A peripheral device coupled to a host includes a network interface, a packet processor, and a Data Processing Unit (DPU). The packet processor receives from a communication network, via the network interface, packets that originated from a source in an original order and received at the peripheral device in as order different from the original order. The packet processor splits the received packets into headers and payloads, sends the payloads for storage in a host memory and sends the headers without the payloads for storage in a DPU memory, and based on the headers produces a hint indicative of processing to be applied to the headers, by the DPU, for identifying the original order. Based on the hint, the DPU identifies the original order of the packets by applying the processing indicated by the hint to respective headers in the DPU memory, and notifies the host of the original order.