Comparison on Ciphertext with Helib Is it possible to do a greater than homomorphic comparison in the form ($c_1 &lt; c_2$) on two ciphertexts using Helib?

The equal comparison ($c_1 == c_2$) can be done in modulus 2 by adding both ciphertexts. Does it give any multiplication and/or addition combination to obtain the greater than comparison ( $&lt;$) on binary numbers?
On the paper Low Depth Circuits for Efficient Homomorphic Sorting (page 5), the authors present circuits to homomorphically evaluate comparisons.
Their &quot;Less Than Circuit&quot; compares $\ell$-bit integers in the following way:
They define a bit level &quot;less than&quot;: $f(x, y) = y \cdot (x + 1) \mod 2$  (where $x$ and $y$ are encryptions of bits).
They define a bit level &quot;equal to&quot;:  $g(x, y) = y + x + 1 \mod 2$.
Then, the less than circuit for two encrypted $\ell$-bit integers is
$$C_{LT}(X, Y) =  \sum_{k=1}^{\ell} (f(X_k, Y_k) \cdot \prod_{k&lt;t&lt;\ell}g(X_t, Y_t))  \mod 2$$
where $X = (X_1, X_2, \cdots, X_\ell)$ is a vector of ciphertexts in which each $X_k$ is the encryption of the $k$-th bit of the first plaintext (and the same for $Y$ regarding the second plaintext).
Since the only thing it requires is the ability to encrypt bit a bit and to homomorphically operate $\mod 2$, it seems you can evaluate this circuit using Helib.