We focus on the problem on security, and to an extent, privacy in optical networks, under the assumption that the wiretap attacker either gains knowledge about secret key and encryption algorithm, or is able to decipher the identity of source and destination, and thus infer the user's privacy of communication. We propose two combined features to address this: (1) to parallelize the transmission between source and destination, i.e., split serial optical flows into multiple flows, and (2) to randomize the traffic forwarding along the parallel paths. To this end, we compare two forwarding methods for parallel transmission: i) explicit forwarding (PAR-EXP), akin to WDM networks with mulitpath routing, ii) random forwarding (PAR-RND), akin to either an optical packet switched network, or a multilayer optical network with Ethernet-based forwarding. The study shows that parallel transmission always increases security compared with serial transmission, whereby random forwarding is potentially more secure than explicit forwarding. We define the \emph{security degree} of the network and show that it depends on various factors, such as the number of wiretap edges, network topology and number of disjoint paths available, and link capacity.