GPU-based Implementation of 128-bit Secure Eta Pairing Over a Binary Field

Utsab Bose, Anup Kumar Bhattacharya, Abhijit Das
Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, West Bengal, India
6th International Conference on Cryptology in Africa (Africacrypt 2013), 2013


   title={GPU-based Implementation of 128-bit Secure Eta Pairing Over a Binary Field},

   author={Bose, Utsab and Bhattacharya, Anup Kumar and Das, Abhijit},



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Eta pairing on a supersingular elliptic curve over the binary field F_2_1223 used to offer 128-bit security, and has been studied extensively for efficient implementations. In this paper, we report our GPU-based implementations of this algorithm on an NVIDIA Tesla C2050 platform. We propose efficient parallel implementation strategies for multiplication, square, square root and inverse in the underlying field. Our implementations achieve the best performance when Lopez-Dahab multiplication with four-bit precomputations is used in conjunction with one-level Karatsuba multiplication. We have been able to compute up to 566 eta pairings per second. To the best of our knowledge, ours is the fastest GPU-based implementation of eta pairing. It is about twice as fast as the only reported GPU implementation, and about five times as fast as the fastest reported single-core SIMD implementation. We estimate that the NVIDIA GTX 480 platform is capable of producing the fastest known software implementation of eta pairing.
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