Key-dependent message security: Generic amplification and completeness

Benny Applebaum*

*Corresponding author for this work

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

Abstract

Key-dependent message (KDM) secure encryption schemes provide secrecy even when the attacker sees encryptions of messages related to the secret-key sk. Namely, the scheme should remain secure even when messages of the form f(sk) are encrypted, where f is taken from some function class double-struck F. A KDM amplification procedure takes an encryption scheme which satisfies ℱ-KDM security and boost it into a double-struck G-KDM secure scheme, where the function class double-struck G should be richer than double-struck F. It was recently shown by Brakerski et al. (TCC 2011) and Barak et al. (EUROCRYPT 2010), that a strong form of amplification is possible, provided that the underlying encryption scheme satisfies some special additional properties. In this work, we prove the first generic KDM amplification theorem which relies solely on the KDM security of the underlying scheme without making any other assumptions. Specifically, we show that an elementary form of KDM security against functions in which each output bit either copies or flips a single bit of the key (aka projections) can be amplified into KDM security with respect to any function family that can be computed in arbitrary fixed polynomial-time. Furthermore, our amplification theorem and its proof are insensitive to the exact setting of KDM security, and they hold in the presence of multiple-keys and in the symmetric-key/public-key and the CPA/CCA cases. As a result, we can amplify the security of all known KDM constructions, including ones that could not be amplified before. Finally, we study the minimal conditions under which full-KDM security (with respect to all functions) can be achieved. We show that under strong notion of KDM security, the existence of cyclic-secure fully-homomorphic encryption is not only sufficient for full-KDM security, as shown by Barak et al., but also necessary. On the other hand, we observe that for standard KDM security, this condition can be relaxed by adopting Gentry's bootstrapping technique (STOC 2009) to the KDM setting.

Original languageEnglish
Title of host publicationAdvances in Cryptology - EUROCRYPT 2011, 30th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings
PublisherSpringer Verlag
Pages527-546
Number of pages20
ISBN (Print)9783642204647
DOIs
StatePublished - 2011
Event30th Annual International Conference on the Theory and Applications of Cryptographic Techniques Advances in Cryptology, EUROCRYPT 2011 - Tallinn, Estonia
Duration: 15 May 201119 May 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6632 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference30th Annual International Conference on the Theory and Applications of Cryptographic Techniques Advances in Cryptology, EUROCRYPT 2011
Country/TerritoryEstonia
CityTallinn
Period15/05/1119/05/11

Fingerprint

Dive into the research topics of 'Key-dependent message security: Generic amplification and completeness'. Together they form a unique fingerprint.

Cite this