NEW DISCRETE LOGARITHM COMPUTATION FOR THE MEDIUM PRIME CASE USING THE FUNCTION FIELD SIEVE

Authors

Madhurima Mukhopadhyay, Indian Statistical Institute, Kolkata
Palash Sarkar, Indian Statistical Institute, Kolkata
Shashank Singh, Indian Institute of Science Education and Research Bhopal
Emmanuel Thomé, Université de Lorraine

Article Type

Research Article

Publication Title

Advances in Mathematics of Communications

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.

First Page

449

Last Page

464

DOI

10.3934/amc.2020119

Publication Date

8-1-2022

Comments

Open Access, Bronze, Green

Recommended Citation

Mukhopadhyay, Madhurima; Sarkar, Palash; Singh, Shashank; and Thomé, Emmanuel, "NEW DISCRETE LOGARITHM COMPUTATION FOR THE MEDIUM PRIME CASE USING THE FUNCTION FIELD SIEVE" (2022). Journal Articles. 3014.
https://digitalcommons.isical.ac.in/journal-articles/3014