Bibliographic Details
| Title: |
PERFECT SECURE COMPUTATION IN TWO ROUNDS. |
| Authors: |
APPLEBAUM, BENNY1 bennyap@post.tau.ac.il, BRAKERSKI, ZVIKA2 zvika.brakerski@weizmann.ac.il, TSABARY, ROTEM2 rotem.tsabary@weizmann.ac.il |
| Source: |
SIAM Journal on Computing. 2021, Vol. 50 Issue 1, p68-97. 30p. |
| Subjects: |
IEEE Computer Society, Computer science, Information-theoretic security, Open-ended questions, Cybernetics, Polynomials |
| Abstract: |
We show that any multiparty functionality can be evaluated using a 2-round protocol with perfect correctness and perfect semihonest security, provided that the ma jority of parties are honest. This settles the round complexity of information-theoretic semihonest multiparty computation, resolving a longstanding open question [Y. Ishai and E. Kushilevitz, Randomizing polynomials: A new representation with applications to round-efficient secure computation, in Proceedings of the 41st Annual Symposium on Foundations of Computer Science FOCS 2000, IEEE Computer Society, 2000, pp. 294-304]. The protocol is efficient for NC1 functionalities. Furthermore, given black-box access to a one-way function, the protocol can be made efficient for any polynomial functionality, at the cost of only guaranteeing computational security. Our results are based on a new notion of multiparty randomized encoding which extends and relaxes the standard notion of randomized encoding of functions [Y. Ishai and E. Kushilevitz, Randomizing polynomials: A new representation with applications to round-efficient secure computation, in Proceedings of the 41st Annual Symposium on Foundations of Computer Science FOCS 2000, IEEE Computer Society, 2000, pp. 294-304]. The property of a multiparty randomized encoding (MPRE) is that if the functionality g is an encoding of the functionality f, then for any (permitted) coalition of players, their respective outputs and inputs in g allow them to simulate their respective inputs and outputs in f, without learning anything else, including the other outputs of f. We further introduce a new notion of effective degree, and show that the round complexity of a functionality f is characterized by the degree of its MPRE. We construct degree-2 MPREs for general functionalities in several settings under different assumptions, and use these constructions to obtain 2-round protocols. Our constructions also give rise to new protocols in the client-server model with optimal round complexity. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
