An equational approach to secure multi-party computation
Daniele Micciancio, Stefano Tessaro · 2013
We present a novel framework for the description and analysis of secure computation protocols that is at the same time mathematically rigorous and notationally lightweight and concise. The distinguishing feature of the framework is that it allows to specify (and analyze) protocols in a manner that is largely independent of time, greatly simplifying the study of cryptographic protocols. At the notational level, protocols are described by systems of mathematical equations (over domains), and can be studied through simple algebraic manipulations like substitutions and variable elimination. We exemplify our framework by analyzing in detail two classic protocols: a protocol for secure broadcast, and a verifiable secret sharing protocol, the second of which illustrates the ability of our framework to deal with probabilistic systems, still in a purely equational way.