What condition is characterized by an itchy, dry scaling of the sole of the foot?

The condition characterized by an itchy, dry scaling of the sole of the foot is known as tinea pedis, commonly referred to as athlete's foot. This is a fungal infection caused primarily by dermatophytes, which thrive in warm, moist environments such as those found in shoes and socks. The symptoms of tinea pedis include not only itchiness and dryness but often additionally redness and flaking of the skin on the feet, particularly between the toes and on the soles.

The other conditions mentioned do not exhibit the same characteristics. Paronychia refers to an infection of the skin around the nails, typically leading to swelling and pus formation rather than scaling of the foot. Lichen planus is a chronic inflammatory condition affecting the skin and mucous membranes, presenting as itchy, flat-topped purple lesions, which is not specific to the feet and does not align with the described symptoms. Tinea capitis is another fungal infection, but it specifically involves the scalp and hair follicles, leading to hair loss and scaling in that area, separate from the conditions affecting the soles of the feet. Therefore, tinea pedis is the appropriate diagnosis for the symptoms described in the question.