  This work considers the problem of privately outsourcing the computation of a
matrix product over a finite field $\mathbb{F}_q$ to $N$ helper servers. These
servers are considered to be honest but curious, i.e., they behave according to
the protocol but will try to deduce information about the user's data.
Furthermore, any set of up to $X$ servers is allowed to share their data.
Previous works considered this collusion a hindrance and the download cost of
the schemes increases with growing $X$. We propose to utilize such linkage
between servers to the user's advantage by allowing servers to cooperate in the
computational task. This leads to a significant gain in the download cost for
the proposed schemes. The gain naturally comes at the cost of increased
communication load between the servers. Hence, the proposed cooperative schemes
can be understood as outsourcing both computational cost and communication
cost. Both information--theoretically secure and computationally secure schemes
are considered, showing that allowing information leakage that is
computationally hard to utilize will lead to further gains.
  The proposed server cooperation is then exemplified for specific secure
distributed matrix multiplication (SDMM) schemes and linear private information
retrieval (PIR). Similar ideas naturally apply to many other use cases as well,
but not necessarily always with lowered costs.
