Catalysis of the reaction: (E)-4-hydroxy-3-methylbut-2-en-1-yl diphosphate + H2O + 2 oxidized ferredoxin = 2-C-methyl-D-erythritol 2,4-cyclodiphosphate + 2 reduced ferredoxin.
(E)-4-hydroxy-3-methylbut-2-en-1-yl-diphosphate:oxidized ferredoxin oxidoreductase activity  systematic_synonym