Cryptology ePrint Archive: Report 2020/113

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

Madhurima Mukhopadhyay and Palash Sarkar and 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.

Category / Keywords: implementation / discrete logarithm problem implementation

Date: received 4 Feb 2020

Contact author: mukhopadhyaymadhurima at gmail com, madhurima_r@isical ac in, palash@isical ac in, shashank@iiserb ac in, Emmanuel Thome@inria fr

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Version: 20200206:144208 (All versions of this report)

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