Experimental performance comparisons between (H)IBE schemes over composite-order and prime-order bilinear groups

The Boneh-Boyen Identity-Based Encryption (IBE) and the Boneh-Boyen-Goh Hierarchical Identity-Based Encryption (HIBE) are elegant schemes built over prime-order bilinear groups. These two schemes are only proven secure under selective security model. For purpose of fully and efficient (H)IBE schemes, Lewko and Waters provided a practical technique, called Dual System, to transform these two schemes proven to be fully secure. Their key technique is to implement these schemes in composite-order bilinear groups equipped with orthogonality. Performance comparisons between these schemes is valuable to guide engineering implementations in practice. In this paper, we provide benchmarks on basic operations in composite-order and prime-order bilinear groups, both at a 256-bit security level. Then, we present software implementations and efficiency comparisons for Boneh-Boyen IBE, Boneh-Boyen-Goh HIBE schemes and their fully-secure variations by Lewko and Waters. The experimental results show much better efficiency of prime-order bilinear groups and advocate the use of prime-order groups when efficiency is strongly required.