If our salvation is all of God and we are unable to boast about doing anything, then faith must be a gift of God. Our salvation is made up of many parts. All of these were purchased by Jesus Christ for the elect on the cross.
Faith is simply one part of the whole process of salvation.
It does not exist all by itself. Now, it does, indeed, seem reasonable to hold that since all of the benefits received through faith have been purchased by the blood of Christ, faith itself should be deemed as purchased also. However, if faith was purchased, it is the only purchased benefit not received through believing, for, obviously, we do not get faith through faith. No, in this case, we get the root without faith, and its fruits through faith. Faith is ours simply by a gracious sovereign bestowment, and not by purchase.