Systems and methods of authentication and encrypted communication between a server and client using independently-generated shared encryption keys are disclosed. Clients with arrays of physical-unclonable-function devices respond to server-issued challenges. The clients derive encryption keys from responses to those challenges generated by measuring PUF devices specified by the challenges. The clients send messages encrypted with the encryption keys to the server. The server independently reproduces the client-generated encryption keys using information about the PUF devices. When the keys match, the clients are authenticated. It may be desirable to inject errors into the challenge responses generated by the clients to improve security. When errors are injected, attackers cannot determine correct challenge responses except by brute force. When a sufficiently large number of errors are introduced, the server has sufficient computational power to successfully authenticate the client, but is computationally infeasible for an attacker to reverse engineer the correct responses.