A lightweight and secure key storage scheme using silicon Physical Unclonable Functions (PUFs) is described. To derive stable PUF bits from chip manufacturing variations, a lightweight error correction code (ECC) encoder / decoder is used. With a register count of 69, this codec core does not use any traditional error correction techniques and is 75% smaller than a previous provably secure implementation, and yet achieves robust environmental performance in 65nm FPGA and 0.13µ ASIC implementations. The security of the syndrome bits uses a new security argument that relies on what cannot be learned from a machine learning perspective. The number of Leaked Bits is determined for each Syndrome Word, reducible using Syndrome Distribution Shaping. The design is secure from a min-entropy standpoint against a machinelearning-equipped adversary that, given a ceiling of leaked bits, has a classification error bounded by ϵ. Numerical examples are given using latest machine learning results.