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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References
Albrecht, M., et al.: (2018). https://eprint.iacr.org/2019/939.pdf
Asmuth, C., Bloom, J.: A modular approach to key safeguarding. IEEE Trans. Inf. Theory 29(2), 208–210 (1983)
Avni, H., Dolev, S., Gilboa, N., Li, X.: SSSDB: database with private information search. In: Karydis, I., Sioutas, S., Triantafillou, P., Tsoumakos, D. (eds.) ALGOCLOUD 2015. LNCS, vol. 9511, pp. 49–61. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29919-8_4
Bitan, D., Dolev, S.: Optimal-round preprocessing-MPC via polynomial representation and distributed random matrix (extended abstract). IACR Cryptology ePrint Arch. 2019, 1024 (2019)
Blakley, G.R.: Safeguarding cryptographic keys. In: Proceedings of the 1979 AFIPS National Computer Conference (1979)
Boyle, E., Gilboa, N., Ishai, Y.: Secure computation with preprocessing via function secret sharing. In: Hofheinz, D., Rosen, A. (eds.) TCC 2019. LNCS, vol. 11891, pp. 341–371. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-36030-6_14
Derbeko, P., Dolev, S.: Polydnn polynomial representation of NN for communication-less SMPC inference. In: Cyber Security Cryptography and Machine Learning - Fifth International Symposium, CSCML 2021, Be’er Sheva, Israel, 8–9 July , 2021, Proceedings, volume 12716 of Lecture Notes in Computer Science. Springer (2021)
Dolev, H., Dolev, S.: Toward provable one way functions (2020)
Dolev, S., Doolman, S.: Blindly follow: Sits CRT and FHE for DCLSMPC of DUFSM. Cryptology ePrint Archive, Report 2021/410 (2021)
Dolev, S., et al.: Secure self-stabilizing computation, Brief announcement (2017)
Dolev, S., Garay, J., Gilboa, N., Kolesnikov, V.: Secret sharing krohn-rhodes: private and perennial distributed computation. In: ITCS, pp. 32–44 (2011)
Dolev, S., Garay, J.A., Gilboa, N., Kolesnikov, V., Kumaramangalam, M.V.: Perennial secure multi-party computation of universal turing machine. Theor. Comput. Sci. 769, 43–62 (2019)
Dolev, S., Garay, J.A., Gilboa, N., Kolesnikov, V., Yuditsky, Y.: Towards efficient private distributed computation on unbounded input streams. J. Math. Cryptology 9(2), 79–94 (2015)
Dolev, S., Gilboa, N., Li, X.: Accumulating automata and cascaded equations automata for communicationless information theoretically secure multi-party computation. Theor. Comput. Sci. 795, 81–99 (2019)
Dolev, S., Lahiani, L., Yung, M.: Secret swarm unit: reactive k-secret sharing. Ad Hoc Netw. 10(7), 1291–1305 (2012)
Dolev, S., Li, Y.: Secret shared random access machine. In: Karydis, I., Sioutas, S., Triantafillou, P., Tsoumakos, D. (eds.) ALGOCLOUD 2015. LNCS, vol. 9511, pp. 19–34. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29919-8_2
Gentry, C.: Fully homomorphic encryption using ideal lattices (2009)
Goldreich, O., Ron, D., Sudan, M.: Chinese remaindering with errors. IEEE Trans. Inf. Theory 46(4), 1330–1338 (2000)
Jaiswal, R.: Chinese remainder codes : using lattices to decode error correcting codes based on Chinese remaindering theorem (2007)
Lamport, L.: Fast paxos. Distrib. Comput. (2006)
Lamport, L.: Time, clocks, and the ordering of events in a distributed system Communication. ACM, July 1978
Rivest, R.L., Adleman, L., Dertouzos, M.L.: On data banks and privacy homomorphisms. In: FOCS, pp. 169–179 (1978)
Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)
Wang, H., Feng, Y., Ding, Y., Tang, S.: A homomorphic arithmetic model via Helib. J. Comput. Theor. Nanosci. 14, 5166–5173 (2017)
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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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