Blockchain-based cross-user data shared auditing

Figures & data

Figure 1. The system model of blockchain-based cross-user shared auditing.

Figure 2. The workflow of BCSAD.

Figure 3. The workflow of BCSAI.

Table 1. Comparisons of functionality.

Schemes	Batch	No fully trusted TPA	Privacy	Shared	Cross-user	Deduplication
Wang et al.	√	×	√	×	×	×
Xu et al.	√	√	×	√	×	√
Yuan et al.	√	√	√	×	×	√
BCSAD	√	√	√	√	√	×
BCSAI	√	√	√	√	√	√

Table 2. Notions.

Notions	Description
n	Number of blocks in file F
y	Number of challenged blocks in auditing
$d_1$	Number of outsourced files
$d_2$	Number of files with same short hash value
$|F|$	Length of the outsourced file F
$|\mathbb{Z}|$	Length of the element in ${\mathbb{Z}}_p$
$|\mathbb{G}|$	Length of the element in $\mathbb{G}$
H	Evaluation of hash function
Exp	Evaluation of exponentiation operation
Pair	Evaluation of bilinear pairing operation
E/D	Evaluation of symmetric encryption/decryption operation
Enc/Dec	Evaluation of additively homomorphic encryption/decryption operation

Table 3. Comparisons of computation costs.

Schemes	Key exchange	Upload	Prove	Verify	Retrieval
Wang et al.	–	$n{d}_1(1\mathsf{\text{H}}+2\mathsf{\text{Exp}})$	$d_1((y+1)\mathsf{\text{Exp}}+1\mathsf{\text{Pair}}+1\mathsf{\text{H}})$	$d_1((y+3)\mathsf{\text{Exp}}+y\mathsf{\text{H}})+(d_1+1)\mathsf{\text{Pair}}$	–
Xu et al.	–	$n{d}_1(1\mathsf{\text{H}}+2\mathsf{\text{Exp}})$	$y{d}_1\mathsf{\text{Exp}}$	$d_1((y+1)\mathsf{\text{Exp}}+y\mathsf{\text{H}})+(d_1+1)\mathsf{\text{Pair}}$	–
Yuan et al.	–	$n{d}_1(3\mathsf{\text{H}}+2\mathsf{\text{Exp}}+1\mathsf{\text{E}})$	$d_1(y\mathsf{\text{Exp}}+1\mathsf{\text{Pair}}+1\mathsf{\text{H}})$	$d_1((y+3)\mathsf{\text{Exp}}+y\mathsf{\text{H}}+(d_1+1)\mathsf{\text{Pair}}$	$n{d}_1(1\mathsf{\text{D}}+1\mathsf{\text{H}})$
BCSAD	$d_1^2\mathsf{\text{Exp}}$	$n{d}_1(1\mathsf{\text{H}}+2\mathsf{\text{Exp}})$	$(y+1)\mathsf{\text{Exp}}+1\mathsf{\text{H}}$	$(y+1))\mathsf{\text{Exp}}+y\mathsf{\text{H}}+2\mathsf{\text{Pair}}$	–
BCSAI	$2(d_2+1)\mathsf{\text{H}}+8d_2\mathsf{\text{Exp}}+(d_2+1)\mathsf{\text{Enc}}+\mathsf{\text{Dec}}$	$n{d}_1(1\mathsf{\text{H}}+2\mathsf{\text{Exp}}+1\mathsf{\text{E}})$	$(y+1)\mathsf{\text{Exp}}+1\mathsf{\text{H}}$	$(y+1))\mathsf{\text{Exp}}+y\mathsf{\text{H}}+2\mathsf{\text{Pair}}$	$n{d}_1\mathsf{\text{D}}$

Table 4. Comparisons of communication and storage costs.

	Communication costs				Storage costs
Schemes	Key exchange	Upload	Auditing	Retrieval	CS	U
Wang et al.	–	$d_1(n|\mathbb{G}|+1|F|)$	$d_1((2y+1)|\mathbb{Z}|+2|\mathbb{G}|)$	$d_1|F|$	$d_1(n|\mathbb{G}|+1|F|)$	$2|\mathbb{Z}|$
Xu et al.	–	$d_1(n|\mathbb{G}|+1|F|)$	$d_1(4|\mathbb{Z}|+(y+1)|\mathbb{G}|)$	$d_1|F|$	$(n|\mathbb{G}|+1|F|)$	$2|\mathbb{Z}|$
Yuan et al.	–	$d_1(n|\mathbb{G}|+1|F|)$	$d_1((3y+1)|\mathbb{Z}|+2|\mathbb{G}|)$	$d_1|F|$	$(n|\mathbb{G}|+1|F|)$	$(n+2)|\mathbb{Z}|$
BCSAD	$d_1(d_1-1)|\mathbb{G}|$	$d_1(n|\mathbb{G}|+1|F|)$	$4|\mathbb{Z}|+2|\mathbb{G}|$	$d_1|F|$	$d_1(n|\mathbb{G}|+1|F|)$	$2|\mathbb{Z}|$
BCSAI	$(4d_2+1)|\mathbb{Z}|+4d_2|\mathbb{G}|$	$d_1(n|\mathbb{G}|+1|F|)$	$4|\mathbb{Z}|+2|\mathbb{G}|$	$d_1|F|$	$(n|\mathbb{G}|+1|F|)$	$2|\mathbb{Z}|$

Figure 4. Computation costs of key exchange.

Figure 5. Computation costs of data upload.

Figure 6. Number of challenged blocks at different block corruption rate.

Figure 7. Computation costs of data auditing (5 checked files). (a) Proof generation and (b) proof verification.

Figure 8. Computation costs of data auditing (460 challenged blocks). (a) Proof generation and (b) proof verification.

Figure 9. Computation costs of data retrieval.