An Efficient Variant of Boneh-Gentry-Hamburg’s Identity-Based Encryption Without Pairing

Abstract

Boneh, Gentry and Hamburg presented an encryption system known as BasicIBE without incorporating pairings. This system has short ciphertext size but this comes at the cost of less time-efficient encryption/decryption algorithms in which their processing time increases drastically with the message length. Moreover, the private key size is $l$ elements in $\mathbb {Z}_{N}$, where $N$ is a Blum integer and $l$ is the message length. In this paper, we optimize this system in two steps. First, we decrease the private key length from $l$ elements in $\mathbb {Z}_{N}$ to only one element. Second, we present two efficient variants of the BasicIBE in terms of ciphertext length and encryption/decryption speed. The ciphertext is as short as the BasicIBE, but with more time-efficient algorithms which do not depend on the message length. The proposed system is very time efficient compared to other IBE systems and it is as secure as the BasicIBE system.