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).

Algorithm 1	CCD	# of HMs
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: ${ŝ}_i^{*}={ŝ}_{i-1}^{*}*{ŝ}_{i-1}^{*}$	$⌊\mathsf{\text{log}}\left(p-2\right)⌋$	1
6: end for
7: For each i = 0,1, ⋯, $\mathcal{h }$
8: ${ŝ}^{*}={ŝ}^{*}*{ŝ}_{{\mathcal{v}}_i}^{*}$	$\begin{array}{l}1+\mathcal{h}\\ +\lfloor \log (p-2)\rfloor \end{array}$	1
9: end for
Total:	$\begin{array}{l}1+\mathcal{h}\\ +\lfloor \log (p-2)\rfloor \end{array}$	$\begin{array}{l}1+\mathcal{h}\\ +\lfloor \log (p-2)\rfloor \end{array}$