I am trying to convert a basic program into an arithmetic circuit. I am stuck on the step of converting the greater than operator into an arithmetic circuit. To be specific, I do not know how to convert the following into an arithmetic circuit (where x,y is input):
if x >= y:
To be clear, I need to be able to express this in terms of an ARITHMETIC circuit. Meaning that I need to be able to compute this using only addition and multiplication of numbers (in Z_p).
I've been searching all of the web for solutions, but everything I find tells me how to do this with boolean circuits. I am aware that I can convert the numbers into their bit string and do this boolean way. I would like to know of any alternative way to do this. This show be possible to do with just addition and multiplication, but I cannot figure out how to.
For context, I'm considering this in the case of Multi-Party Computation. Therefore, taking advantage of how I represent my number (i.e. two's complement) will not work because my number will be split into secret shares.