Restless legs syndrome (RLS) is a common neurological disorder characterized by a sensorimotor condition, where patients feel an uncontrollable urge to move the lower limbs in the evening and/or during the night. RLS does not only have a profound impact on quality of life due to the disturbed night-time sleep, but there is growing evidence that untreated or insufficiently managed RLS might also cause cognitive changes in patients affected by this syndrome. It has been proposed that RLS is caused by alterations in the signal-to-noise ratio (SNR) and in dopamine (DA) neurotransmission in the nervous system. Based on this evidence, we propose the "SNR-DA hypothesis" as an explanation of how RLS could affect cognitive performance. According to this hypothesis, variations/reductions in the SNR underlie RLS-associated cognitive deficits, which follow an inverted U-shaped function: In unmedicated patients, low dopamine levels worsen the SNR, which eventually impairs cognition. Pharmacological treatment enhances DA levels in medicated patients, which likely improves/normalizes the SNR in case of optimal doses, thus restoring cognition to a normal level. However, overmedication might push patients past the optimal point on the inverted U-shaped curve, where an exaggerated SNR potentially impairs cognitive performance relying on cortical noise such as cognitive flexibility. Based on these assumptions of SNR alterations, we propose to directly measure neural noise via "1/f noise" and related metrics to use transcranial random noise stimulation (tRNS), a noninvasive brain stimulation method which manipulates the SNR, as a research tool and potential treatment option for RLS.