In this paper, we define the Lightweight Cryptography (LWC) Hardware Application Programming Interface (API) for the implementations of lightweight authenticated ciphers, hash functions, and cores combining both functionalities. In particular, our API is intended to meet the requirements of all candidates submitted to the NIST Lightweight Cryptography standardization process. The major parts of our specification include minimum compliance criteria, interface, communication protocol, and timing characteristics supported by the LWC core. All of these criteria have been defined with the goals of guaranteeing (a) compatibility among implementations of the same algorithm by different designers, and (b) fair benchmarking of hardware cores implementing an authenticated cipher, a hash function, or both functionalities. Since 2016, a similar API has been successfully used to implement and benchmark all candidates qualified to Rounds 2 and 3 of the CAESAR competition for authenticated ciphers.