Optical networks are the most adequate platform for the transport of ever increasing bandwidth-hungry applications and services (BwGAS). Additionally, these networks cope with the continuous growth of the number of Internet users. Optical Burst Switching (OBS) paradigm is expected to be the backbone infrastructure of near-future all-optical Internet. In OBS, data and control packet known as burst header packet (BHP) are sent out of band (i.e., control packets and data bursts are carried by different channels) and it is sent ahead of the data burst to reserve necessary network resources for the corresponding burst. After the elapse of a predetermined time known as offset time, the data burst is sent with the hope that, the control packet was able to make necessary reservations. Sending the BHP ahead of the burst exposes the burst to different security challenges, particularly data burst redirection and denial of service attacks. If the BHP is compromised the corresponding burst will definitely be compromised. Less efforts have been dedicated to investigate control packet security issues in OBS. In this paper, we propose and evaluate a solution to address Data Burst Redirection (DBR) Attack in OBS networks. The solution is designed based on Rivest-Shamir-Adleman (RSA) public-key encryption algorithm. We evaluated the algorithm via computer simulation. Evaluation metrics are burst loss ratio and throughput. The obtained results demonstrate that, the proposed algorithm has succeeded in protecting the network against DBR attacks reducing the number of compromised BHP. In the future, the authors will work on denial of service issues considering reliability aspects.