Abstract
In traditional multiple precision large integer multiplication algorithm, the required number of additions approximates the number of multiplications needed. In some platforms, the great number of add instructions will occupy about half of computing latency in the overall implementation. In this paper, we propose a multiplication algorithm using separated multiply-add-with-carry instruction supported by NVIDIA GPUs. In the algorithm, we reorder the computational sequence, in which nearly all additions and carry flags handling can be combined with the multiplication instructions. The number of add instructions needed decreases from \(O(n^2)\) in prevailing schoolbook algorithm to \(O(n)\). Our resulting 256-bit modular multiplication and modular square over Mersenne prime respectively achieve 3.3837 billion and 5.9928 billion operations per second and reach 96 % of GPU hardware limitation. An elliptic curve point multiplication implementation using our algorithm achieves 43.6 % speedup compared to the existing fastest work.
F. Zheng—This work was partially supported by the National 973 Program of China under award No. 2013CB338001 and the Strategic Priority Research Program of Chinese Academy of Sciences under Grant XDA06010702.
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Zheng, F., Pan, W., Lin, J., Jing, J., Zhao, Y. (2015). Exploiting the Potential of GPUs for Modular Multiplication in ECC. In: Rhee, KH., Yi, J. (eds) Information Security Applications. WISA 2014. Lecture Notes in Computer Science(), vol 8909. Springer, Cham. https://doi.org/10.1007/978-3-319-15087-1_23
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