Physical unclonable functions (PUFs) are relatively new security primitives used for device authentication and device-specific secret key generation. In this paper we focus on SRAM- PUFs. The SRAM-PUFs enjoy uniqueness and randomness properties stemming from the intrinsic randomness of SRAM memory cells, which is a result of manufacturing variations. This randomness can be translated into the cryptographic keys thus avoiding the need to store and manage the device cryptographic keys. Therefore these properties, combined with the fact that SRAM memory can be often found in today's IoT devices, make SRAM-PUFs a promising candidate for securing and authentication of the resource-constrained IoT devices. PUF observations are always affected by noise and environmental changes. Therefore secret- generation schemes with helper data are used to guarantee reliable regeneration of the PUF-based secret keys. Error correction codes (ECCs) are an essential part of these schemes. In this work, we propose a practical error correction construction for PUF-based secret generation that are based on polar codes. The resulting scheme can generate 128-bit keys using 1024 SRAM-PUF bits and 896 helper data bits and achieve a failure probability of 10^{-9} or lower for a practical SRAM-PUFs setting with bit error probability of 15%. The method is based on successive cancellation combined with list decoding and hash-based checking that makes use of the hash that is already available at the decoder. In addition, an adaptive list decoder for polar codes is investigated. This decoder increases the list size only if needed.

Fuzzy commitment and syndrome-based schemes are two well-known helper data schemes used to bind and generate, respectively, a secret key to/from SRAM-PUF observations. To allow the decoder to reconstruct this secret key from a new (verification) observation of an SRAM-PUF, an encoder has to generate so-called helper data. This helper data is a function of an SRAM-PUF enrollment observation and, in case of fuzzy commitment, the secret key. The helper data is assumed to be public and thus must leak no information about the secret key. It is known that both schemes can achieve secrecy capacity equal to the mutual information between enrollment and verification SRAM-PUF observations at zero secrecy leakage, when the observations are unbiased and a single enrollment is performed. We study here the situation when multiple SRAM-PUF observations are used to create multiple secret keys. First, we introduce a symmetry property for multiple SRAM-PUF observations. For such symmetric SRAM-PUFs, we show that, in both helper data schemes, the helper data corresponding to multiple SRAM-PUF observations provide no information about any of the secret keys.