Communication Lower Bounds for Perfect Maliciously Secure MPC [article]

Ivan Damgård, Nikolaj I. Schwartzbach
2020 IACR Cryptology ePrint Archive  
We prove a lower bound on the communication complexity of perfect maliciously secure multiparty computation, in the standard model with n = 3t + 1 parties of which t are corrupted. We show that for any n and all large enough g ∈ N there exists a Boolean circuit C with g gates, where any perfectly secure protocol implementing C must communicate Ω(ng) bits. The results easily extends to constructing similar circuits over any fixed finite field. Our results also extend to the case where the
more » ... ld t is suboptimal. Namely if n = 3t + s the bound is Ω(ng/s), which corresponds to known optimizations via packed secretsharing. Using known techniques, we also show an upper bound that matches the lower bound up to a constant factor (existing upper bounds are a factor lg n off for Boolean circuits).
dblp:journals/iacr/DamgardS20 fatcat:glqimx5avbhtvmqr7y3rrtt74y