A Survey of Research Progress and Development Tendency of Attribute-Based Encryption

Table 3

Comparison of computational overhead in different CP-ABE schemes.

Scheme	Encryption	Decryption
Cheung and Newport [14]	(𝑛+1)𝐺1+2𝐺2	(𝑛+1)𝐶𝑒+(𝑛+1)𝐺2
Nishide et al.’s [15]	(2𝑁^′+1)𝐺1+2𝐺2	(3𝑛+1)𝐶𝑒+(3𝑛+1)𝐺2
Emura et al.’s [16]	(𝑛+1)𝐺1+2𝐺2	2𝐶𝑒+2𝐺2
Bethencourt et al.’s [8]	(2𝐴𝐶+1)𝐺1+2𝐺2	2𝐴𝑈𝐶𝑒+(2|𝑆|+2)𝐺2
Ibraimi et al.’s [18]	(𝐴𝐶+1)𝐺1+2𝐺2	(𝜔^′+1)𝐶𝑒+(𝜔^′+1)𝐺2
Waters’ [13]	(4𝐴𝐶+1)𝐺1+2𝐺2	2𝐴𝑈𝐶𝑒+3𝐴𝑈𝐺2
Lewko et al.’s [19]	(4𝐴𝐶+1)𝐺1+2𝐺2	2𝐴𝑈𝐶𝑒+3𝐴𝑈𝐺2

𝐴_𝑐: attributes of ciphertext 𝐶; 𝐴_𝑢: attribute of user 𝑢.
|∗|: Number of element in *; 𝐶_𝑒: 𝑒 operation, where 𝑒 denotes bilinear paring.
𝐺_𝑖: Group or operation in group, 𝑖=1 or 2; 𝑔 is a random generator of 𝐺.
𝑆: Least interior nodes satisfying an access structure (include root node).
𝐿^∗: Bit length of element in *; n: number of attributes in systems.
𝑁^′=∑^𝑛_𝑖=1𝑛_𝑖: Total number of possible value of attributes, where 𝑛_𝑖 is the number of possible values for attribute 𝑖.