Searchable symmetric encryption enables a cloud server to answer queries directly over encrypted data. Two key requirements are a strong security guarantee and a sub-linear search performance. The bucketization approach in the literature addresses these requirements at the expense of downloading false positives and requiring the local search at the client side. In this work, we propose a novel approach to meet these requirements while minimizing the client's work and communication cost. First, a relaxed notion of ciphertext indistinguishability on partitioned data is formalized, called class indistinguishability, which provides a level of ciphertext indistinguishability similar to that of bucketization but allows the server to perform search of relevant data and filter false positives. We present a construction for achieving these goals through a two-phase search algorithm. The first phase finds a candidate set through a sub-linear search. The second phase finds the exact query result using a linear search applied to the candidate set. The experiment results on large real-world data-sets show that our approach outperforms the state-of-the-art. This work focuses on the class of equality conjunction search, but it applies to the general class of Boolean queries of equalities because the latter can be reduced to several equality conjunction queries.