If you can do arbitrary computations, you can do loops and conditionals and whatever else you want. FHE claims to support arbitrary computations, so by definition it must support the ability to do any loop or any conditional.
Think of it this way: A conditional is "if this, do that." If the conditional is true, then the branch is executed. The output of the branch is still encrypted, but it's not true that you need the decryption key just to evaluate the branch. Right?
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You can do arbitrary computations, but you only get the encrypted result. So you can't actually tell whether x == y unless you have the key.
If you can do arbitrary computations, you can do loops and conditionals and whatever else you want. FHE claims to support arbitrary computations, so by definition it must support the ability to do any loop or any conditional.
Think of it this way: A conditional is "if this, do that." If the conditional is true, then the branch is executed. The output of the branch is still encrypted, but it's not true that you need the decryption key just to evaluate the branch. Right?