A privacy-preserving and efficient data sharing scheme with trust authentication based on blockchain for mHealth

Figures & data

Figure 1. Data-sharing mHealth system with conventional CP-ABE.

Figure 2. Blockchain structure.

Figure 3. System model.

Table 1. Function comparison.

		On/offline	On/offline	Access	Outsourced
Scheme	Large universe	KeyGen	encryption	authen	decryption	Blockchain	Group order
Lai et al. (2012)	✗	✗	✗	✓	✗	✗	Composite
L. Liu et al. (2016)	✗	✗	✗	✗	✗	✗	Composite
Y. Zhang (2018)	✓	✗	✗	✓	✗	✗	Composite
Cui et al. (2016)	✓	✗	✗	✗	✗	✗	Prime
G. Hu et al. (2020)	✓	✗	✗	✓	✓	✗	Prime
Z. Zhang et al. (2021)	✓	✗	✗	✓	✗	✗	Prime
Y. Zhang et al. (2018)	✗	✓	✓	✗	✗	✗	Composite
Ours	✓	✓	✓	✓	✓	✓	Prime

Table 2. Notations and Meaning.

Notations	Meaning
$T_P$	Time for pairing operation
${G^{\xi },G_T^{\xi }}_{\xi =1,2,\dots }$	A multiplication cyclic group of composite order with ξ subgroups
${T_e^{\xi },T_E^{\xi }}_{\xi =1,2\dots }$	Time cost of exponentiation operation in $G^{\xi }$ and $G_T^{\xi }$
$\left|Z_p^{\ast }\right|,\left|G^{\xi }\right|,\left|G_T^{\xi }\right|$	Bit length of element in $Z_p^{\ast }/G^{\xi }/G_T^{\xi }|$
n	The scale of attributes in the system
l	The scale of rows in an access matrix
ϖ	The scale of attributes in user attribute list

Table 3. A comparative result in computing overhead.

	KeyGen	Encryption	Decryption	Authentication
Scheme	offline/online	offline/online	cloud/user	blockchain/user
Y. Zhang (2018)	✗	✗	✗	✗
	/$(\varpi +4)T_e^4$	/$(6l+3)T_e^4+{2T}_E^4$	/$(2\varpi +1)T_P+\varpi T_E^4$	✗
Cui et al. (2016)	✗	✗	✗	✗
	/$(9\varpi +7)T_e^1$	/$(8l+3)T_e^1+T_E^1$	/$(6\varpi +1)T_P+\varpi T_E^1$	/$2T_P+2\varpi T_E^4$
G. Hu et al. (2020)	✗	✗	$(4\varpi +1)T_P+\varpi T_E^1$	✗
	/$(6\varpi +5)T_e^1$	/$(8l+3)T_e^1+{2T}_E^1$	/$T_P+T_E^1$	/$\varpi T_P+\varpi T_E^1$
Ours	$(6\varpi +5)T_e^1$	$(6l+3)T_e^1+{2T}_E^1$	$(4\varpi +1)T_P+\varpi T_E^1+4\varpi T_e^1$	$\varpi T_P+\varpi T_E^1$
	/$\varpi T_e^1$	/$(l+2)T_e^1$	/$T_E^1$	/✗

Table 4. Running time for each operation (MS).

Operations	Smartphone	PC
Exponentiation on Group G	12.3	5.68
Exponentiation on Group $G_T$	3.56	0.47
Bilinear pairing	23.2	4.06

Figure 4. The average time cost of: (a) Computation overhead in Online keyGen; (b) Computation overhead in Online encryption; (c) Computation overhead in authentication and (d) Computation overhead in user decryption.

Figure 5. The response time of transaction.

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