolowski at epfl ch

**Available format(s): **PDF | BibTeX Citation

**Version: **20180706:125721 (All versions of this report)

**Short URL: **ia.cr/2018/647

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