Quantum key distribution (QKD) has been researched for almost four decades and is currently making its way to commercial applications. However, deployment of the technology at scale is challenging, because of the very particular nature of QKD and its physical limitations. Among others, QKD is computationally intensive in the post-processing phase and devices are therefore complex and power hungry, which leads to problems in certain application scenarios. In this work we study the possibility to offload computationally intensive parts in the QKD post-processing stack in a secure way to untrusted hardware. We show how error correction can be securely offloaded for discrete-variable QKD to a single untrusted server and that the same method cannot be used for long distance continuous-variable QKD. Furthermore, we analyze possibilities for multi-server protocols to be used for error correction and privacy amplification. Even in cases where it is not possible to offload to an external server, being able to delegate computation to untrusted hardware components on the device could improve the cost and certification effort for device manufacturers.