Computer-Aided Proofs for Multiparty Computation with Active Security

H. Haagh, A. Karbyshev, S. Oechsner, B. Spitters, P. Strub

Research output: Contribution to book/anthology/report/proceedingArticle in proceedingsResearchpeer-review

22 Citations (Scopus)

Abstract

Secure multi-party computation (MPC) is a general cryptographic technique that allows distrusting parties to compute a function of their individual inputs, while only revealing the output of the function. It has found applications in areas such as auctioning, email filtering, and secure teleconference. Given their importance, it is crucial that the protocols are specified and implemented correctly. In the programming language community, it has become good practice to use computer proof assistants to verify correctness proofs. In the field of cryptography, EasyCrypt is the state of the art proof assistant. It provides an embedded language for probabilistic programming, together with a specialized logic, embedded into an ambient general purpose higher-order logic. It allows us to conveniently express cryptographic properties. EasyCrypt has been used successfully on many applications, including public-key encryption, signatures, garbled circuits and differential privacy. Here we show for the first time that it can also be used to prove security of MPC against a malicious adversary. We formalize additive and replicated secret sharing schemes and apply them to Maurer's MPC protocol for secure addition and multiplication. Our method extends to general polynomial functions. We follow the insights from EasyCrypt that security proofs can often be reduced to proofs about program equivalence, a topic that is well understood in the verification of programming languages. In particular, we show that for a class of MPC protocols in the passive case the non-interference-based (NI) definition is equivalent to a standard simulation-based security definition. For the active case, we provide a new non-interference based alternative to the usual simulation-based cryptographic definition that is tailored specifically to our protocol.

Original languageEnglish
Title of host publicationProceedings - IEEE 31st Computer Security Foundations Symposium, CSF 2018
Number of pages13
Volume2018
Place of publicationOxford
PublisherIEEE
Publication date1 Jul 2018
Pages119-131
Article number8429300
ISBN (Print) 978-1-5386-6681-4
ISBN (Electronic)978-1-5386-6680-7
DOIs
Publication statusPublished - 1 Jul 2018
Event2018 IEEE 31st Computer Security Foundations Symposium (CSF) - Oxford, United Kingdom
Duration: 9 Jul 201812 Jul 2018
Conference number: 31
https://www.cs.ox.ac.uk/conferences/csf2018/

Conference

Conference2018 IEEE 31st Computer Security Foundations Symposium (CSF)
Number31
Country/TerritoryUnited Kingdom
CityOxford
Period09/07/201812/07/2018
Internet address
SeriesProceedings of the IEEE Computer Security Foundations Symposium
Number31
ISSN1940-1434

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