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How to Search on Encrypted Data (2013)

6/Oct 2013

This is the first part of a series on searching on encrypted data.
See parts


I recently finished giving a series of talks on one of my favorite topics:
searching on encrypted data. My slides are available
but given the current interest in this topic I thought it might be useful to
turn the talk into a series of posts.

Over the years, the problem of encrypted search has become an important problem
in security and cryptography. I think this is due to a combination of three
things: (1) search is now the primary way we access our data; (2) we are
outsourcing more and more of our data to third parties; and (3) we trust these
third parties less and less (for obvious reasons!).

Because of this, the problem of encrypted search is now of interest to many
sub-fields in computer science (e.g., databases, security, cryptography,
privacy) but also to industry and to governments.

While a-priori searching on encrypted data may sound impossible and
even contradictory, we know of many ways to do it. Some methods are
more practical than others, some are more secure than others and some are more

Some History

The problem of searching on encrypted data was first considered explicitly by
Song, Wagner and Perrig in this
from 2001. When I
first read this paper as a graduate student, I thought this was amazing! I had
never imagined one could do anything like this with encryption and, amazingly,
the construction even seemed practical. Combined with the obvious sense that
these “searchable encryption” schemes could have a huge impact, I got really
excited about this problem.

I later understood that perhaps I shouldn’t have been so surprised (but no less
impressed!) about the possibility of searching on encrypted data since
prior work on
oblivious RAMs by
Goldreich and Ostrovsky and on
secure two-party computation
by Yao also provided solutions to this problem—albeit a
lot less efficiently.

It’s been about 10 years since the Song, Wagner and Perrig paper, 20 years
since the Goldreich and Ostrovsky paper and 30 years since Yao’s paper. So
where do we stand with respect to encrypted search?

The short answer is that we’ve made a ton of progress and we’ re at the point
where encrypted search is reasonably well understood , efficient and could be
deployed. Of course, like any cryptographic technology there are tradeoffs one
has to consider and one of the goals of this series will be to make these
tradeoffs clear.

The Setup

To structure our discussion and to allow for comparisons of the different
solutions, we’ll assume the following setting. We have two parties: a client and
a server; that interact in two phases: a setup phase and a search phase.

During the setup phase, the client will take $n$ documents $(D_1, dots, D_n)$
and generate:

  1. an encrypted database (EDB),
  2. a set of encrypted documents $(c_1, dots, c_n)$.

We’ll assume the documents are encrypted using
a standard encryption scheme (e.g., AES using your favorite mode of operation)
so the interesting part will be how exactly the EDB is constructed.

So as a concrete example if the documents are an email collection, the client
will generate an EDB and then encrypt each email separately using, say, AES.
After generating the EDB and encrypted documents, it will send everything to the
server, concluding the setup phase.

During the search phase, the client wants the server to send back all the
encrypted documents associated with some keyword $w$. To do this, the client
will send a token that encapsulates $w$ without revealing information about
it. The server will then use the token with the EDB to somehow figure
out which encrypted documents it should send back.


We know of six different ways to search on encrypted data, each
based on one of the following cryptographic primitives:

  • property-preserving encryption
  • functional encryption
  • fully-homomorphic encryption
  • searchable symmetric encryption
  • oblivious RAMs
  • secure two-party computation

In the rest of this series we’ ll go through some of these approaches and see
the various tradeoffs they provide between efficiency, security and

Read More



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