CHICAGO — Detectives have long wondered what secrets serial killer John Wayne Gacy and other condemned murderers took to the grave when they were executed — particularly whether they had other unknown victims.

Now, the Cook County Sheriff’s Department is trying to find out by entering the killers’ DNA profiles into a national database shared with other law enforcement agencies. The move is based on an ironic legal distinction: The men were technically listed as homicide victims themselves because they were put to death by the state.