  From first principles, I present a concrete realization of Carlip's idea on
the black hole entropy from the conformal field theory on the horizon in any
dimension. New formulation is free of inconsistencies encountered in Carlip's.
By considering a correct gravity action, whose variational principle is well
defined at the horizon, I $derive$ a correct $classical$ Virasoro generator for
the surface deformations at the horizon through the canonical method. The
existence of the classical Virasoro algebra is crucial in obtaining an operator
Virasoro algebra, through canonical quantization, which produce the right
central charge and conformal weight $\sim A_+/\hbar G$ for the semiclassical
black hole entropy. The coefficient of proportionality depends on the choice of
ground state, which has to be put in by hand to obtain the correct numerical
factor 1/4 of the Bekenstein-Hawking (BH) entropy. The appropriate ground state
is different for the rotating and the non-rotating black holes but otherwise it
has a $universality$ for a wide variety of black holes. As a byproduct of my
results, I am led to conjecture that {\it non-commutativity of taking the limit
to go to the horizon and computing variation is proportional to the Hamiltonian
and momentum constraints}. It is shown that almost all the known uncharged
black hole solutions satisfy the conditions for the universal entropy formula.
