# Exploring Differential Obliviousness

## TL;DR

This paper investigates the concept of differential obliviousness, a relaxed privacy notion for algorithms, demonstrating its potential benefits in property testing and tasks with input-dependent exploration, beyond traditional oblivious algorithms.

## Contribution

It extends the understanding of differential obliviousness by analyzing its advantages in property testing and input-dependent tasks, highlighting scenarios where it outperforms full obliviousness.

## Key findings

- Differential obliviousness offers nearly linear overhead improvements in dense graph property testing.
- Quadratic overhead improvements are possible in bounded degree graph models.
- Differential obliviousness can maintain input-dependent exploration behaviors, unlike full obliviousness.

## Abstract

In a recent paper Chan et al. [SODA '19] proposed a relaxation of the notion of (full) memory obliviousness, which was introduced by Goldreich and Ostrovsky [J. ACM '96] and extensively researched by cryptographers. The new notion, differential obliviousness, requires that any two neighboring inputs exhibit similar memory access patterns, where the similarity requirement is that of differential privacy. Chan et al. demonstrated that differential obliviousness allows achieving improved efficiency for several algorithmic tasks, including sorting, merging of sorted lists, and range query data structures. In this work, we continue the exploration and mapping of differential obliviousness, focusing on algorithms that do not necessarily examine all their input. This choice is motivated by the fact that the existence of logarithmic overhead ORAM protocols implies that differential obliviousness can yield at most a logarithmic improvement in efficiency for computations that need to examine all their input. In particular, we explore property testing, where we show that differential obliviousness yields an almost linear improvement in overhead in the dense graph model, and at most quadratic improvement in the bounded degree model. We also explore tasks where a non-oblivious algorithm would need to explore different portions of the input, where the latter would depend on the input itself, and where we show that such a behavior can be maintained under differential obliviousness, but not under full obliviousness. Our examples suggest that there would be benefits in further exploring which class of computational tasks are amenable to differential obliviousness.