In this paper, we propose a novel traffic measurement based detection of network attack symptoms on high speed Internet backbone links. In order to do so, we characterize the traffic patterns from the normal and the network attacks appeared on Internet backbone links, and we derive two efficient measures for representing the network attack symptoms at aggregate traffic level. The two measures are the power spectrum and the ratio of packet counts to traffic volume of the aggregate traffic. And, we propose a new methodology to detect networks attack symptoms by measuring those traffic measures. Experimental results show that the proposed scheme can detect the network attack symptoms very exactly and quickly. Unlike existing methods based on Individual packets or flows, since the proposed method is operated on the aggregate traffic level. the computational complexity can be significantly reduced and applicable to high speed Internet backbone links.