  Temporal broadening of pulsar signals results from electron density
fluctuations in the interstellar medium that cause the radiation to travel
along paths of different lengths. The Gaussian theory of fluctuations predicts
that the pulse temporal broadening should scale with the wavelength as
lambda^4, and with the dispersion measure (corresponding to distance to the
pulsar) as DM^2. For large dispersion measure, DM > 20 pc/cm^3, the observed
scaling is lambda^4 DM^4, contradicting the conventional theory. Although the
problem has existed for 30 years, there has been no resolution to this paradox.
  We suggest that scintillations for distant pulsars are caused by
non-Gaussian, spatially intermittent density fluctuations with a power-like
probability distribution. This probability distribution does not have a second
moment in a large range of density fluctuations, and therefore the previously
applied conventional Fokker-Planck theory does not hold. Instead, we propose to
apply the theory of Levy distributions (so-called Levy flights). Using the
scaling analysis (confirmed by numerical simulations of ray propagation) we
show that the observed scaling is recovered for large DM, if the density
differences, delta N, have Levy distribution decaying as |delta N|^{-5/3}.
