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Here's the TL;DR:

> The parasite node creates 2n specially constructed messages designed to evaluate a potential solution. The design of the message, exploiting the TCP checksum, is described in Fig. 3. These messages are sent to many target servers throughout the Internet. ...

> The message received by a target servercontains an IP header, a TCP header, and a candidate solution (values for x(i)). The operators in the Boolean equation determine the value of the checksum, which is in the TCP header. The parasite node injects each message into the network at the IP level (Fig. 1), bypassing TCP. After receiving the message, the target server verifies the data integrity of the TCP segment by calculating a TCP checksum.

> The construction of the message (Fig. 3) ensures that the TCP checksum fails for all messages containing an invalid solution to the posed SAT problem. Thus, a message that passes the TCP checksum contains a correct solution. The target server will respond to each message it receives (even if it does not understand the request). As a result, all messages containing invalid solutions are dropped in the TCP layer. Only a message which encodes a valid solution `reaches' the target server, which sends a response to the `request' it received.

References: http://web.archive.org/web/20161106073051/http://www3.nd.edu...



Another bit about the practical usefulness at this point:

> The TCP checksum provides a series of additions and a comparison at the cost of hundreds of machine cycles to send and receive messages, which makes it computationally inefficient. To make the model viable, the computation-to-communication ratio must increase in order that the computation exported by the parasitic node is larger than the amount of cycles required by the node to solve the problem itself instead of sending it to the target. However, it is important to emphasize that these are drawbacks of the presented implementation and do not represent fundamental obstacles for parasitic computing. It remains to be seen whether a higher-level implementation of a parasitic computer could execute in an efficient manner.




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