Ciphertext Expansion in Limited-Leakage Order-Preserving Encryption: A Tight Computational Lower Bound

Gil Segev*, Ido Shahaf

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Order-preserving encryption emerged as a key ingredient underlying the security of practical database management systems. Boldyreva et al. (EUROCRYPT ’09) initiated the study of its security by introducing two natural notions of security. They proved that their first notion, a “best-possible” relaxation of semantic security allowing ciphertexts to reveal the ordering of their corresponding plaintexts, is not realizable. Later on Boldyreva et al. (CRYPTO ’11) proved that any scheme satisfying their second notion, indistinguishability from a random order-preserving function, leaks about half of the bits of a random plaintext. This unsettling state of affairs was recently changed by Chenette et al. (FSE ’16), who relaxed the above “best-possible” notion and constructed a scheme satisfying it based on any pseudorandom function. In addition to revealing the ordering of any two encrypted plaintexts, ciphertexts in their scheme reveal only the position of the most significant bit on which the plaintexts differ. A significant drawback of their scheme, however, is its substantial ciphertext expansion: Encrypting plaintexts of length m bits results in ciphertexts of length bits, where determines the level of security (e.g., in practice). In this work we prove a lower bound on the ciphertext expansion of any order-preserving encryption scheme satisfying the “limited-leakage” notion of Chenette et al. with respect to non-uniform polynomial-time adversaries, matching the ciphertext expansion of their scheme up to lower-order terms. This improves a recent result of Cash and Zhang (TCC ’18), who proved such a lower bound for schemes satisfying this notion with respect to computationally-unbounded adversaries (capturing, for example, schemes whose security can be proved in the random-oracle model without relying on cryptographic assumptions). Our lower bound applies, in particular, to schemes whose security is proved in the standard model.

Original languageAmerican English
Title of host publicationTheory of Cryptography - 16th International Conference, TCC 2018, Proceedings
EditorsAmos Beimel, Stefan Dziembowski
PublisherSpringer Science and Business Media Deutschland GmbH
Pages177-191
Number of pages15
ISBN (Print)9783030038090
DOIs
StatePublished - 2018
Event16th International Conference on Theory of Cryptography, TCC 2018 - Panaji, India
Duration: 11 Nov 201814 Nov 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11240 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th International Conference on Theory of Cryptography, TCC 2018
Country/TerritoryIndia
CityPanaji
Period11/11/1814/11/18

Bibliographical note

Publisher Copyright:
© 2018, International Association for Cryptologic Research.

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