In previous works, we have introduced the notion of supranet. Supranets are virtual networks -- private to a group of users -- that can be built on top of a physical network (e.g., the Internet) by any user of such a network making use of an appropriate software toolkit. We expect supranets to be used in the future by many different types of groups, each with different requirements in terms of security. Since it is necessary to meet very different needs, one of our design goals has been to allow the users to choose the security level they feel is more appropriate in each case. This can be done, for instance, by specifying appropriate options at supranet construction time. This paper discuses the ideals on which supranets are based as well as the security issues to be considered when designing supranets on top of the Internet.