  Web searching is becoming an essential activity because it is often the most
effective and convenient way of finding information. However, a Web search can
be a threat to the privacy of the searcher because the queries may reveal
sensitive information about the searcher. Private Web search (PWS) solutions
allow users to find information on the Internet while preserving their privacy.
Here, privacy means maintaining the confidentiality of the identity of the
communicating users. According to their underlying technology, existing PWS
solutions can be divided into three types: proxy-based solutions,
obfuscation-based solutions, and cryptography-based solutions. Of these,
cryptography-based PWS (CB-PWS) systems are particularly interesting because
they provide strong privacy guarantees in the cryptographic sense. In this
paper, we present a round-efficient CB-PWS protocol that preserves
computational efficiency compared to other known CB-PWS systems. Assuming a
broadcast channel, our protocol is a \emph{four-round} cryptographic scheme
that requires $O(n)$ communication complexity. However, if only point-to-point
interaction is available, with the users emulating the broadcast channel, our
protocol requires an expected $O(1)$-round complexity and the same computation
and communication overhead. Further analyzing the efficiency of our protocol
shows that our proposal requires only $3n$ modular exponentiations for $n$
users. To evaluate the security of our protocol, we demonstrate that our
construction is secure in terms of a semi-honest model. We then discuss how to
enhance its security to render it secure in the presence of malicious
adversaries. We provide a specific protocol for managing users' groups, which
is also an advantage over existing systems.
