A technique for secure computation obfuscates program execution such that observers cannot detect what instructions are being run at any given time. Rather, program execution and memory access patterns are made to appear uniform. A processor operates based on encrypted inputs and produces encrypted outputs. In various examples, obfuscation is achieved by exercising computational circuits in a similar way for a wide range of instructions, such that all such instructions, regardless of their operational differences, affect the processor's power dissipation and processing time substantially uniformly. Obfuscation is further achieved by limiting memory accesses to predetermined time intervals, with memory interface circuits exercised regardless of whether a running program requires a memory access or not. The resulting processor thus reduces leakage of any meaningful information relating to the program or its inputs, which could otherwise be detectable to observers.