Lightweight Data Aggregation Scheme against Internal Attackers in Smart Grid Using Elliptic Curve Cryptography

Table 3

Notations about related operations and runtime results (microseconds).

Notation	Description	Runtime
	BGN encryption	8.315
	BGN decryption	4.056
	Exponentiation related to BGN algorithm	8.096
	Multiplication related to BGN algorithm	0.032
	Bilinear pairing	17.001
	Hash-to-point	14.293
	Point multiplication related to the bilinear pairing	5.485
	Point multiplication with a short exponent related to the bilinear pairing	0.343
	Point addition related to the bilinear pairing	0.023
	Exponentiation related to the bilinear pairing	0.874
	Multiplication related to the bilinear pairing	0.005
	Exponentiation related to the DL problem	1.295
	Exponentiation with a short exponent related to the DL problem	0.081
	Multiplication related to the DL problem	0.012
	Point multiplication related to ECC	0.986
	Point multiplication with a short exponent related to ECC	0.061
	Point addition related to ECC	0.004
	General hash function	0.001