Prepare brining solution and brine shrimp for 20-25 minutes -- remove shrimp feet and devein with shells left on (this isn't absolutely necessary but it does seem to result in moister grilled shrimp), rinse and dry.
Using mortar& pestle smash garlic and salt into a smooth paste.
Add cayenne and paprika and mix well.
Add olive oil and lemon to form a thin paste.
(NOTE: Make sure the paste isn't too loose or it will not cling to the shrimp.) Toss shrimp with paste until evenly coated.
(This mixture can be covered and refrigerated for up to an hour before grilling).
Grill until shells are bright pink- 2-3 minutes per side.