hnforcing 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 preprocessing that brings leakage to the acceptable range.The fourth author is financed by the COMPETE 2020 Programme within project POCI-01-0145-FEDER-006961, by the FCT within project UID/EEA/50014/2013 and grant SFRH/BPD/121389/2016. The second author is financed by Project NanoSTIMA/NORTE-01-0145-FEDER-000016 through the NORTE 2020 Programme