  We study the differentially private multi group aggregation (PMGA) problem.
This setting involves a single server and $n$ users. Each user belongs to one
of $k$ distinct groups and holds a discrete value. The goal is to design
schemes that allow the server to find the aggregate (sum) of the values in each
group (with high accuracy) under communication and local differential privacy
constraints. The privacy constraint guarantees that the user's group remains
private. This is motivated by applications where a user's group can reveal
sensitive information, such as his religious and political beliefs, health
condition, or race. We propose a novel scheme, dubbed Query and Aggregate
(Q\&A) for PMGA. The novelty of Q\&A is that it is an interactive aggregation
scheme. In Q\&A, each user is assigned a random query matrix, to which he sends
the server an answer based on his group and value. We characterize the Q\&A
scheme's performance in terms of accuracy (MSE), privacy, and communication. We
compare Q\&A to the Randomized Group (RG) scheme, which is non-interactive and
adapts existing randomized response schemes to the PMGA setting. We observe
that typically Q\&A outperforms RG, in terms of privacy vs. utility, in the
high privacy regime.
