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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).

From: FORESEE: Fully Outsourced secuRe gEnome Study basEd on homomorphic Encryption

Algorithm 1 CCD # of HMs
1: Let ŝ 0 * = ŵ , ŝ * = m ^ .
2: Let u * = log p - 2
3: Decompose p - 2 = i = 0 h 2 v i
4:For each i = 1,2, , u*
5: ŝ i * = ŝ i - 1 * * ŝ i - 1 * log p - 2 1
6: end for
7: For each i = 0,1, ,
8: ŝ * = ŝ * * ŝ v i * 1 + h + log ( p - 2 ) 1
9: end for   
Total: 1 + h + log ( p - 2 ) 1 + h + log ( p - 2 )