Abstract
Most generic and memory-efficient algorithms for solving the discrete logarithm
problem construct a certain random graph consisting of group element nodes and return the
solution when a collision is found among the graph nodes.
In this work, we develop a technique for traveling through the random graph without
fully computing each node and also provide an extension to the distinguished point colli-
sion detection method that is suitable for this new situation. Concrete constructions of this
technique for multiplicative subgroups of the finite fields are given. Our implementations
confirm that the proposed technique provides practical speedup over existing algorithms.
Published Papers
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