Enforcing Ideal-World Leakage Bounds in Real-World Secret Sharing MPC Frameworks

We give a language-based security treatment of domain-specific languages and compilers for secure multi-party computation, a cryptographic paradigm that enables collaborative computation over encrypted data. Computations are specified in a core imperative language, as if they were intended to be executed by a trusted-third party, and formally verified against an information-flow policy modelling (an upper bound to) their leakage. This allows non-experts to assess the impact of performance-driven authorized disclosure of intermediate values. Specifications are then compiled to multi-party protocols. We formalize protocol security using (distributed) probabilistic information-flow and prove security-preserving compilation: protocols only leak what is allowed by the source policy. The proof exploits a natural but previously missing correspondence between simulation-based cryptographic proofs and (composable) probabilistic non-interference. Finally, we extend our framework to justify leakage cancelling, a domain-specific optimization that allows to first write an efficient specification that fails to meet the allowed leakage upper-bound, and then apply a probabilistic pre-processing that brings leakage to the acceptable range.