Efficient Pairings on Various Platforms

Abstract

Pairings have found a range of applications in many areas of cryptography. As such, to utilize the enormous potential of pairing-based protocols one needs to efficiently compute pairings across various computing platforms. In this thesis, we give an introduction to pairing-based cryptography and describe the Tate pairing and its variants. We then describe some recent work to realize efficient computation of pairings. We further extend these optimizations and implement the O-Ate pairing on BN-curves on ARM and x86-64 platforms. Specifically, we extend the idea of lazy reduction to field inversion, optimize curve arithmetic, and construct efficient tower extensions to optimize field arithmetic. We also analyze the use of affine coordinates for pairing computation leading us to the conclusion that they are a competitive choice for fast pairing computation on ARM processors, especially at high security level. Our resulting implementation is more than three times faster than any previously reported implementation on ARM processors.