I have been aware of the benefits of the Paleo Diet for some time, but recently became aware of the Ketogenic Diet which is even more carb restrictive, and which has benefited many in reversing cancer, among other health problems.
The Ketogenic Diet transforms the body's metabolism to function on ketone bodies as an energy source rather than glucose or sugar. Cancer cells are unable to use ketone bodies as an energy source and starve to death, while normal cells function perfectly well on them.
Because sugar contributes to aging, and to deterioration of blood vessels associated with heart problems, eliminating it should improve longevity substantially.
Here are a couple of links to more information about the Ketogenic Diet.
Mercola's Ketogenic Diet article
Ketogenic Diet Resource Site