Cryptology ePrint Archive: Report 2021/410

Blindly Follow: SITS CRT and FHE for DCLSMPC of DUFSM

Shlomi Dolev and Stav Doolman

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.

Category / Keywords: cryptographic protocols / SMPC, CRT, Secret Sharing, FHE

Original Publication (with major differences): CSCML 2021

Date: received 26 Mar 2021, last revised 27 Mar 2021

Contact author: shlomidolev at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20210327:072033 (All versions of this report)

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