What kind of fungal infection causes grey nails?

The causative fungus for grey nails is mostly ringworm of the skin that causes tinea cruris, followed by Candida and, to a lesser extent, yeast.
The nail is susceptible to damage due to the fungal invasion of the nail plate and the underlying nail tissue. The nail is itchy or asymptomatic at first, but then the nail surface thickens, becomes uneven, loses its lustre, becomes greyish-brown, and eventually the nail plate becomes brittle, sometimes with a hollowed out middle or incomplete, and the finger (toe) nail is deformed.
Therefore, once detected, treatment should be promptly administered.