Identity-Based Encryption Protocols Using Bilinear Pairing

Table 10.3: Comparison of HIBE protocols Secure in Generalised Selective-ID Model.
protocol id public max pvt decryption
comp. parameter key size subkey size
H 1 Z p n + h + 3 h + 1 h + 1
H 2 Z p 3 + (n + 1)h h + 1 h + 1
ccHIBE Z ∗ p 4 + nh 2 + n(h − 1) 2
G 2 Z p 3 + (n + 1)h h + 1 + n(h − 1) 2
protocol ciphertext encryption decryption security
expansion efficiency efficiency model
H 1 h + 1 h(n + 1) + 1 h + 1 M 1
H 2 h + 1 h(n + 1) + 1 h + 1 M 2
ccHIBE 2 nh + 2 2 M 2
G 2 2 nh + 2 2 M + 2
For a HIBE of maximum height h, the columns for public parameter, max pvt key size, decryption
subkey size and ciphertext expansion denote the number of elements of G 1 , encryption
efficiency denotes the number of scalar multiplications in G 1 and decryption efficiency
denotes the number of pairing computations.
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