Beaver Triple Generator from Multiplicatively Homomorphic Key Management Protocol

SPDZ, the nickname of secure multi-party computation (MPC) protocol of Damgård et al. from Crypto 2012, is an elegant secret value splitting technique which enjoys highly scalable and efficient multiplications with the help of off-line Beaver (multiplicative) triples. Since an arithmetic circuit defined over a finite field can be implemented by addition and multiplication gates, and also since an implementation of addition gate is almost cost free within the SPDZ framework, a design of efficient secure multi-party computations within the SPDZ framework is reduced to that of Beaver (multiplicative) triples. This paper studies Beaver (multiplicative) triple generators and our contributions are two-fold: