Lower and upper bounds on obtaining history independence

Niv Buchbinder, Erez Petrank

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

History independent data structures, presented by Micciancio, are data structures that possess a strong security property: even if an intruder manages to get a copy of the data structure, the memory layout of the structure yields no additional information on the data structure beyond its content. In particular, the history of operations applied on the structure is not visible in its memory layout. Naor and Teague proposed a stronger notion of history independence in which the intruder may break into the system several times without being noticed and still obtain no additional information from reading the memory layout of the data structure. An open question posed by Naor and Teague is whether these two notions are equally hard to obtain. In this paper we provide a separation between the two requirements for comparison based algorithms. We show very strong lower bounds for obtaining the stronger notion of history independence for a large class of data structures, including, for example, the heap and the queue abstract data structures. We also provide complementary upper bounds showing that the heap abstract data structure may be made weakly history independent in the comparison based model without incurring any additional (asymptotic) cost on any of its operations. (A similar result is easy for the queue.) Thus, we obtain the first separation between the two notions of history independence. The gap we obtain is exponential: some operations may be executed in logarithmic time (or even in constant time) with the weaker definition, but require linear time with the stronger definition.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsDan Boneh
PublisherSpringer Verlag
Pages445-462
Number of pages18
ISBN (Print)9783540406747
DOIs
StatePublished - 2003
Externally publishedYes

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2729
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Keywords

  • History independent data-structures
  • Lower bounds
  • Privacy
  • The heap data-structure
  • The queue data-structure

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