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Searchable Symmetric Encryption Improved
Definitions and Efficient Constructions

• Reza Curtmola Juan Garay Seny Kamara
  Rafail Ostrovsky
• Johns Hopkins Bell Labs
  Johns Hopkins UCLA

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Remote Storage

• Remote storage is ubiquitous
• data backups
• GMail, Yahoo Mail etc...
• Q How do we store sensitive data on an untrusted
  server?
• A Encryption
• hides all partial information about data
• client must download all data, decrypt and
  perform operations locally
• Can we enable the server to help ?

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Outline

• Motivation
• Brief overview of different models for private
  searching
• Our focus Searchable Symmetric Encryption (SSE)
• Revisiting security definitions for SSE
• point out subtle (but serious) issues with
  previous definitions
• Two new notions of security for SSE
• Non-adaptive security
• Adaptive security
• Two new constructions
• Extensions

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Private Searching

• MPC general, but inefficient Yao82, GMW87,
  BGW88, CCD88
• Searching (explicitly) -- different settings
• public data unencrypted (e.g., stock-quotes,
  news articles)
• client wishes to hide which element is accessed
• PIR and its variants CGKS,KO97,...
• user-owned data symmetrically encrypted
• client can upload additional encrypted data
  structures to help search
• Oblivious RAMs, searchable symmetric encryption
  O90, OG96, SWP00, Goh03, CM05
• third-party data public-key encrypted
• data comes encrypted to server from users other
  than client BKOS07
• public-key searchable encryption BDOP05,BW06...

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Searchable Symmetric Encryption

• We consider the following scenario
• client has a collection of documents that
  consists of a set of words
• encrypts document collection together with
  additional data structure
• sends everything to server
• Functionality server should support the
  following types of queries
• find all documents that contain a particular
  keyword
• Privacy allow server to help, but reveal as
  little as possible

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Prior work on SSE

• SSE can be achieved using oblivious RAMs Ost,
  GO
• functionality can simulate any data structure in
  a hidden way, and can support conjunctive
  queries, B-trees etc...
• privacy hides everything, even the access
  pattern
• efficiency logarithmic number of rounds per each
  read/write
• Q Can we search over encrypted data in
  single/constant rounds?
• with absolute privacy, recently solved by
  Boneh-Kushilevitz-Ostrovsky-Skeith wish sqrtDB
  communication.
• This paper what if we relax the security
  requirements to get better performance?

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How do we relax the security definition ?

• Informal answer
• leak the access pattern but nothing else
• What does it mean to leak the access pattern but
  nothing else ?
• defining this formally is delicate
• in fact, there are issues with 3 previous attempts

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Constant-round SSE with relaxed security

• 3 previous constant-round solutions that leak
  access pattern
• Practical techniques for searches on encrypted
  data SWP00
• Secure Indexes Goh03
• Privacy-preserving keyword searches on remote
  encrypted data CM05
• BKOS-07 is constant round but sqrt(DB)
  communication

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Outline

• Motivation
• Overview of privacy-preserving searching
• Searchable symmetric encryption
• Revisiting security definitions for SSE
• Non-adaptive definitions and construction
• Adaptive definitions and construction
• Extensions

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Revisiting SSE security definitions

• SWP00,Goh03,CM05 A secure SSE scheme should
  not leak anything beyond the outcome of a search
• search outcome memory addresses of documents
  that contain a hidden keyword (precise definition
  later)
• Important to note different keyword requests may
  lead to the same search outcome
• search pattern whether two queries were for
  the same keyword or not
• A (slightly) better intuition
• A secure SSE scheme should not leak anything
  beyond the outcome and the pattern of a search

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Issues with SWPs security definition

• SWP00 implicitly use indistinguishability
  GM84 as a security definition
• any function of the plaintext that can be
  computed from the ciphertext can be computed from
  the length of the plaintext
• Issue adversary gets to see search outcomes and
  search pattern
• SWP00 does not model the fact that this
  additional information is revealed.
• There are also issues with definitions in
  Goh03,CM05, but to explain these well need to
  define the model more precisely

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SSE Algorithms

• Keygen(1k) outputs symmetric key K
• BuildIndex(K, D1, ..., Dn) outputs secure
  index I
• Trapdoor(K, w) outputs a trapdoor Tw
• Search(I, Tw) outputs identifiers of documents
  containing w (id1, ..., idm)

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SSE System Operation

• Secure index additional data structure that
  helps the server to search (following Goh03
  terminology)
• Symmetrically encrypted data client performs
  encryption himself
• Trapdoors associate a trapdoor to keywords which
  enables server to search while keeping keyword
  hidden

keyword
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Our model

• History documents and keywords
• View encrypted documents, index, trapdoors
• Trace length of documents, search outcomes,
  search pattern

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Our Intuition

• Previous intuition
• A secure SSE scheme should not leak anything
  beyond the outcome and the pattern of a search
• A more formal intuition
• any function about the documents and the
  keywords that can be computed from the encrypted
  documents, the index and the trapdoors can be
  computed from the length of the documents, the
  search outcomes and the search pattern

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Issues with Gohs SSE security definition

• IND2-CKA indistinguishability against
  chosen-keyword attacks
• any function of the documents that can be
  computed from the encrypted documents and the
  index can be computed from the length of the
  documents and the search outcomes
• Issue says nothing about keywords or trapdoors
• Important Note Goh03 considers more than SSE
  and notes that secure trapdoors is not necessary
  for all the applications considered. Also Z-IDX
  has secure trapdoors.
• Why not prove index secure in the sense of
  IND2-CKA and trapdoors secure using another
  definition?
• We show that there exists an SSE scheme that has
• IND2-CKA indexes and trapdoors that are secure
• but when taken together, adversary can recover
  keyword

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Issues with CMs SSE security definition

• CM security
• any function that can be computed about the
  documents and keywords given the ciphertexts, the
  index and the trapdoors can be computed from the
  length of the documents and the search outcomes
• Issues
• leaves out search pattern (proofs assume unique
  queries)
• order of quantifiers implies that there will
  always exist a simulator that can evaluate
  function on documents and keywords
• Only guarantees security against non-adaptive
  adversaries

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What is adaptiveness?

• Non-adaptive adversaries make search queries
  without seeing the outcome of previous searches
• Adaptive adversaries can make search queries as a
  function of the outcome of previous searches
• What are the implications of adaptiveness?

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Modeling adaptiveness
Non-Adaptive SWP00,Goh03,CM05,...
Adaptive (new)
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Outline

• Motivation
• Overview of privacy-preserving searching
• Searchable symmetric encryption
• Revisiting security definitions for SSE
• Non-adaptive definitions and construction
• Adaptive definitions and construction
• Extensions

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Non-adaptive security

• any function about the history that can be
  computed from the view can be computed from the
  trace
• history documents and keywords
• view encrypted documents, index, trapdoors,
• trace document lengths, search outcomes, search
  pattern

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SSE-1

• Building a Secure Index

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SSE-1

• Building a Secure Index

Austin Baltimore Washington
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SSE-1

• Building a Secure Index
• P PRP
• F PRF

F(Austin) KA
Austin
Baltimore
F(Baltimore) KB
Washington
F(Washington) KW
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SSE-1

• Searching

addr P(Baltimore)
key F(Baltimore)
Baltimore
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Technical issues

• We overlooked many technical details
• padding and shuffling
• Efficient storage of sparse tables
• large address space small number of entries
• FKS dictionaries Fredman-Komlos-Szemeredi84
• storage O(entries)
• lookup O(1)

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Outline

• Motivation
• Overview of privacy-preserving computation
• Searchable symmetric encryption
• Revisiting security definitions for SSE
• Non-adaptive definitions and construction
• Adaptive definitions and construction
• Extensions

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Adaptive security

• any function about the partial history that can
  be computed from the partial view can be computed
  from the partial trace
• partial history documents and keywords
• partial view encrypted documents, index,
  trapdoors,
• partial trace document lengths, search outcomes,
  search pattern

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Adaptive security

• Do we need revised SSE constructions?
• Are previous constructions adaptively secure?
• Technical challenge simulator must be able to
  fake trapdoors after having committed to index
• Previous constructions do not have this property
• Unfortunately, this is expensive!

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SSE-2

• Similar to SSE-1
• Pre-processing and padding
• simulator can commit to an index before query is
  issued
• and still build valid trapdoors after query is
  issued
• Constant blowup in
• size of trapdoors
• size of index
• server search time

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Comparison

• n total of documents d of
  documents that contain word

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Outline

• Motivation
• Overview of privacy-preserving searching
• Searchable symmetric encryption
• Revisiting security definitions for SSE
• Non-adaptive definitions and construction
• Adaptive definitions and construction
• Extensions

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Multi-User SSE
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Multi-User SSE

• Indexes and trapdoors require same security
  notions as single-user SSE
• Revocation owner can revoke searching privileges
• robust against user collusions
• Anonymity server should not know who initiated
  search
• Simple construction that transforms single-user
  SSE schemes to multi-user SSE schemes
• broadcast encryption (revocation)
• PRPs

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Open Questions

• Constant-round schemes that hide everything, even
  the access pattern
• Constant-round Searching for Boolean combinations
  of keywords (note that with logarithmic rounds
  already follows from Ost,GO.)
• Conjunctive searchable encryption GSW04, PKL04,
  BW06
• Disjunctive ?

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Conclusions

• Weakening complete security is delicate
• point out issues with previous attempts
• Introduce new definitions
• non-adaptive simulation and indistinguishability-
  based
• adaptive simulation and indistinguishability-base
  d
• Efficient and practical constructions
• Multi-user setting