In Poe's "The Cask of Amontillado," to what brotherhood did Fortunato ask Montressor if he belonged, and how did Montressor prove his membership?

The Brotherhood is the Masons or Freemasons, a powerful
secret brotherhood that still exists.  Fortunado  asks Fortunado if he is a Freemason. 
When asked if he is in the Masons, he replies with a gesture the narrator considers rude
because he is not in the Masons and does not understand it.  Although it does not
specify what the grotesque movement is, it seems to be some kind of sign.  Fortunado
does not believe that the narrator is actually a
Mason.

  “You
are not of the masons.”

“Yes, yes,” I said; “yes,
yes.”

“You? Impossible! A
mason?”

“A mason,” I
replied.

“A sign,” he said, “a
sign.”

“It is this,” I answered, producing from beneath the
folds of my roquelaire a
trowel.

Fortunado
does not take the narrator seriously.  They leave it at that, and continue.  This is a
sign that the narrator has some evil plans however.  Why else would he bring a trowel? 
Fortunado does not realize the significance of the trowel.  Its presences, and the
discussion of the Masons, foreshadows Fortunado’s untimely end.  The narrator uses the
trowel to brick him up in the crypt.