A cryptographic primitive is a collection of predefined cryptographic algorithms designed to be executed by users, providing security protections within a specific application context. These algorithms, encapsulated within primitives, are merely syntax that define inputs and outputs. In this chapter, we summarize the characteristics of cryptographic algorithms for cryptographic primitives in the context of syntax definitions. We employ identity-based encryption and its variants as illustrative examples and classify four distinct categories of algorithms to help understand the role played by syntax definitions.