Lattice PUF: A Strong Physical Unclonable Function Provably Secure against Machine Learning Attacks (1909.13441v2)

Abstract: We propose a strong physical unclonable function (PUF) provably secure against ML attacks with both classical and quantum computers. Its security is derived from cryptographic hardness of learning decryption functions of public-key cryptosystems. Our design compactly realizes the decryption function of the learning-with-errors (LWE) cryptosystem. Due to the fundamental connection of LWE to lattice problems, we call the construction the lattice PUF. Lattice PUF is constructed using a physically obfuscated key (POK), an LWE decryption function block, and a linear-feedback shift register (LFSR) as a pseudo-random number generator. The POK provides the secret key of the LWE decryption function; its stability is ensured by a fuzzy extractor (FE). To reduce the challenge size, we exploit distributional relaxations of space-efficient LWEs. That allows only a small challenge-seed to be transmitted with the full-length challenge generated by the LFSR, resulting in a 100X reduction of communication cost. To prevent an active challenge-manipulation attack, a self-incrementing counter is embedded into the challenge seed. We prototyped the lattice PUF with 2^136 challenge-response pairs (CRPs) on a Spartan 6 FPGA, which required 45 slices for the PUF logic proper and 233 slices for the FE. Simulation-based evaluation shows the mean (std) of uniformity to be 49.98% (1.58%), of uniqueness to be 50.00% (1.58%), and of reliability to be 1.26% (2.88%). The LWE concrete hardness estimator guarantees that a successful ML attack of the lattice PUF will require the infeasible 2^128 CPU operations. Several classes of empirical ML attacks, including support vector machine, logistic regression, and deep neural networks, are used: in all attacks, the prediction error remains above 49.76% after 1 million training CRPs.