The detection of anomalies in network traffic is an important task in today's Internet. Among various anomaly detection methods, the techniques based on examination of the long-range dependence (LRD) behavior of network traffic stands out to be powerful. In this paper, we reveal anomalies in aggregated network traffic by examining the LRD behavior based on the cross-correlation function of the bidirectional control and data planes traffic. Specifically, observing that the conventional cross-correlation function has a low measure of dissimilarity between the two planes, which leads to a reduced anomaly detection performance, we propose a modification of the cross-correlation function to mitigate this issue. The performance of the proposed method is analyzed using a relatively recent Internet traffic captured at King Saud University. The results demonstrate that using the modified cross-correlation function has the ability to detect low volume and short duration attacks. It also compensates for some misdetections exhibited by using the autocorrelation structures of the bidirectional traffic of the control, data, and WHOLE (combined control and data) planes traffic. 1 | INTRODUCTION Internet services have been rapidly evolving due to continuous emergence of new technologies and high bandwidth applications. According to Cisco, the annual global IP traffic is expected to reach 3.30 Zettabyte by 2021. 1 This growth has introduced many challenges in terms of securing information, reliability of data transfer, and detection of traffic anomalies and attacks. Anomalies are patterns of data that deviate from normal behavior. A broad variety of such patterns in Internet traffic are frequently faced by network operators. These patterns could represent genuine abnormalities induced by physical or technical issues, such as high-rate flows, network outage, and sudden changes due to flash crowds. 2 However, such patterns could also be generated by malicious activities such as cyber intrusions, distributed denial of service (DDoS) attacks, port scanning, and worm propagation. 3,4 This type of malicious activities could likely introduce disastrous effects on the proper operation of networks. The mentioned malicious activities are considerably growing with time. According to the worldwide infrastructure security report, 5 it is evident that the volume of these attacks on data centers, networks infrastructures, and