In recent years, Network-on-Chip (NoC) has established itself as an important concept for fast and efficient data transmission in Multiprocessor System-on-Chip (MPSoC). Due to the complexity of MPSoCs, third-party components are often integrated to reduce development time and costs. However, the use of third-party components also increases the attack surface, e.g., by the injection of Hardware Trojans that may be used for a variety of attacks. In this paper, we focus on active attacks, particularly, the modification or deletion of transmitted data. The use of appropriate security mechanisms can ensure that such attacks are detected. However, the transmission of modified or deleted data has to be repeated. On the one hand, retransmissions increase network load and latencies; on the other hand, they may even not be successful if the same path is used for the retransmission. Within this paper, we propose a trust-based adaptive routing strategy that aims to select paths that are not controlled by an attacker in order to mitigate the impact of retransmissions. Simulations confirm that the reliability of a successful transmission can be significantly improved even in case of multiple attackers.