An Elementary Completeness Proof for Secure Two-Party Computation Primitives
This work offers an incremental improvement by simplifying the proof for researchers in cryptography and secure computation.
The paper tackles the problem of characterizing which communication primitives enable secure two-party computation for any function, providing a simple, self-contained proof using elementary information-theoretic tools.
In the secure two-party computation problem, two parties wish to compute a (possibly randomized) function of their inputs via an interactive protocol, while ensuring that neither party learns more than what can be inferred from only their own input and output. For semi-honest parties and information-theoretic security guarantees, it is well-known that, if only noiseless communication is available, only a limited set of functions can be securely computed; however, if interaction is also allowed over general communication primitives (multi-input/output channels), there are "complete" primitives that enable any function to be securely computed. The general set of complete primitives was characterized recently by Maji, Prabhakaran, and Rosulek leveraging an earlier specialized characterization by Kilian. Our contribution in this paper is a simple, self-contained, alternative derivation using elementary information-theoretic tools.