Abstract
Boneh and Franklin proposed a practical Identity-Based Encryption (IBE) in 2001 [1]. In order to embed an identity of users in the IBE, we need a hash function, called HashToPoint. The dominant computation of HashToPoint is the scalar multiplication by a large cofactor $c$, which is relatively expensive compared with other cryptographic functions in the IBE. In this paper, we present a list of cofactor $c$ with Hamming weight two, which can accelerate the computation of HashToPoint. Indeed the timing of our implementation of HashToPoint using the proposed cofactor is reduced by about 30% on a desktop PC.
