  In data-driven applications, preserving user privacy while enabling valuable
computations remains a critical challenge. Technologies like Differential
Privacy (DP) have been pivotal in addressing these concerns. The shuffle model
of DP requires no trusted curators and can achieve high utility by leveraging
the privacy amplification effect yielded from shuffling. These benefits have
led to significant interest in the shuffle model. However, the computation
tasks in the shuffle model are limited to statistical estimation, making the
shuffle model inapplicable to real-world scenarios in which each user requires
a personalized output. This paper introduces a novel paradigm termed Private
Individual Computation (PIC), expanding the shuffle model to support a broader
range of permutation-equivariant computations. PIC enables personalized outputs
while preserving privacy, and enjoys privacy amplification through shuffling.
We propose a concrete protocol that realizes PIC. By using one-time public
keys, our protocol enables users to receive their outputs without compromising
anonymity, which is essential for privacy amplification. Additionally, we
present an optimal randomizer, the Minkowski Response, designed for the PIC
model to enhance utility. We formally prove the security and privacy properties
of the PIC protocol. Theoretical analysis and empirical evaluations demonstrate
PIC's capability in handling non-statistical computation tasks, and the
efficacy of PIC and the Minkowski randomizer in achieving superior utility
compared to existing solutions.
