Cryptanalysis of SDLP

On the quantum side the question of quantum equivalence of SDLP and the CDH-type problem underpinning semidirect product key exchange (SCDH) remains unproven, though we have strong cause to suspect their equivalence given the quantum equivalence of the heavily related vectorisation and parallelisation problems. The decomposition attack of Imran and Ivanyos, providing in some cases a reduction of SDLP to the abelian hidden subgroup problem, relies on the quantum ability to quickly compute a composition series of a solvable group. Whether similar quantum speedups in the computation series exist for non-solvable groups remains open.

On the classical side, we would like to develop a kind of Sylow theory for the projected sets implied by the semidirect product structure. It would also be useful to develop a classical method of computing the size of the acting group when one considers the semigroup variant of SDLP (currently we have only quantum methods).