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

Madhurima Mukhopadhyay (1) , Palash Sarkar (1) , Shashank Singh (2) , Emmanuel Thomé (3)

1 Applied Statistics Unit
2 IISER Bhopal - Indian Institute of Science Education and Research Bhopal
3 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms

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.

Mots clés: Finite fields and rings; Discrete logarithm problem; Function field sieve

Domaines: Cryptographie et sécurité [cs.CR]

Madhurima Mukhopadhyay, Palash Sarkar, Shashank Singh, Emmanuel Thomé. New Discrete Logarithm Computation for the Medium Prime Case Using the Function Field Sieve. Advances in Mathematics of Communications, 2022, 16 (3), pp.449-464. ⟨10.3934/amc.2020119⟩. ⟨hal-02964002⟩