Table 8 Complexity analysis in terms of cumulative circuit depth2 (CCD) and the number of homomorphic multiplications (HMs) for secure errorless division protocol (Algorithm 1).

1: Let ${ŝ}_0*=ŵ,ŝ*=\widehat{m}$.

2: Let $u^{*}=⌊\mathsf{\text{log}}\left(p-2\right)⌋$

3: Decompose $p-2=\sum _{i=0}^{\mathcal{h}}{2}^{{\mathcal{v}}_i}$

−

4:For each i = 1,2, ⋯, u*

5: ${ŝ}_i^{*}={ŝ}_{i-1}^{*}*{ŝ}_{i-1}^{*}$

$⌊\mathsf{\text{log}}\left(p-2\right)⌋$

6: end for

7: For each i = 0,1, ⋯, $\mathcal{h }$

8: ${ŝ}^{*}={ŝ}^{*}*{ŝ}_{{\mathcal{v}}_i}^{*}$

$\begin{array}{l}1+\mathcal{h}\\ +\lfloor \log (p-2)\rfloor \end{array}$

9: end for

$\begin{array}{l}1+\mathcal{h}\\ +\lfloor \log (p-2)\rfloor \end{array}$

$\begin{array}{l}1+\mathcal{h}\\ +\lfloor \log (p-2)\rfloor \end{array}$