Simply use the existing MD5/SHA1 hash as input to bcrypt and update all password hashes in your database in one go. Then, whenever the user logs in you first apply the old hash function followed by bcrypt before comparing with what you have in the DB.
Simply use the existing MD5/SHA1 hash as input to bcrypt and update all password hashes in your database in one go. Then, whenever the user logs in you first apply the old hash function followed by bcrypt before comparing with what you have in the DB.