  Much research has been conducted to securely outsource multiple parties' data
aggregation to an untrusted aggregator without disclosing each individual's
data, or to enable multiple parties to jointly aggregate their data while
preserving privacy. However, those works either assume to have a secure channel
or suffer from high complexity. Here we consider how an external aggregator or
multiple parties learn some algebraic statistics (e.g., summation, product)
over participants' data while any individual's input data is kept secret to
others (the aggregator and other participants). We assume channels in our
construction are insecure. That is, all channels are subject to eavesdropping
attacks, and all the communications throughout the aggregation are open to
others. We successfully guarantee data confidentiality under this weak
assumption while limiting both the communication and computation complexity to
at most linear.
