I didn't realise, it's from last Asiacrypt!

(as mentioned earlier, further it increases the ciphertext dimension, whereas the decryption circuit is only defined for "linear" ciphertexts).

As per my understanding, leveled FHE given in BGV paper gives only a bounded noise ciphertext, and the decryption circuit falls within this level, if one has to do one more multiplication, if one multiplies ciphertexts, it increases the noise,

3) Clearly f_mult can't be the multiplication of two ciphertexts as the bootstrapping operation is defined only for linear ciphertexts, isn't it?

4) and would like to know how bootstrapping helps in noise reduction?

2) how is f_mult gate constructed using the bootstrapping operation

Is it f_mult = Dec(ct1, s) x Dec(ct2, s), if so will this circuit be within the level L for the leveled FHE? ( For the lower level ciphertexts)

[[\sum_i (c1 2^i) s_i + c_0]_q]_p is the decryption circuit

1) how is the mod p operation performed using the bootstrapping key? And do we treat the decryption circuit as a function over R_q?