Seems thats a job for you..
Denial is not a river in Egypt...-Captain Obvious..
It's really not that hard, but since I made the claim, here's the straight dope:
dopeYou might notice the relation since alcohol is sometimes referred to as "sauce" ("He's on the sauce").
1807, Amer.Eng., "sauce, gravy," from Du. doop "thick dipping sauce." Extension to "drug" is 1889, from practice of smoking semi-liquid opium preparation. Meaning "foolish, stupid person" is older (1851) and may have a sense of "thick-headed." Sense of "inside information" (1901) may come from knowing before the race which horse had been drugged to influence performance. Dope-fiend is attested from 1896.