Finding a string in a table

I want to make a smart login server. If you logged in, it will add you to a table of authenticated ID's. But how do I make the server scan the table for the ID to see if it is authenticated or not?

Im guessing you just index the table numerically, so in that case you can just use a for loop

tId = {
  1 = "derp",
  2 = "derpy"
}
function check(id)
  for i=1,#tId do --the # returns the number of numerical keyes from 1 to the first nil, so here it will return 2
	if tId[i] == id then
	  return true
	end
end
if check"derp" then
  print"id found!"
end

On the other hand, if you were to index the table using the IDs themselves, you'd just perform a simple existence check.

tId = {
  ["derp"] = true,
  ["derpy"] = true
}

function check(id)
  return tId[id]
end

if check("derp") then
  print("id found!")
end

More entries can be added to the table later by using code along the lines of:

tId[user] = true