Comparison on Gentry's Fully homomorphic Encryption?
Yes, it is possible. I remember at least of the article Low Depth Circuits for Efficient Homomorphic Sorting in which comparisons are discussed.

Encrypt you $\ell$-bit integers $a$ and $b$ bit by bit generating to $\ell$-dimensional vectors $(a_1, ..., a_\ell)$ and ($b_1, ..., b_\ell)$.

Than, to test homomorphically whether $a \le b$, do

$$C_{LT} =  \sum_{k=1}^{\ell} (f(a_k, b_k) \cdot \prod_{k&lt;t&lt;\ell}g(a_t, b_t))  \mod 2$$

Where $f(a_k, b_k) = b_k \cdot (a_k + 1) \mod 2$ is "less than" for bits and $g(a_t, b_t) = b_t + a_t + 1 \mod 2$ is a "equal to" for bits.

Notice that the product from $k$ to $\ell$ can be performed in depth $\log(\ell - k)$ instead of in depth $\ell - k$.

You will probably find other results about homomorphically comparison by searching for articles that cite the one I put here.