Systems and methods for providing authentication and secure cryptographic communication between a client and server are described. The client includes an addressable array of PUF devices. The client receives or generates a set of instructions usable to determine a range of PUF addresses. The client measures the PUF addresses and generates a first set of responses. The responses are used to encrypt a session key, which is stored, along with the instructions and a hash of the responses, at the client. Later, the client may recover the session key by using the instructions to measure the PUF again, resulting in a second set of responses. Using a response-based cryptography search engine, the client may then iteratively modify and hash the second set of responses until a response set is uncovered that matches the first response set. This modified response set may then be used to uncover the session key.