As cloud computing becomes mainstream, the need to ensure the privacy of the data entrusted to third parties keeps rising. Cloud providers resort to numerous security controls and encryption to thwart potential attackers. Still, since the actual computation inside cloud microprocessors remains unencrypted, the opportunity of leakage is theoretically possible. Therefore, in order to address the challenge of protecting the computation inside the microprocessor, we introduce a novel general purpose architecture for secure data processing, called HEROIC (Homomorphically EncRypted One Instruction Computer). This new design utilizes a single instruction architecture and provides native processing of encrypted data at the architecture level. The security of the solution is assured by a variant of Paillier's ho-momorphic encryption scheme, used to encrypt both instructions and data. Experimental results using our hardware-cognizant software simulator, indicate an average execution overhead between 5 and 45 times for the encrypted computation (depending on the security parameter), compared to the unencrypted variant, for a 16-bit single instruction architecture.