Best practice to convert sfix comparison results to sbit for "Free XOR" logic?

[Fannxy]

Hi,

I am implementing a logic to determine which interval a secret value x belongs to (One-hot encoding based on thresholds).

Here is my current implementation using sfix:

# x is an sfix, test is a list of plain integers/floats
x = sfix(0.5)
test=[1, 2, 3] # for example
comp = [x >= i for i in test]

# Detecting the edge to get the one-hot vector
# Logical goal: (comp[i] XOR comp[i-1])
xor_comp = [comp[i] ^ comp[i-1] for i in range(1, len(comp))] + [comp[-1]]

Since sfix comparisons return sintbit (0 or 1 in the field), the ^ operator in the list comprehension is evaluated as Arithmetic XOR (a+b−2ab). This introduces 1 multiplication (communication round) for every interval check.

I would like to utilize the "Free XOR" (or local operation) property usually associated with binary types.
Is there an efficient way (or intrinsic) to obtain the comparison result directly as sbit (or a bit-decomposed form) to avoid the arithmetic multiplication overhead during the XOR step?

Thanks!

[mkskeller]

You could convert the comparison results to binary using sbitvec(...). However, it is more efficient and easier to use subtraction, which is possible because the sequence is monotone. Some mixed-circuit protocols will have the comparison in binary internally, but there isn't currently any infrastructure to access it.

[Fannxy]

Thanks!

Subtraction is a great solution, which saves one round of communication.