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

Madhurima Mukhopadhyay; Palash Sarkar; Shashank Singh; Emmanuel Thome

Paper 2020/113

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

Madhurima Mukhopadhyay, Palash Sarkar, Shashank Singh, and Emmanuel Thome

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.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Preprint. MINOR revision.
Keywords: discrete logarithm problem implementation
Contact author(s): mukhopadhyaymadhurima @ gmail com
madhurima_r @ isical ac in
palash @ isical ac in
shashank @ iiserb ac in
Emmanuel Thome @ inria fr
History: 2020-02-06: received
Short URL: https://ia.cr/2020/113
License: 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},
      url = {https://eprint.iacr.org/2020/113}
}