On the BFV fully homomorphic scheme, given a polynomial secret key, we can encrypt polynomial plaintexts and generate polynomial ciphertexts.
So, for example, if we have 2 ciphertexts, we can compare them with the less than function, which is 1 if the left polynomial coefficient is less than or equal to the right one, and 0 otherwise. HOWEVER, the result is also an encrypted polynomial, which when decrypted, gives these 0 and 1 numbers.
The question is: how to extract information? How to learn from encrypted data without decrypting it?
Suppose I want to store encrypted latitudes of clients, and learn if they traveled more than 100km in one day. How would I extract such information? I can certainly calculate the difference between the 2 latitudes, but it would be an encrypted difference. Then what?