The shuffle model has recently emerged as a popular setting for differential privacy, where clients can communicate with a central server using anonymous channels or an intermediate message shuffler. This model was also explored in the context of cryptographic tasks such as secure aggregation and private information retrieval (PIR). However, this study was almost entirely restricted to the stringent notion of information-theoretic security.

We present the first computationally sound symbolic analysis of Yao's garbled circuit construction for secure two party computation. Our results include an extension of the symbolic language for cryptographic expressions from previous work on computationally sound symbolic analysis, and a soundness theorem for this extended language. We then demonstrate how the extended language can be used to formally specify not only the garbled circuit construction, but also the formal (symbolic) simulator required by the definition of security. The correctness of the simulation is proved in a purely syntactical way, within the symbolic model of cryptography, and then translated into a concrete computational indistinguishability statement via our general computational soundness theorem. We also implement our symbolic security framework and the garbling scheme in Haskell, and our experiment shows that the symbolic analysis performs well and can be done within several seconds even for large circuits that are useful for real world applications.

The Tor network is designed to provide users with low-latency anonymous communications. Tor clients build circuits with publicly listed relays to anonymously reach their destinations. However, since the relays are publicly listed, they can be easily blocked by censoring adversaries. Consequently, the Tor project envisioned the possibility of unlisted entry points to the Tor network, commonly known as bridges. We address the issue of preventing censors from detecting the bridges by observing the communications between them and nodes in their network. We propose a model in which the client obfuscates its messages to the bridge in a widely used protocol over the Internet. We investigate using Skype video calls as our target protocol and our goal is to make it difficult for the censoring adversary to distinguish between the obfuscated bridge connections and actual Skype calls using statistical comparisons.