Endomorphisms for faster elliptic curve cryptography on a large class of curves

  • Galbraith S
  • Lin X
  • Scott M
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Efficiently computable homomorphisms allow elliptic curve point multiplication to be accelerated using the Gallant-Lambert-Vanstone (GLV) method. Iijima, Matsuo, Chao and Tsujii gave such homomorphisms for a large class of elliptic curves by working over Fp2 .We extend their results and demonstrate that they can be applied to the GLV method. In general we expect our method to require about 0.75 the time of previous best methods (except for subfield curves, for which Frobenius expansions can be used). We give detailed implementation results which show that the method runs in between 0.70 and 0.83 the time of the previous best methods for elliptic curve point multiplication on general curves. International Association for Cryptologic Research 2009.

Author-supplied keywords

  • Elliptic curves
  • GLV method
  • Isogenies
  • Multiexponentiation
  • Point multiplication

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  • Steven D. Galbraith

  • Xibin Lin

  • Michael Scott

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