An Improved Scalar-Multiplication Algorithm in Galois Field
Ming Liu · Journal of Beijing Institute of Technology · 2002
Studies scalarmultiplication algorithms to speed up the elliptic curve cryptosystem. By analyzing features of scalarmultiplication, it is found that reducing the number of elliptic operations can lead to a marked speeding up scalarmultiplication. For the base point's scalarmultiplication, an important scalarmultiplication, the signedwindow method is improved, and the powertable method is designed, to reduce the number of elliptic operations. On the PC, compared to a system with the 4width signedwindow method, the speed of a 113 bit ECElGamal cryptosystem is improved 1/3. Powertable method improves the base point's scalarmultiplication, by using the principle of signedwindow method. With analysis and experiments, it is proved that pwoertable method can remarkably speed up encoding of ECElGamal cryptosystem.