Implementing information-theoretically secure oblivious transfer from packet reordering

If we assume that adversaries have unlimited computational capabilities, secure computation between mutually distrusting players can not be achieved using an error-free communication medium. However, secure multi-party computation becomes possible when a noisy channel is available to the parties. For instance, the Binary Symmetric Channel (BSC) has been used to implement Oblivious Transfer (OT), a fundamental primitive in secure multi-party computation. Current research is aimed at designing protocols based on real-world noise sources, in order to make the actual use of information-theoretically secure computation a more realistic prospect for the future. In this paper, we introduce a modified version of the recently proposed Binary Discrete-time Delaying Channel (BDDC), a noisy channel based on communication delays. We call our variant Reordering Channel (RC), and we show that it successfully models packet reordering, the common behavior of packet switching networks that results in the reordering of the packets in a stream during their transit over the network. We also show that the protocol implementing oblivious transfer on the BDDC can be adapted to the new channel by using a different sending strategy, and we provide a functioning implementation of this modified protocol. Finally, we present strong experimental evidence that reordering occurrences between two remote Internet hosts are enough for our construction to achieve statistical security against honest-but-curious adversaries.