Hydrogen bomb is based on the principle of

The gigantic energy released by a hydrogen bomb comes from the fusion of light nuclei such as $$^{2}H$$ (deuterium) and $$^{3}H$$ (tritium).
Fusion reactions need a temperature of the order of $$10^{7}\,\text{K}$$; a small fission (atomic) bomb is first exploded to supply this temperature, after which the nuclei fuse to form heavier nuclei (for example, $$^{4}He$$) with a tremendous release of energy according to Einstein’s relation $$E = mc^{2}$$.

Thus the fundamental principle behind a hydrogen or thermonuclear bomb is nuclear fusion.

Why the other options are incorrect:
A. Nuclear fission powers ordinary atomic bombs and nuclear reactors, not hydrogen bombs.
B. Natural radioactivity involves spontaneous decay of unstable nuclei; it is unrelated to bomb mechanisms.
D. Artificial radioactivity refers to man-made production of radioactive isotopes, again not the working principle of a hydrogen bomb.

Hence, the correct choice is:

Option C which is: Nuclear fusion