Lower Bounds for Oblivious Data Structures

Riko Jacob, Kasper Green Larsen, Jesper Buus Nielsen

Research output: Conference Article in Proceeding or Book/Report chapterArticle in proceedingsResearchpeer-review


An oblivious data structure is a data structure where the memory access patterns reveals no information about the operations performed on it. Such data structures were introduced by Wang et al. [ACM SIGSAC’14] and are intended for situations where one wishes to store the data structure at an untrusted server. One way to obtain an oblivious data structure is simply to run a classic data structure on an oblivious RAM (ORAM). Until very recently, this resulted in an overhead of ω(lg n) for the most natural setting of parameters. Moreover, a recent lower bound for ORAMs by Larsen and Nielsen [CRYPTO’18] show that they always incur an overhead of at least Ω(lg n) if used in a black box manner. To circumvent the ω(lg n) overhead, researchers have instead studied classic data structure problems more directly and have obtained efficient solutions for many such problems such as stacks, queues, deques, priority queues and search trees. However, none of these data structures process operations faster than Θ(lg n), leaving open the question of whether even faster solutions exist. In this paper, we rule out this possibility by proving Ω(lg n) lower bounds for oblivious stacks, queues, deques, priority queues and search trees.
Original languageEnglish
Title of host publicationProceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms
PublisherSociety for Industrial and Applied Mathematics
Publication date6 Jan 2019
ISBN (Electronic) 978-1-61197-548-2
Publication statusPublished - 6 Jan 2019
EventThirtieth Annual ACM-SIAM Symposium on Discrete Algorithms - San Diego, United States
Duration: 6 Jan 20199 Jan 2019


ConferenceThirtieth Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CitySan Diego


  • Oblivious data structures
  • Memory access patterns
  • Oblivious RAM (ORAM)
  • Data structure lower bounds
  • Untrusted servers


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