# How HomNAND has been computed in Leo Ducas and Daniele Micciancio's FHEW?

In section 4.1 of Leo Ducas and Daniele Micciancio's paper FHE Bootstrapping in less than a second, HomNAND has been computed as follows: $$(\textbf{a}, b) = HomNAND((\textbf{a}_0, b_0),(\textbf{a}_1, b_1)) = (-\textbf{a}_0 - \textbf{a}_1, \frac{5q}{8} - b_0 -b_1),\ using \ 2t = 8$$ Can anyone please elaborate how this equation was derived?

• Hi. Please, what do you mean by "how to compute this equation"? You receive two ciphertexts, $(a_0, b_0)$ and $(a_1, b_1)$, so, all the values in the right-hand side are know and you just need to perform those subtractions. – Hilder Vitor Lima Pereira Oct 29 '18 at 9:57
• By "how to compute this equation" I meant how the result $(-\textbf{a}_0 -\textbf{a}_1, \frac{5q}{8} - b_0 -b_1)$ was derived. – Morshed Oct 29 '18 at 10:03
• What on earth does "by using 2t" mean? Provide more details so that the question can be understood easily. – kodlu Oct 29 '18 at 21:21