All values are from a finite field $Z_t$.I want to write a function greater than like this$GT(x,y) = \begin{cases}  1, & \text{if } x > y, \\  0, & \text{otherwise}.\end{cases}$using only additions, multiplications, subtractions and preferably not divisions.The equality function $EQU(x,y) = \begin{cases}  1, & \text{if } x == y, \\  0, & \text{otherwise}.\end{cases}$can be computed like this $EQU(x,y) = 1 - (x-y)^p$, where p is the Euler totient function $p=phi(t)=t-1$ because $t$ is prime.Can a greater than function be written in a similar way ?The greater than function would be used for a homomorphic encryption application to find the maximum integer value from a vector of encrypted integers.
It is possible to implement a *greater than* function using only addition, substractions and multiplications?
algorithms;linear algebra