Does shroud prevent the permanent's controller from targeting it with their own spells?

Shroud is defined in CR 702.18a: a permanent or player with shroud cannot be the target of spells or abilities. The rule makes no distinction between the controller of the permanent and any other player. This is the key difference between shroud and hexproof.

Hexproof (CR 702.11a) protects only from spells and abilities controlled by opponents, meaning you can still target your own hexproof permanent. Shroud offers no such exception — it blocks targeting universally.

If you try to target your own shroud permanent with a spell or ability, that target is illegal at the time you choose targets (CR 601.2c requires targets to be legal). If shroud is somehow gained after targets are chosen, the spell or ability is countered on resolution because its only target is now illegal (CR 608.2b).

Concrete example: You control a creature with shroud and want to cast Giant Growth on it to save it in combat. You cannot — Giant Growth requires you to target a creature, and your own shroud creature is an illegal target for you just as it is for your opponent. You must choose a different creature or the spell cannot be cast.

If you want a permanent that protects from opponents but can still be targeted by its controller, look for hexproof instead of shroud.