Implementing the 4-dimensional GLV method on GLS elliptic curves with j-invariant 0
Designs, Codes and Cryptography
Four-Dimensional gallant-lambert-vanstone scalar multiplication
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Lambda coordinates for binary elliptic curves
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
High-Performance scalar multiplication using 8-dimensional GLV/GLS decomposition
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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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 ${\mathbb{F}}_{p^{2}}$. 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.