## Abstract

Searchable symmetric encryption (SSE) enables a client to store a database on an untrusted server while supporting keyword search in a secure manner. Despite the rapidly increasing interest in SSE technology, experiments indicate that the performance of the known schemes scales badly to large databases. Somewhat surprisingly, this is not due to their usage of cryptographic tools, but rather due to their poor locality (where locality is defined as the number of noncontiguous memory locations the server accesses with each query). The only known schemes that do not suffer from poor locality suffer either from an impractical space overhead or from an impractical read efficiency (where read efficiency is defined as the ratio between the number of bits the server reads with each query and the actual size of the answer). We construct the first SSE schemes that simultaneously enjoy optimal locality, optimal space overhead, and nearly optimal read efficiency. Specifically, for a database of size N, under the modest assumption that no keyword appears in more than N^{1−1/log log N} documents, we construct a scheme with read efficiency Õ(log log N). This essentially matches the lower bound of Cash and Tessaro (EUROCRYPT'14) showing that any SSE scheme must be suboptimal in either its locality, its space overhead, or its read efficiency. In addition, even without making any assumptions on the structure of the database, we construct a scheme with read efficiency Õ(log N). Our schemes are obtained via a two-dimensional generalization of the classic balanced allocations (“balls and bins”) problem that we put forward. We construct nearly optimal two-dimensional balanced allocation schemes, and then combine their algorithmic structure with subtle cryptographic techniques.

Original language | English |
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Pages (from-to) | 1501-1536 |

Number of pages | 36 |

Journal | SIAM Journal on Computing |

Volume | 50 |

Issue number | 5 |

DOIs | |

State | Published - 2021 |

### Bibliographical note

Funding Information:∗Received by the editors December 2, 2019; accepted for publication (in revised form) June 7, 2021; published electronically September 21, 2021. A preliminary and shorter version appeared in STOC ’16, ACM, New York, 2016, pp. 1101–1114. https://doi.org/10.1137/19M1303186 Funding: This work was supported in part by the Israel Science Foundation (grants 483/13, 950/15, 2439/20 and 2686/20), by the Israeli Centers of Research Excellence (I-CORE) Program (Center 4/11), by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office, by the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement 891234, and by the European Union’s Horizon 2020 Framework Program (H2020) via an ERC Grant (grant 714253).

Funding Information:

We thank Raphael Bost, Ang?le Bossuat, Pierre-Alain Fouque, and Brice Minaud for observing that our bound on the probability of the event ?E0 in the proof of Theorem 3.2 was incorrect in a previous version of this paper. We additionally thank the SICOMP reviewers for their valuable comments.

Publisher Copyright:

© 2021 Society for Industrial and Applied Mathematics

## Keywords

- Balanced allocations
- Locality
- Searchable symmetric encryption