FPGA accelerated tate pairing based cryptosystems over binary fields

Abstract

Tate pairing based cryptosystems have recently emerged as an alternative to traditional public key cryptosystems because of their ability to be used in multi-party identity-based key management schemes. Due to the inherent parallelism of the existing pairing algorithms, high performance can be achieved via hardware realizations. Three schemes for Tate pairing computations have been proposed in the literature: cubic elliptic, binary elliptic, and binary hyperelliptic. For our implementation we have chosen the binary elliptic case because of the simple underlying algorithms and efficient binary arithmetic. In this paper, we propose a new FPGA-based architecture of the Tate pairing-based computation over the binary fields F₂₂₃₉ and F ₂₂₈₃. Even though our field sizes are larger than in the architectures based on cubic elliptic curves or binary hyperelliptic curves with the same security strength, nevertheless fewer multiplications in the underlying field need to performed. As a result, the computational latency for a pairing computation has been reduced, and our implementation runs 10-to-20 times faster than the equivalent implementations of other pairing-based schemes at the same level of security strength. At the same time, an improvement in the product of latency by area by a factor between 12 and 46 for an equivalent type of implementation has been achieved