  We present a new method for time-efficient and accurate extraction of the
power spectrum from future cosmic microwave background (CMB) maps based on
properties of peaks and troughs of the Gaussian CMB sky. We construct a
statistic describing their angular clustering - analogously to galaxies, the
2-point angular correlation function, $\xi_\nu(\theta)$. We show that for
increasing peak threshold, $\nu$, the $\xi_\nu(\theta)$ is strongly amplified
and becomes measurable for $\nu\geq$1 on angular scales $\leq 10^\circ$. Its
amplitude at every scale depends uniquely on the CMB temperature correlation
function, $C(\theta)$, and thus the measured $\xi_\nu$ can be uniquely inverted
to obtain $C(\theta)$ and its Legendre transform, the power spectrum of the CMB
field. Because in this method the CMB power spectrum is deduced from high
peaks/troughs of the CMB field, the procedure takes only $[f(\nu)]^2N^2$
operations where $f(\nu)$ is the fraction of pixels with $|\delta T|\geq\nu$
standard deviations in the map of $N$ pixels and is e.g. 0.045 and 0.01 for
$\nu$=2 and 2.5 respectively. We develop theoretical formalism for the method
and show with detailed simulations, using MAP mission parameters, that this
method allows to determine very accurately the CMB power spectrum from the
upcoming CMB maps in only $\sim(10^{-4}-10^{-3})\times N^2$ operations.
