TY - JOUR

T1 - Searchable symmetric encryption

T2 - Optimal locality in linear space via two-dimensional balanced allocations

AU - Asharov, Gilad

AU - Naor, Moni

AU - Segev, Gil

AU - Shahaf, Ido

N1 - Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics

PY - 2021

Y1 - 2021

N2 - 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 N1−1/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.

AB - 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 N1−1/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.

KW - Balanced allocations

KW - Locality

KW - Searchable symmetric encryption

UR - http://www.scopus.com/inward/record.url?scp=85116777435&partnerID=8YFLogxK

U2 - 10.1137/19m1303186

DO - 10.1137/19m1303186

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AN - SCOPUS:85116777435

SN - 0097-5397

VL - 50

SP - 1501

EP - 1536

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

IS - 5

ER -