Improving the Polynomial time Precomputation of Frobenius Representation Discrete Logarithm Algorithms - Simplified Setting for Small Characteristic Finite Fields.
Antoine Joux, Cécile Pierrot · 2014
Abstract. In this paper4, we revisit the recent small characteristic dis-crete logarithm algorithms. We show that a simplified description of the algorithm, together with some additional ideas, permits to obtain an im-proved complexity for the polynomial time precomputation that arises during the discrete logarithm computation. With our new improvements, this is reduced to O(q6), where q is the cardinality of the basefield we are considering. This should be compared to the best currently documented complexity for this part, namely O(q7). With our simplified setting, the complexity of the precomputation in the general case becomes similar to the complexity known for Kummer (or twisted Kummer) extensions. 1