A TCP-targeted low-rate denial of service (LDoS) attack exploits the vulnerabilities of TCP congestion control mechanism. The most widely used TCP congestion control algorithm, CUBIC, increases the resilience to LDoS. This paper explores high-potency patterns of LDoS attacks against CUBIC TCP under the RED queue management scenario, and develops two attack models, the D- and S-models to maximize attack potency (i.e., the damage-to-cost ratio). Theoretical analyses and extensive experiments are conducted to validate the proper function of the models and evaluate their performance. Test results show that the models can effectively throttle CUBIC TCP throughput. Under standard-configured network parameters, one attack unit can damage up to about 21 and 26 TCP units for the D- and S-models, respectively, which represents an increase in attack potency about 20%. The attack potencies of our proposed models are at least 250% greater than that of the traditional attack model. In addition, with variations in different network parameters, these two models are still efficient and alternatively maximize the attack potency. Finally, attack countermeasures are outlined. The present study offers a basis to explore new attack manners which may be exploited by attackers and inspires researchers to develop new measurements against such attack.