This paper analyzes the robustness of RSA countermeasures against electromagnetic analysis and collision attacks. The proposed RSA cryptosystem uses residue number systems (RNS) for fast executions of the modular calculi with large numbers. The parallel architecture is protected at arithmetic and algorithmic levels by using the Montgomery Ladder and the Leak Resistant Arithmetic countermeasures. Because the architecture can leak information through control and memory executions, the hardware RNS-RSA also relies on the randomization of RAM accesses. Experimental results, obtained with and without randomization of the RNS moduli sets, suggest that the RNS-based RSA with bases randomization and secured RAM accesses is protected.