" In this dissertation we explore a new paradigm emerging from the subtleties of cryptographic implementations and relating to theoretical aspects of cryptography. This new paradigm, namely physical variables (PVs), simply describes properties of physical objects designed to be identical but are not due to manufacturing variability. In the first part of this dissertation, we focus our attention on scenarios which require the unique identification of physical objects and we show how Gaussian PVs can be used to fulfill such a requirement. Using this framework we present and analyze a new technique for fingerprinting compact discs (CDs) using the manufacturing variability found in the length of the CDs' lands and pits. Although the variability measured is on the order of 20 nm, the technique does not require the use of microscopes or any advanced equipment. Instead, the electrical signal produced by the photo-detector inside the CD reader will be sufficient to measure the desired variability. We thoroughly investigate the new technique by analyzing data collected from 100 identical CDs and show how to extract a unique fingerprint for each CD. In the second part, we shift our attention to physically parameterized functions (PPFs). Although all the constructions we provide are centered around delay-based physically unclonable functions (PUFs), we stress that the use of the term PUF could be misleading as most circuits labeled with the term PUF are in reality clonable on the protocol level. We argue that using a term like PPFs to describe functions parameterized by a PV is a more accurate description. Herein, we thoroughly analyze delay-PUFs and use a mathematical framework to construct two authentication protocols labeled PUF-HB and HB+PUF. Both these protocols merge the known HB authentication family with delay-based PUFs. The new protocols enjoy the security reduction put forth by the HB portion of the protocol and at the same time maintain a level of hardware security provided by the use of PUFs. We present a proof of concept implementation for HB+PUF which takes advantage of the PUF circuit in order to produce the random bits typically needed for an HB-based authentication scheme. The overall circuit is shown to occupy a few thousand gates. Finally, we present a new authentication protocol that uses 2-level PUF circuits and enables a security reduction which, unlike the previous two protocols, stems naturally from the usage of PVs. "