There have been proposals down through the years to incorporate checking logic on ALU's to make sure that the calculations were correct. I believe that IBM made some progress along these lines back in the 1960's. More recently, timing/power/radio/sound emission attacks on encryption have led to computations in which random numbers are inserted early in the calculation, only to later drop out, in order to mask the side-channel information of the actual calculation being performed. I don't know the precise name for these "masking numbers & calculations", but they fall short of fully homomorphic encryption, which would allow an *arbitrary* but unknown calculation to be performed. There are also worries of compromised hardware which looks for *specific constants* being used as operands, and upon encountering such operands, the hardware squirrels away some of the other -- presumably private -- data for illicit use. Some forms of "masked arithmetic" could also reduce the capabilities of this type of compromised hardware. Are there any papers which develop a theory of "masked arithmetic" which would be substantially simpler (& more efficient) than fully homomorphic encryption?