In this chapter, the author discusses all aspects of the searchable encryption scheme in a public-key setting. Like any encryption scheme, the searchable encryption scheme also consists of the four basic algorithms: the key generation, index generation, trapdoor generation, and search. These algorithms are derived from the algorithms in an encryption scheme, and the authors discuss the similarity and relationship between each algorithm and the algorithms in any standard public-key encryption scheme. The searchable encryption schemes may either be designed using the core of the underlying encryption scheme or may use a transformation method that converts the underlying encryption scheme into the searchable encryption. Mamta et al. introduced a CP-Attribute-based searchable encryption scheme that can handle non-monotonic access structure. They made use of a reduced ordered binary decision diagram to represent the access structure and achieved the non-monotonic property.