Security of helper data schemes for SRAM-PUF in multiple enrollment scenarios

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.