## Abstract

Oblivious RAM (ORAM), first introduced in the ground-breaking work of Goldreich and Ostrovsky (STOC ’87 and J. ACM ’96) is a technique for provably obfuscating programs’ access patterns, such that the access patterns leak no information about the programs’ secret inputs. To compile a general program to an oblivious counterpart, it is well-known that Ω (log N) amortized blowup is necessary, where N is the size of the logical memory. This was shown in Goldreich and Ostrovksy’s original ORAM work for statistical security and in a somewhat restricted model (the so called balls-and-bins model), and recently by Larsen and Nielsen (CRYPTO ’18) for computational security. A long standing open question is whether there exists an optimal ORAM construction that matches the aforementioned logarithmic lower bounds (without making large memory word assumptions, and assuming a constant number of CPU registers). In this paper, we resolve this problem and present the first secure ORAM with O(log N) amortized blowup, assuming one-way functions. Our result is inspired by and non-trivially improves on the recent beautiful work of Patel et al. (FOCS ’18) who gave a construction with O(log N· log log N) amortized blowup, assuming one-way functions. One of our building blocks of independent interest is a linear-time deterministic oblivious algorithm for tight compaction: Given an array of n elements where some elements are marked, we permute the elements in the array so that all marked elements end up in the front of the array. Our O(n) algorithm improves the previously best known deterministic or randomized algorithms whose running time is O(n · log n) or O(n · log log n), respectively.

Original language | English |
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Title of host publication | Advances in Cryptology – EUROCRYPT 2020 - 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings |

Editors | Anne Canteaut, Yuval Ishai |

Publisher | Springer |

Pages | 403-432 |

Number of pages | 30 |

ISBN (Print) | 9783030457235 |

DOIs | |

State | Published - 2020 |

Event | 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020 - Zagreb, Croatia Duration: 10 May 2020 → 14 May 2020 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 12106 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2020 |
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Country/Territory | Croatia |

City | Zagreb |

Period | 10/05/20 → 14/05/20 |

### Bibliographical note

Publisher Copyright:© International Association for Cryptologic Research 2020.

### Funding

Acknowledgments. We are grateful to Hubert Chan, Kai-Min Chung, Yue Guo, and Rafael Pass for helpful discussions. This work is supported in part by a Simons Foundation junior fellow award awarded to G.A., an AFOSR Award FA9550-18-1-0267, NSF grant CNS-1601879, a DARPA Brandeis award, a Packard Fellowship, a Sloan Fellowship, Google Faculty Research Awards, a VMware Research Award, and a Baidu Research Award. G.A. and I.K. were with Cornell Tech during most this research.

Funders | Funder number |
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National Science Foundation | CNS-1601879 |

Air Force Office of Scientific Research | FA9550-18-1-0267 |

Defense Advanced Research Projects Agency | |

Simons Foundation | |

## Keywords

- Oblivious RAM
- Randomized algorithms
- Tight compaction