  A major algorithmic challenge in designing applications intended for secure
remote execution is ensuring that they are oblivious to their inputs, in the
sense that their memory access patterns do not leak sensitive information to
the server. This problem is particularly relevant to cloud databases that wish
to allow queries over the client's encrypted data. One of the major obstacles
to such a goal is the join operator, which is non-trivial to implement
obliviously without resorting to generic but inefficient solutions like
Oblivious RAM (ORAM).
  We present an oblivious algorithm for equi-joins which (up to a logarithmic
factor) matches the optimal $O(n\log n)$ complexity of the standard non-secure
sort-merge join (on inputs producing $O(n)$ outputs). We do not use use
expensive primitives like ORAM or rely on unrealistic hardware or security
assumptions. Our approach, which is based on sorting networks and novel
provably-oblivious constructions, is conceptually simple, easily verifiable,
and very efficient in practice. Its data-independent algorithmic structure
makes it secure in various different settings for remote computation, even in
those that are known to be vulnerable to certain side-channel attacks (such as
Intel SGX) or with strict requirements for low circuit complexity (like secure
multiparty computation). We confirm that our approach is easily realizable
through a compact implementation which matches our expectations for performance
and is shown, both formally and empirically, to possess the desired security
characteristics.

Databases;Cryptography and Security;Data Structures and Algorithms