Protease that catalyzes two essential functions in the SUMO pathway: processing of full-length SUMO1, SUMO2 and SUMO3 to their mature forms and deconjugation of SUMO1, SUMO2 and SUMO3 from targeted proteins. Deconjugates SUMO1 from HIPK2. Deconjugates SUMO1 from HDAC1, which decreases its transcriptional repression activity.