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.