Hard learning problems have recently attracted significant attention within the cryptographic community, both as a versatile assumption on which to build various protocols, and as a potentially sound basis for lightweight (possibly side-channel and fault resistant) implementations. Yet, in this second case, a recurrent drawback of primitives based on the Learning Parity with Noise and Learning With Errors problems is their additional randomness requirements to generate noise or errors. In parallel, the move towards nanoscale devices renders modern implementations increasingly prone to various types of errors. As a result, inexact computing has emerged as a new paradigm to efficiently deal with the challenges raised by such erroneous computations, and mitigate the cost and power consumption overheads they cause. In this paper, we show that these cryptographic and electronic challenges can actually be turned into new opportunities, and provide an elegant solution one to the other. That is, we show that inexact implementations of inner product computations lead to a natural way to define new Learning with Physical Noise or Error assumptions, paving the way to more efficient and physically secure implementations, with potential interest for securing emerging Internet of Things applications.