Does homomorphic encryption hide the algorithm itself? The question is rather simple, but finding resources and answers quite tricky. Homomorphic encryption should enable us to compute over encrypted data. What if the algorithm for computing should be kept in secret as well? Given we have a functioning homomorphic encryption in place, is the algorithm which is applied to the input data also secure?
Is it possible for an intruder to understand how the data is computed and learn about the algorithm, given the intruder has access to the program which does the computation?
Update
I tried to ask about circuit privacy or protection with this question. Luckily and unfortunately I learned about this term only by asking this question, which was misleading a bit.
So the question should have been: Does FHE offer circuit privacy?
With this term I found some papers which answer my question.
FHE does not offer circuit privacy by default, but can it can be upgraded to do so:


https://eprint.iacr.org/2016/164.pdf
https://eprint.iacr.org/2016/381.pdf


In brief, the extra cost for circuit privacy is actually very small (just a few noisy-dummy bootstraps at the end of your circuit)... in the honest-but-curious model ! For stronger variants of circuit privacy, you need to certify that the FHE public key is correctly generated; and FHE public key are already quite large, so I let you imagine how proving ZK statements about them would be.