Recently, the Discrete Logarithm Problem (DLP) on finite fields saw groundbreaking improvements. This includes a quasi-polynomial algorithm for finite fields of "small"-prime characteristic and several world records during a few months. There are many open problems left in this exciting new direction. The fastest practical algorithm for DLP does not use a quasi-polynomial idea. One problem we are going to investigate is developing efficient algorithms for DLP in small-prime fields. Also we will investigate the extensibility of these ideas to larger-prime characteristics.
Seznam odborné literatury
[1] Antoine Joux, Cécile Pierrot: Technical history of discrete logarithms in small characteristic finite fields - The road from subexponential to quasi-polynomial complexity. Des. Codes Cryptography 78(1): 73-85 (2016)
[2] Faruk Göloglu, Robert Granger, Gary McGuire, Jens Zumbrägel: On the Function Field Sieve and the Impact of Higher Splitting Probabilities - Application to Discrete Logarithms in GF(2^1971) and GF(2^3164). Advances in cryptology—CRYPTO 2013. Part II, 109–128, Lecture Notes in Comput. Sci., 8043, Springer, Heidelberg, 2013.
- zadáno a potvrzeno stud. odd.