. 2024 Jul 10;26(7):590. doi: 10.3390/e26070590

Table 2.

Execution time of basic cryptographic operations and element size.

Symbols	Meanings	Time (ms)/Size (Byte)
$T_{i n v e r s e}$	$Time of module inverse on Z_{q}^{*}$	0.0181 ms
$T_{\mod}$	$Time of \mod operation on Z_{q}^{*}$	0.0020 ms
$T_{e}$	$Time of module exponential on Z_{q}^{*}$	0.0434 ms
$T_{m}$	$Time of module multiplication on Z_{q}^{*}$	0.0044 ms
$T_{S E}$	Encryption time of AES algorithm	10.0761 ms
$T_{D E}$	Decryption time of AES algorithm	0.1759 ms
$T_{\oplus}$	Time of XOR operation	0.0009 ms
$T_{b p}$	Time of bilinear pairing	8.7985 ms
$T_{b p m 1}$	$Time of multiplication on bilinear group G_{1}$	0.1361 ms
$T_{b p e 1}$	$Time of exponential on bilinear group G_{1}$	1.3451 ms
$T_{b p m 2}$	$Time of multiplication on bilinear group G_{2}$	0.0069 ms
$T_{b p e 2}$	$Time of exponential on bilinear group G_{2}$	0.0869 ms
$T_{e m}$	Time of scalar multiplication on ecliptic curve group $G$	1.4944 ms
$T_{e a}$	Time of point addition on ecliptic curve group $G$	0.1376 ms
$T_{h}$	Time of one-way hash function	0.3018 ms
$T_{m t p}$	Time of hash mapped to point	48.3228 ms
$\| T \|$	Size of timestamp	4 bytes
$\| I D \|$	Size of ID	8 bytes
$\| A E S \|$	The ciphertext size of AES algorithm	32 bytes
$\| G \|$	Size of elements on elliptic curve $G$	64 bytes
$\| G_{1} \|$	Size of elements on bilinear group $G_{1}$	128 bytes
$\| G_{2} \|$	Size of elements on bilinear group $G_{2}$	128 bytes
$\| Z_{q}^{*} \|$	$Size of elements on Z_{q}^{*}$	32 bytes
$\| H \|$	Output size of hash function	32 bytes