Continuous scaling of CMOS technology beyond sub-nanometer region has aggravated short-channel effects, resulting in increased leakage current and high power densities. Furthermore, elevated leakage current and power density render CMOS based security-critical applications vulnerable to power-side-channel attacks. Carbon Nanotubes (CNT) is a promising alternative to CMOS technology. It offers superior transport properties, excellent thermal conductivities, high current capacities, and low power densities. Besides area, power and performance, adherence to hardware security aspects have become an important criteria today. In this work, we present the first study on power-side-channel analysis of ciphers implemented using CNTFETs. Our simulation results show that for 130 power traces, the simple power analysis (SPA) attack success rate is less than 0.35 for CNTFET based ciphers, whereas it is greater than 0.95 for CMOS based ciphers. For correlation power analysis, the difference of correlation coefficient of the correct key and closest wrong key guess is 1.3 for CMOS based design, and less than 0.56 for CNTFET based ciphers for 20,000 power traces, which implies lesser distinguishability of correct key in case of CNTFETs. These results indicate that CNT offers a higher resilience to power-side-channel attacks than CMOS.