8Transcranial random noise stimulation (tRNS) has been used to improve cognitive 9 performance in patients and healthy individuals in different domains. It is therefore 10 considered as a promising method for cognitive enhancement and rehabilitation. 11However, the mechanistic underpinnings of tRNS are poorly understood, mainly due 12 to difficulties in separating neural signal from stimulation artefact. Here we suggest 13 a procedure to successfully remove the tRNS artefact in both the time and frequency 14 domains, leading to electroencephalography (EEG) data that are comparable between 15 participants in active and sham (placebo) tRNS conditions. Such a procedure affords 16 us a unique opportunity to examine the neurophysiological mechanisms that are 17 altered by tRNS during complex mental arithmetic. We recorded EEG data in 69 18 participants who received arithmetic training concurrently with active or sham tRNS 19 above the dlPFC. We successfully found that active tRNS improved arithmetic 20 performance compared to sham tRNS. The underlying event-related potentials 21 revealed that the tRNS effect was associated with increases in components that are 22 associated with domain-general, rather than domain-specific, changes as indicated 23 by alteration in amplitude of attention and preparatory markers. The results indicate 24 that the enhancement effect of tRNS when applied above the dlPFC acts by effecting 25 general attentional mechanisms during cognitive training, which explains the 26 potential improvement seen over a large array of cognitive tasks. In addition, our 27 procedure to remove the tRNS artefact effectively allows future investigation of the 28 mechanisms underlying the effect of tRNS on human behaviour. 29 30 31 32 65 changes evoked by tRNS have done so by looking at pre/post changes in brain activity 66 (e.g., Harty & Cohen Kadosh, 2019). To a degree, this reflects difficulties in 67 simultaneously recording the electrical activity from the brain whilst delivering 68 electrical stimulation, which is often done at amplitudes an order of magnitude larger 69 than the physiological signal measured by EEG equipment. However, one cannot be 70 sure that the changes that follow from the end of the stimulation (termed "offline 71 effect") are reflective of the altered neural response that might occur during 72 stimulation itself (termed "online effect"). An effective procedure to overcome these 73 difficulties could help elucidate possible mechanisms responsible for tRNS-evoked 74 changes. 75 Recently, Rufener, Ruhnau, Heinze, & Zaehle (2017) used frequency band-pass 76 filters to remove tRNS-induced artefacts from EEG data analysed in the time domain, 77 3 3revealing reduced N1 latency in the tRNS group compared to the sham during a pitch 78 discrimination task. Whilst this method allows demonstration of changes in the time 79 domain, EEG data are multidimensional; we can characterise it not just in the time 80 domain, but also in various facets of the frequency domain, including power, phase, 81 and ...