Improved Composite Order Bilinear Pairing on Graphics Hardware

Composite-order bilinear pairing has been applied in many cryptographic constructions, such as identity based encryption, attribute based encryption, and leakage resilient cryptography. However, the computation of such pairing is relatively slow since the composite order should be at least 1024 bits. Thus the elliptic curve group order n and the base field are large. The efficiency of these pairings becomes the bottleneck of the schemes. Existing solutions, such as converting composite-order pairings to prime-order ones or computing many pairings in parallel cannot solve the problem. The former is only valid for certain constructions and the latter is only helpful when many pairings are needed. In this paper, we make use of the huge number of threads available on Graphics Processing Units (GPUs) to speed up composite-order computation, both between pairings and within a single pairing. The experimental result shows that our method can speed up paring computation. Our method can also be ported to other platforms such as cloud systems.