A Provably Secure Strong PUF based on LWE: Construction and Implementation

We construct a strong PUF with provable security against ML attacks on both classical and quantum computers. The security is guaranteed by the cryptographic hardness of learning decryption functions of public-key cryptosystems, and the hardness of the learning-with-errors (LWE) problem defined on integer lattices. We call our construction the lattice PUF. We construct lattice PUF with a physically obfuscated key and an LWE decryption function block. To allow deployments in different scenarios, we demonstrate designs with different latency-area trade-offs. A compact design uses a highly serialized LFSR and LWE decryption function, while a latency-optimized design uses an unrolled LFSR and a parallel datapath. We prototype lattice PUF designs with 2136 challenge-response pairs (CRPs) on a Spartan 6 FPGA. In addition to theoretical security guarantee, we evaluate empirical resistance to the various leading ML techniques: the prediction error remains above 49.76% after 1 million training CRPs. The resource-efficient design requires only 45 slices for the PUF logic proper, and 351 slices for a fuzzy extractor. The latency-optimized design achieves a 148X reduction in latency, at a 10X increase in PUF hardware utilization. The mean uniformity of PUF responses is 49.98%, the mean uniqueness is 50.00%, and the mean reliability is 1.26%.