The best way to "secure a cookie" is not to use one at all. Keep the data server-side.
The second-best way is to only transmit it via SSL/TLS.
The jsessionid cookie is a special case, since it may exist before the user switched to secure communications (usually by logging in). In that particular case, the value of jsessionID is changed AFTER entering secure communications mode and the original jsessionid value becomes meaningless. Which is why webapps and server-side code should not play with the jsessionid themselves.
"privilege" comes from the Latin words for "private" and "law" (legal) and dates to feudal times. To "claim privilege" meant that you were above the laws that applied to the common people.
The moth suit and wings road is much more exciting than taxes. Or this tiny ad: