The employment of intelligent reflecting surfaces (IRSs) is a potential and promising solution to increase the spectral and energy efficiency of wireless communication networks. Despite their many advantages, IRS-aided communications have limitations as they are subject to high propagation losses. To overcome this, the phase rotation (shift) at each element needs to be designed in such a way as to increase the channel gain at the destination. However, this increases the system's complexity as well as its power consumption. In this paper, we present an analytical framework for the performance of random rotation-based IRS-aided communications. Under this framework, we propose four low-complexity and energy efficient schemes, based on a coding or a selection approach. Both of these approaches employ random phase rotations and require limited knowledge of channel state information. Specifically, the coding-based schemes use time-varying random phase rotations to produce an equivalent time-varying channel. On the other hand, the selection-based schemes select a partition of the IRS elements based on the received signal power at the destination. Analytical expressions for the achieved outage probability and energy efficiency of each scheme are derived. It is demonstrated that all schemes can provide significant performance gains as well as full diversity order.