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Table 9 Complexity analysis in terms of cumulative circuit depth2 (CCD) and the number of homomorphic multiplications (HMs) for secure approximation division (Algorithm 3).

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

Algorithm 3 CCD # of HMs
1: Compute X ^ log d - 1 + 1 d − 1
2: Compute X ^ log C - 2 + log d - 1 + 2 C − 2
3:For c = 0,1, , C − 1
4: For i = 0,1, , d − 1
5: Calculate h ^ c d + i x ^ i
6: end for
7: end for
8: a ^ = 0 ^
9: For c = 0,1, , C − 1
10: a ^ = 0 ^
11: For i = 0,1, , d − 1
12: a ^ = a ^ + ĥ c d + i x ^ i
13: end for
14: a ^ = a ^ + a ^ x ^ c d log C - 2 + log d - 1 + 3 1
15: end for
Total: log C - 2 + log d - 1 + 3 2C + d − 3