Abstract
A Statistical Information Theoretic Secure (SITS) system utilizing the Chinese Remainder Theorem (CRT), coupled with Fully Homomorphic Encryption (FHE) for Distributed Communication-less Secure Multiparty Computation (DCLSMPC) of any Distributed Unknown Finite State Machine (DUFSM) is presented. Namely, secret shares of the input(s) and output(s) are passed to/from the computing parties, while there is no communication between them throughout the computation. We propose a novel approach of transition table representation and polynomial representation for arithmetic circuits evaluation, joined with a CRT secret sharing scheme and FHE to achieve SITS communication-less within computational secure execution of DUFSM. We address the severe limitation of FHE implementation over a single server to cope with a malicious or Byzantine server. We use several distributed memory-efficient solutions that are significantly better than the majority vote in replicated state machines, where each participant maintains an FHE replica. A Distributed Unknown Finite State Machine (DUFSM) is achieved when the transition table is secret shared or when the (possible zero value) coefficients of the polynomial are secret shared, implying communication-less SMPC of an unknown finite state machine.
Partially supported by the Rita Altura Trust Chair in Computer Science, a grant from the Ministry of Science and Technology, Israel & the Japan Science and Technology Agency (JST), and the German Research Funding (DFG, Grant#8767581199). A detailed version appears in [9].
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Dolev, S., Doolman, S. (2021). Blindly Follow: SITS CRT and FHE for DCLSMPC of DUFSM (Extended Abstract). In: Dolev, S., Margalit, O., Pinkas, B., Schwarzmann, A. (eds) Cyber Security Cryptography and Machine Learning. CSCML 2021. Lecture Notes in Computer Science(), vol 12716. Springer, Cham. https://doi.org/10.1007/978-3-030-78086-9_35
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