Weak unclonable function (PUF) encryption key means that the manufacturer of the hardware can clone the key but not anybody else. Strong unclonable function (PUF) encryption key means that even the manufacturer of the hardware is unable to clone the key. In this paper, first we introduce an "ultra" strong PUF with intrinsic dynamical randomness, which is not only unclonable but also gets renewed to an independent key (with fresh randomness) during each use via the unconditionally secure key exchange. The solution utilizes the Kirchhoff-law-Johnson-noise (KLJN) method for dynamical key renewal and a one-time-pad secure key for the challenge/response process. The secure key is stored in a flash memory on the chip to provide tamper-resistance and nonvolatile storage with zero power requirements in standby mode. Simplified PUF keys are shown: a strong PUF utilizing KLJN protocol during the first run and noise-based logic (NBL) hyperspace vector string verification method for the challenge/response during the rest of its life or until it is re-initialized. Finally, the simplest PUF utilizes NBL without KLJN thus it can be cloned by the manufacturer but not by anybody else.