Title: Searchable%20Symmetric%20Encryption:%20Improved%20Definitions%20and%20Efficient%20Constructions
1Searchable Symmetric Encryption Improved
Definitions and Efficient Constructions
- Reza Curtmola Juan Garay Seny Kamara
Rafail Ostrovsky - Johns Hopkins Bell Labs
Johns Hopkins UCLA -
2Remote 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 ?
3Outline
- 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
4Private 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...
5Searchable 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
6Prior 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?
7How 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
8Constant-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
9Outline
- Motivation
- Overview of privacy-preserving searching
- Searchable symmetric encryption
- Revisiting security definitions for SSE
- Non-adaptive definitions and construction
- Adaptive definitions and construction
- Extensions
10Revisiting 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
11Issues 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
12SSE 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)
13SSE 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
14Our model
- History documents and keywords
- View encrypted documents, index, trapdoors
- Trace length of documents, search outcomes,
search pattern
15Our 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
16Issues 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
17Issues 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
18What 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?
19Modeling adaptiveness
Non-Adaptive SWP00,Goh03,CM05,...
Adaptive (new)
20Outline
- Motivation
- Overview of privacy-preserving searching
- Searchable symmetric encryption
- Revisiting security definitions for SSE
- Non-adaptive definitions and construction
- Adaptive definitions and construction
- Extensions
21Non-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
22SSE-1
23SSE-1
Austin Baltimore Washington
24SSE-1
- Building a Secure Index
- P PRP
- F PRF
F(Austin) KA
Austin
Baltimore
F(Baltimore) KB
Washington
F(Washington) KW
25SSE-1
addr P(Baltimore)
key F(Baltimore)
Baltimore
26Technical 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)
27Outline
- Motivation
- Overview of privacy-preserving computation
- Searchable symmetric encryption
- Revisiting security definitions for SSE
- Non-adaptive definitions and construction
- Adaptive definitions and construction
- Extensions
28Adaptive 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
29Adaptive 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!
30SSE-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
31Comparison
- n total of documents d of
documents that contain word
Ost90,GO96 SWP00 Goh03 CM05 SSE-1 SSE-2
access pattern yes no no no no no
server comp.
server storage
rounds 1 1 1 1 1
comm.
adaptive yes no no no no yes
32Outline
- Motivation
- Overview of privacy-preserving searching
- Searchable symmetric encryption
- Revisiting security definitions for SSE
- Non-adaptive definitions and construction
- Adaptive definitions and construction
- Extensions
33Multi-User SSE
34Multi-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
35Open 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 ?
36Conclusions
- 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