Maximum-likelihood decoding of device-specific multi-bit symbols for reliable key generation

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Abstract
We present a PUF key generation scheme that uses the provably optimal method of maximum-likelihood (ML) detection on symbols derived from PUF response bits. Each device forms a noisy, device-specific symbol constellation, based on manufacturing variation. Each detected symbol is a letter in a codeword of an error correction code, resulting in non-binary codewords. We present a three-pronged validation strategy: i. mathematical (deriving an optimal symbol decoder), ii. simulation (comparing against prior approaches), and iii. empirical (using implementation data). We present simulation results demonstrating that for a given PUF noise level and block size (an estimate of helper data size), our new symbol-based ML approach can have orders of magnitude better bit error rates compared to prior schemes such as block coding, repetition coding, and threshold-based pattern matching, especially under high levels of noise due to extreme environmental variation. We demonstrate environmental reliability of a ML symbol-based soft-decision error correction approach in 28nm FPGA silicon, covering -65°C to 105°C ambient (and including 125°C junction), and with 128bit key regeneration error probability ≤ 1 ppm.