1. A method for detecting and mitigating denial of service attacks, comprising: initiating a computer communication session on a communication network between a receiving computer and a sending computer on a network; executing in a router a set of permit rules for permitting flow of communication packets for user-initiated sessions through said router to the receiving computer; in response to the receiving computer being a victim of an attack by the sending computer, sending an attack notification to an administrator; establishing a low bandwidth link between said receiving computer and a next hop router; establishing a high bandwidth link between said next hop router and an edge router to an Internet service provider (ISP) network, wherein the low bandwidth link has a lower bandwidth than the high bandwidth link; permitting said next hop router to handle both valid and invalid traffic between said next hop router and said ISP network via the high bandwidth link, wherein said invalid traffic is from the attack by the sending computer; establishing said low bandwidth link as a one and only congestion point for traffic going from the ISP network to the receiving computer; establishing timing out rules that time out permit rules, wherein the permit rules permitted communication with said receiving computer before termination of a transaction session; establishing a sequence of exotic port numbers for identifying at least one trusted computer for communication with said receiving computer irrespective of said permit rules, wherein all of the exotic port numbers have values less than a predetermined number; operating a plurality of small computers that each utilize an instantiation of said low bandwidth link to said next hop router; recording origination of each session in said next hop router for preventing spoofing of a source of traffic directed to said small computers by other computers; responsive to initiation of an outbound session by said small computers, operating said next hop router to extract session header information including source address and destination address provided by said small computers; responsive to said session header information, said next hop router establishing at least one permit rule; responsive to said outbound session terminating, deleting said permit rule; maintaining a list of destination devices that have been predetermined to be critical to a selected user computer; monitoring attack levels experienced at said next hop router with respect to said selected user computer; responsive to detecting an increasing attack level directed to said selected user computer, utilizing said list of destination devices that have been predetermined to be critical to said selected user computer in order to drop all existing permit rules with respect to said selected user computer and to allow only other rules that have been pre-established for said selected user computer; determining if a physical port on an incoming packet matches an allocated source address, and if not, blocking said incoming packet; if said incoming packet is not blocked, determining if a permit rule exists for said incoming packet, and if not, executing a synchronization algorithm to establish said permit rule based on source address, destination address, and destination port of said small computers; and if said permit rule exists for an incoming packet which is a finish packet, then in response to the receiving computer receiving said finish packet, executing a finish algorithm to remove said permit rule and to allow said finish packet through said next hop router, wherein the finish packet indicates that no more data will be forthcoming from an originator of said finish packet, and wherein the finish algorithm: obtains a 5-tuple from a 5-tuple list for said selected user, wherein the 5-tuple list identifies trusted packets for said selected user, and wherein the 5-tuple includes and identifies a source Internet Protocol (IP) address of said incoming packet, a destination IP address for said incoming packet, a source port for said incoming packet, a destination port for said incoming packet, and a protocol for said incoming packet; deletes said permit rules for said selected user; and allows said finish packet through to finish said computer communication session.