Does a creature with shroud prevent its controller from equipping it?

Shroud is a static ability that means the permanent cannot be the target of spells or abilities (CR 702.18a). Crucially, shroud protects against targeting by anyone — opponents and the controller alike.

Equipping a creature requires activating the Equipment's equip ability, which uses the word 'target' (CR 301.5b). Because the equip ability targets a creature, a creature with shroud is an illegal target for that ability. The controller cannot equip a creature they own if it has shroud (CR 114.4).

This is the key difference between shroud and hexproof: hexproof only prevents opponents from targeting the permanent (CR 702.11a), so a controller can equip their own hexproof creature. With shroud, no one can target the creature, including its controller.

Example: You control a Sword of Fire and Ice and a Asceticism (which grants shroud to your creatures). When you try to activate the Sword's equip ability targeting your own creature, the activation is illegal — the creature has shroud and cannot be targeted, even by you. You simply cannot attach the Equipment that way.

Note: If an Equipment somehow becomes attached to a shroud creature through a non-targeting effect (e.g., a spell that says 'attach' without the word 'target'), the attachment is valid. Shroud only blocks targeting (CR 702.18a).