The generation of ultrastrong attosecond pulses through laser-plasma interactions offers the opportunity to surpass the intensity of any known laboratory radiation source, giving rise to new experimental possibilities, such as quantum electrodynamical tests and matter probing at extremely short scales. Here we demonstrate that a laser irradiated plasma surface can act as an efficient converter from the femto- to the attosecond range, giving a dramatic rise in pulse intensity. Although seemingly similar schemes have been described in the literature, the present setup differs significantly from the previous attempts. We present a model describing the nonlinear process of relativistic laser-plasma interaction. This model, which is applicable to a multitude of phenomena, is shown to be in excellent agreement with particle-in-cell simulations. The model makes it possible to determine a parameter region where the energy conversion from the femto- to the attosecond regime is maximal. Based on the study we propose a concept of laser pulse interaction with a target having a groove-shaped surface, which opens up the potential to exceed an intensity level of $10^{26}$ W/cm$^2$ and observe effects due to nonlinear quantum electrodynamics with upcoming laser sources.