Research Article
GLV/GLS Scalar Multiplication on Twisted Edwards Curves
@INPROCEEDINGS{10.1007/978-3-030-96791-8_24, author={Chuangui Ma and Ruijie Zhang and Lei Niu and Fushan Wei}, title={GLV/GLS Scalar Multiplication on Twisted Edwards Curves}, proceedings={Security and Privacy in New Computing Environments. 4th EAI International Conference, SPNCE 2021, Virtual Event, December 10-11, 2021, Proceedings}, proceedings_a={SPNCE}, year={2022}, month={3}, keywords={Elliptic curve Twisted edwards curve Scalar multiplication GLV method Computable endomorphism}, doi={10.1007/978-3-030-96791-8_24} }- Chuangui Ma
Ruijie Zhang
Lei Niu
Fushan Wei
Year: 2022
GLV/GLS Scalar Multiplication on Twisted Edwards Curves
SPNCE
Springer
DOI: 10.1007/978-3-030-96791-8_24
Abstract
At present, GLV/GLS scalar multiplication mainly focuses on finding and constructing more and more efficient computable endomorphisms. We research on the applications of GLV/GLS algorithms on twisted Edwards curves. Firstly, we present the concrete construction of efficiently computable endomorphism for this type of curves over prime field by exploiting birational equivalence between curves, and obtain 2-dimensional GLV method. Using birational equivalence and Frobenius mapping between curves, we present methods to construct efficiently computable endomorphisms of this type of curves and obtain 2-dimensional GLS method. Finally, we obtain the 4-dimensional GLV algorithm by using higher degree twists. The experimental conclusion demanstrates that the speedups of 2-dimensional and 4-dimensional GLV methods than 5-NAF method exceed 37.4% and 104.9% for twisted Edwards curves respectively.
