Emerging Security Algorithms and Techniques by Ahmad Khaleel;

Author:Ahmad, Khaleel;
Language: eng
Format: epub
Publisher: CRC Press (CAM)
Published: 2019-01-24T16:00:00+00:00

10.2.4.1 Algorithms of HIBE

Unlike single IBE scheme, HIBE has five algorithms (Chatterjee & Sarkar, 2006b):

Root setup: For the working of the top level of the hierarchy, parameters are created.

Lower-level setup: For the working of each of the other level and for the one-time execution of the lower level, additional parameters are created here.

Extract, encryption, and decryption have the same functionality as they have in single IBE scheme.

10.2.5 Boneh–Boyen HIBE (BB-HIBE)

In this section, we will discuss the single-level Boneh–Boyen IBE (BB-IBE) scheme which is extended to an l-level hierarchical IBE (HIBE) scheme using the technique developed by Boneh, Boyen, and Goh (BBG) with parameters = (G1, G2, ê, n, P, P1, P3, H1, H2, v) and master secret α assuming that |G1| = p (Boneh, Boyen, & Halevi, 2006).

The resulting HIBE scheme security depends on the difficulty of the BDHP (bilinear Diffie–Hellman problem). The attacker who is able to decrypt such a system can also be able to crack down BDHP. If we take BDHP as hard to crack down or solve, the basic BBG scheme is resistant to chosen-ciphertext attacks and adaptive (Chatterjee & Sarkar, 2006c) chosen-identity attacks. On the other hand, the full BBG is resistant to chosen-ciphertext and adaptive chosen-identity attacks.

Thus, we will discuss BBG-HIBE (Basic).

Note:

For limiting the HIBE construction to a single-level, PKG initiates the BB-IBE scheme discussed in Section 10.2.3.

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