With the dramatic expansion of computers and communication networks, computer crimes, such as threatening letters, fraud, and theft of intellectual property have been growing at a dreadful rate. The increasing frequency of malicious computer attacks on government agencies and Internet businesses has caused severe economic waste and unique social threats. The problems of protecting data and information on computers and communication networks has become even more critical and challenging, since the widespread adoption of the Internet and the Web. Consequently, it is very urgent to design an integrated network-security architecture so as to make information safer, proactively or reactively defeat any network attack, make attackers accountable, and help the law enforcement system to collect the forensic evidences. Among a variety of attacks on computer servers or communication networks, a prevalent, famous, and serious network-security subject is known as "Denial of Service" (DoS) or "Distributed Denial of Service" (DDoS) attacks. According to an investigation on computer crime conducted by CSI/FBI in 2003, Internet DoS/DDoS have increased in frequency, severity, and sophistication, and have caught international attentions to the vulnerability of the Internet. DoS/DDoS attacks consume the resources of a remote host or network, thereby denying or degrading service to legitimate users. Such attacks are among the hardest security problems to address because they are simple to implement, difficult to prevent, and very difficult to trace. Therefore, this dissertation will firstly concentrate on how to resolve these troublesome DoS/DDoS problems. This is considered as the first step to overcome generic network security problems, and to achieve the final goal for accomplishing a total solution of network security. Instead of tolerating DoS/DDoS attacks by mitigating their effect, to trace back the attacking source for eliminating the attacker is an aggressive and better approach. However, it is difficult to find out the true attacking origin by utilizing the incorrect source IP address faked by the attacker. Accordingly, this dissertation will aim at conquering this representative network security problem, i.e. DoS/DDoS attacks, with IP traceback, and designing an optimal IP traceback. IP traceback ¡X the ability to trace IP packets to their origins¡Xis a significant step toward identifying, and thus stopping, attackers. A promising solution to the IP traceback is probabilistic packet marking (PPM). This traceback approach can be applied during or after an attack, and it does not require any additional network traffic, router storage, or packet size increase. Therefore, the IP traceback research on countering DoS/DDoS attacks will be based on PPM scheme. In this dissertation, three outstanding improvements among four PPM criteria¡Xthe convergency, the computational overhead, and the incomplete PPM deployment problem¡Xhas been achieved. PPM-NPC is proposed to improve the PPM convergency and computational overhead. With non-preemptively compensation, the probability of each marked packet arrived at the victim equals its original marking probability. Therefore, PPM-NPC will efficiently achieve the optimal convergent situation by simply utilizing a 2-byte integer counter. Another better scheme, CPPM, is also proposed, such that the marked packets can be fully compensated as well while they are remarked. With CPPM, the probability of each marked packet arrived at the victim will also equal its original marking probability. Consequently, CPPM will achieve the optimal convergent situation efficiently as well. Furthermore, RPPM-NPC is presented to advance the accuracy of a reconstructed path in an incomplete PPM deployment environment by correcting and recovering any discontinuous individual transparent router and any segment of consecutive double transparent routers. This scheme may also reduce the deployment overhead without requiring the participation of all routers on the attack path. Except for these improved criteria, PPM robustness, some weak assumptions in PPM, and a few unsolved problems for PPM, e.g. reflective DDoS attacks, will also be improved in the future. It is also interesting in combining other network security researches, such as IDS, system access control mechanism, etc., for constructing a more complete network security architecture. Therefore, this research hereby is done in order to completely resolve the troublesome flood-style DoS/DDoS problems, and as the basis for accomplishing a total solution of network security.