A collaborative auditing scheme with dynamic data updates based on blockchain

Figures & data

Figure 1. Struct of PIL for handling data dynamics.

Figure 2. The system model.

Figure 3. The workflow of the scheme.

Table 1. Notions.

Notions	Description
U	User
$G_1,G_2,G_T$	Multiplicative cyclic groups
p, g	Generator of a multiplicative group
h, H	Hash function
sk	Private key of user
pk	Public key of user
F	File
n	Number of data blocks
$m_i$	The ith data block of the file
σ	Integrity metadata
S	Challenge set
prove	Integrity proof

Table 2. Notions.

Notions	Description
H	Single hash function operation cost
E	Single exponential operation cost on groups
M	Single multiplication operation cost on groups
A	Single addition operation cost on groups
P	Single bilinear pair operation cost
f	Single pseudorandom function operation cost
n	Number of data blocks
$|b|$	Size of single data block
$|p|$	Size of elements in $Z_p$
$|G|$	Size of elements in G
c	Number of challenges

Table 3. Comparisons of computation costs.

	DO	TPA	Blockchain	CSP
Our	$(H+M+2E)\times n$		$c\times f+(c+1)\times H+2c\times M+c\times E+c\times A+p$	$c\times f+(c+1)\times H+2c\times M+(c+2)\times E+2p$
Li et al. (2022)	$(H+M+2E)\times n$	$2p+2c\times M+(c+1)\times H+(c+2)\times E$		$2c\times f+2c\times M+A+H+(c+2)\times E$
Fan et al. (2020)	$(H+M+2E)\times n$	2p+2E+2M+H+A		$c\times f+(2c+2)\times E+(c+1)\times H+(3c-3)\times A+(c+1)\times M$
Xu et al. (2020)	$(2H+2M+3E)\times n$	$3p+(c+1)\times M+(c-1)\times A+(c+2)\times E+(c+1)\times H$		$(c-1)\times M+cE+cM+(c-1)\times A$

Table 4. Comparisons of communication costs.

	Upload	Auditing
Our	$n|G|+n|b|+|p|$	$3|G|+|p|$
Li et al. (2022)	$n|b|+(n+2)|G|$	$2|G|+4|p|$
Fan et al. (2020)	$n|G|+n|b|$	$3|G|+|p|$
Xu et al. (2020)	$n|b|+(n+1)|G|+2|p|$	$|G|+|p|$

Figure 4. The comparison of tag generation.

Figure 5. The computation costs of proof generation.

Figure 6. The comparison of dynamic structures size.

Figure 7. The comparison of data insertion operations.

Figure 8. The comparison of data deletion operations.

Figure 9. The comparison of data modification operations.

Li, A., Tian, G., Miao, M., & Gong, J. (2022). Blockchain-based cross-user data shared auditing. Connection Science, 34(1), 83–103. https://doi.org/10.1080/09540091.2021.1956879

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