Solving a $6120$-bit DLP on a Desktop Computer

Faruk Golouglu; Robert Granger; Gary McGuire; Jens Zumbragel

Paper 2013/306 Original: eprint.iacr.org/2013/306 ↗

Solving a $6120$-bit DLP on a Desktop Computer

Faruk Golouglu

Robert Granger

Gary McGuire

Jens Zumbragel

Abstract

In this paper we show how some recent ideas regarding the discrete logarithm problem (DLP) in finite fields of small characteristic may be applied to compute logarithms in some very large fields extremely efficiently. By combining the polynomial time relation generation from the authors' CRYPTO 2013 paper, an improved degree two elimination technique, and an analogue of Joux's recent small-degree elimination method, we solved a DLP in the record-sized finite field of $2^{6120}$ elements, using just a single core-month. Relative to the previous record set by Joux in the field of $2^{4080}$ elements, this represents a $50\%$ increase in the bitlength, using just $5\%$ of the core-hours. We also show that for the fields considered, the parameters for Joux's $L_Q(1/4 + o(1))$ algorithm may be optimised to produce an $L_Q(1/4)$ algorithm.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2019-01-25: last updated; 2013-05-25: published
Short URL: https://ia.cr/2013/306
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2013/306,
      author = {Faruk Golouglu and Robert Granger and Gary McGuire and Jens Zumbragel},
      title = {Solving a $6120$-bit DLP on a Desktop Computer},
      howpublished = {Cryptology {ePrint} Archive, Paper 2013/306},
      year = {2013},
      url = {https://eprint.iacr.org/2013/306}
}