Paper 2026/451

Oblivious Single Access Machines are Concretely Efficient

Abstract

Oblivious algorithms allow a space-constrained client program to securely outsource storage to an untrusted server. Any program can be compiled to an oblivious form via Oblivious RAM (ORAM), but this is asymptotically and concretely expensive. Recent work (Appan et al., CCS'24) proposed a weakening of ORAM called Oblivious Single Access Machine (OSAM), which offers asymptotically-improved oblivious compilation for many programs, including those that manipulate graph data structures. While of theoretical interest, OSAM graph algorithms were worse than generic ORAM, even for large graphs (tested on graphs of size up to $2^{25}$). This work improves the concrete costs of OSAM-based oblivious algorithms. In short, the original work on OSAM proposed algorithms for manipulating objects with pointers to other objects, but their management of pointers involves non-trivial and concretely-expensive algorithms. Our work greatly simplifies and improves the efficiency of OSAM-based pointer handling by co-designing (1) pointer-friendly modifications to the underlying Path ORAM algorithm and (2) new algorithms for managing pointers and building graphs from pointers. Our work provides generic and easy-to-use oblivious tools with concretely better performance than state-of-the-art generic tools. Natural graph algorithms can now be automatically compiled to an oblivious form while enjoying up to a $4$x improvement in performance as compared to generic Path ORAM (and at least $8$x as compared to the original OSAM).

Note: Preprint, addition of concrete counter example, and performance testing on real graph datasets.