### New Discrete Logarithm Computation for the Medium Prime Case Using the Function Field Sieve

##### Abstract

The present work reports progress in discrete logarithm computation for the general medium prime case using the function field sieve algorithm. A new record discrete logarithm computation over a 1051-bit field having a 22-bit characteristic was performed. This computation builds on and implements previously known techniques. Analysis indicates that the relation collection and descent steps are within reach for fields with 32-bit characteristic and moderate extension degrees. It is the linear algebra step which will dominate the computation time for any discrete logarithm computation over such fields. Keywords: finite field, discrete logarithm, function field sieve.

Available format(s)
Category
Implementation
Publication info
Preprint. MINOR revision.
Keywords
discrete logarithm problem implementation
Contact author(s)
palash @ isical ac in
shashank @ iiserb ac in
Emmanuel Thome @ inria fr
History
Short URL
https://ia.cr/2020/113

CC BY

BibTeX

@misc{cryptoeprint:2020/113,
author = {Madhurima Mukhopadhyay and Palash Sarkar and Shashank Singh and Emmanuel Thome},
title = {New Discrete Logarithm Computation for the Medium Prime Case Using the Function Field Sieve},
howpublished = {Cryptology ePrint Archive, Paper 2020/113},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/113}},
url = {https://eprint.iacr.org/2020/113}
}

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