TY - GEN
T1 - On the power of an honest majority in three-party computation without broadcast
AU - Alon, Bar
AU - Cohen, Ran
AU - Omri, Eran
AU - Suad, Tom
N1 - Publisher Copyright: © International Association for Cryptologic Research 2020.
PY - 2020
Y1 - 2020
N2 - Fully secure multiparty computation (MPC) allows a set of parties to compute some function of their inputs, while guaranteeing correctness, privacy, fairness, and output delivery. Understanding the necessary and sufficient assumptions that allow for fully secure MPC is an important goal. Cleve (STOC’86) showed that full security cannot be obtained in general without an honest majority. Conversely, by Rabin and Ben-Or (FOCS’89), assuming a broadcast channel and an honest majority enables a fully secure computation of any function. Our goal is to characterize the set of functionalities that can be computed with full security, assuming an honest majority, but no broadcast. This question was fully answered by Cohen et al. (TCC’16) – for the restricted class of symmetric functionalities (where all parties receive the same output). Instructively, their results crucially rely on agreement and do not carry over to general asymmetric functionalities. In this work, we focus on the case of three-party asymmetric functionalities, providing a variety of necessary and sufficient conditions to enable fully secure computation. An interesting use-case of our results is server-aided computation, where an untrusted server helps two parties to carry out their computation. We show that without a broadcast assumption, the resource of an external non-colluding server provides no additional power. Namely, a functionality can be computed with the help of the server if and only if it can be computed without it. For fair coin tossing, we further show that the optimal bias for three-party (server-aided) r-round protocol remains Θ(1 / r) (as in the two-party setting).
AB - Fully secure multiparty computation (MPC) allows a set of parties to compute some function of their inputs, while guaranteeing correctness, privacy, fairness, and output delivery. Understanding the necessary and sufficient assumptions that allow for fully secure MPC is an important goal. Cleve (STOC’86) showed that full security cannot be obtained in general without an honest majority. Conversely, by Rabin and Ben-Or (FOCS’89), assuming a broadcast channel and an honest majority enables a fully secure computation of any function. Our goal is to characterize the set of functionalities that can be computed with full security, assuming an honest majority, but no broadcast. This question was fully answered by Cohen et al. (TCC’16) – for the restricted class of symmetric functionalities (where all parties receive the same output). Instructively, their results crucially rely on agreement and do not carry over to general asymmetric functionalities. In this work, we focus on the case of three-party asymmetric functionalities, providing a variety of necessary and sufficient conditions to enable fully secure computation. An interesting use-case of our results is server-aided computation, where an untrusted server helps two parties to carry out their computation. We show that without a broadcast assumption, the resource of an external non-colluding server provides no additional power. Namely, a functionality can be computed with the help of the server if and only if it can be computed without it. For fair coin tossing, we further show that the optimal bias for three-party (server-aided) r-round protocol remains Θ(1 / r) (as in the two-party setting).
KW - Broadcast
KW - Coin flipping
KW - Honest majority
KW - Impossibility result
KW - Multiparty computation
KW - Point-to-point communication
UR - http://www.scopus.com/inward/record.url?scp=85098267872&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-030-64378-2_22
DO - https://doi.org/10.1007/978-3-030-64378-2_22
M3 - منشور من مؤتمر
SN - 9783030643775
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 621
EP - 651
BT - Theory of Cryptography - 18th International Conference, TCC 2020, Proceedings
A2 - Pass, Rafael
A2 - Pietrzak, Krzysztof
PB - Springer Science and Business Media Deutschland GmbH
T2 - 18th International Conference on Theory of Cryptography, TCCC 2020
Y2 - 16 November 2020 through 19 November 2020
ER -