Physically Unclonable Functions (PUFs) are cryptographic primitives used to implement low-cost device authentication and secure secret key generation. Weak PUFs (i.e., devices able to generate a single signature or to deal with a limited number of challenges) and Strong PUFs (i.e., devices able to deal with large number of challenges) are widely discussed in literature. Strong PUFs are susceptible to machine learning and modeling attacks. In this paper we propose a solution where the challenges of a Strong PUF are encrypted in order to remove the linear challenge-response correlation that can be exploited by those attacks. In this context, a ZeroBit Error Rate Weak PUF generates the encryption key so that all PUF instances have a different, nonlinear correlation between respective challenges and responses. We present two implementations of the proposed solution, and we demonstrate their resilience against machine learning attacks.