Catalyzes the formation of sulfite from phosphoadenosine 5'-phosphosulfate (PAPS) using thioredoxin as an electron donor. [thioredoxin]-disulfide + adenosine 3',5'-bisphosphate + 2 H(+) + sulfite = 3'-phosphoadenylyl sulfate + [thioredoxin]-dithiol Severely inhibited by reagents which covalently modify Cys groups in proteins. Sulfur metabolism; hydrogen sulfide biosynthesis; sulfite from sulfate: step 3/3. Homodimer. The open, reduced form of PAPS reductase is able to bind PAPS, whereas the closed oxidized form cannot. A movement between the two monomers of the dimer may allow this switch in conformation to occur. Belongs to the PAPS reductase family. CysH subfamily.