  We present EasyCritics, an algorithm to detect strongly-lensing groups and
clusters in wide-field surveys without relying on a direct recognition of arcs.
EasyCritics assumes that light traces mass in order to predict the most likely
locations of critical curves from the observed fluxes of luminous red
early-type galaxies in the line of sight. The positions, redshifts and fluxes
of these galaxies constrain the idealized gravitational lensing potential as a
function of source redshift up to five free parameters, which are calibrated on
few known lenses. From the lensing potential, EasyCritics derives the critical
curves for a given, representative source redshift. The code is highly
parallelized, uses fast Fourier methods and, optionally, GPU acceleration in
order to process large datasets efficiently. The search of a $\smash{1 \,
\mathrm{deg}^2}$ field of view requires less than 1 minute on a modern
quad-core CPU, when using a pixel resolution of $0.25''/\mathrm{px}$. In this
first part of a paper series on EasyCritics, we describe the main underlying
concepts and present a first demonstration on data from the
Canada-France-Hawaii-Telescope Lensing Survey. We show that EasyCritics is able
to identify known group- and cluster-scale lenses, including a cluster with two
giant arc candidates that were previously missed by automated arc detectors.
