  We have investigated electrical transport in a diffusive multiwalled carbon
nanotube contacted using superconducting leads made of Al/Ti sandwich
structure. We find proximity-induced superconductivity with measured critical
currents up to I_cm = 1.3 nA, tunable by gate voltage down to 10 pA. The
supercurrent branch displays a finite zero bias resistance which varies as R_0
proportional to I_cm^-alpha with alpha=0.74. Using IV-characteristics of
junctions with phase diffusion, a good agreement is obtained with Josephson
coupling energy in the long, diffusive junction model of A.D Zaikin and G.F.
Zharkov (Sov. J. Low Temp. Phys. 7, 184 (1981)).
