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We construct a strong PUF with provable security against ML attacks on bothclassical and quantum computers. The security is guaranteed by thecryptographic hardness of learning decryption functions of public-keycryptosystems, and the hardness of the learning-with-errors (LWE) problemdefined on integer lattices. We call our construction the lattice PUF.  We construct lattice PUF with a physically obfuscated key and an LWEdecryption function block. To allow deployments in different scenarios, wedemonstrate designs with different latency-area trade-offs. A compact designuses a highly serialized LFSR and LWE decryption function, while alatency-optimized design uses an unrolled LFSR and a parallel datapath.  We prototype lattice PUF designs with $2^{136}$ challenge-response pairs(CRPs) on a Spartan 6 FPGA. In addition to theoretical security guarantee, weevaluate empirical resistance to the various leading ML techniques: theprediction error remains above $49.76\%$ after $1$ million training CRPs. Theresource-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 $1.26\%$.

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