  In a convolution neural network, a composition of linear scalar product,
non-linear activation function and maximum pooling computations are intensively
invoked. As such, to design and implement privacy-preserving, high efficiency
machine learning mechanisms, one highly demands a practical crypto tool for
secure arithmetic computations. SPDZ, an interesting framework of secure
multi-party computations is a promising technique deployed for industry-scale
machine learning development if one is able to generate Beaver (multiplication)
triple offline efficiently. This paper studies secure yet efficient Beaver
triple generators leveraging privacy-preserving scalar product protocols which
in turn can be constructed from additive-only homomorphic encryptions(AHEs).
Different from the state-of-the-art solutions, where a party first splits her
private input into a shared vector and then invokes an AHE to compute scalar
product of the shared vectors managed by individual MPC server, we formalize
Beaver triple generators in the context of 2-party shared scalar product
protocol and then dispense the generated shares to MPC servers. As such, the
protocol presented in this paper can be viewed as a dual construction of the
state-of-the-art AHE based solutions. Furthermore, instead of applying the
Paillier encryption as a basis of our previous constructions or inheriting from
somewhat homomorphic encryptions, we propose an alternative construction of AHE
from polynomial ring learning with error (RLWE) which results in an efficient
implementation of Beaver triple generators.
