TY - JOUR
ID - 3090
TI - Efficient elliptic curve cryptosystems
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Saleh, Mohammad
AU - Darweesh, Kamal
AD - Mathematics Department, Birzeit University, P.O. Box 14, Palestine
AD - Applied Mathematics Department, Palestine Technical University--Kadoorie, Tulkarm, Palestine
Y1 - 2018
PY - 2018
VL - 9
IS - 1
SP - 161
EP - 174
KW - cryptography
KW - elliptic curves
KW - affine coordinates
DO - 10.22075/ijnaa.2018.11642.1581
N2 - Elliptic curve cryptosystems (ECC) are new generations of public key cryptosystems that have a smaller key size for the same level of security. The exponentiation on elliptic curve is the most important operation in ECC, so when the ECC is put into practice, the major problem is how to enhance the speed of the exponentiation. It is thus of great interest to develop algorithms for exponentiation, which allow efficient implementations of ECC. In this paper, we improve efficient algorithm for exponentiation on elliptic curves defined over Fp in terms of affine coordinates. The algorithm computes directly from random points P and Q on an elliptic curve, without computing the intermediate points. Moreover, we apply the algorithm to exponentiation on elliptic curves with width-w Mutual Opposite Form (wMOF) and analyze their computational complexity. This algorithm can speed up the wMOF exponentiation of elliptic curves of size 160-bit about (21.7 %) as a result of its implementation with respect to affine coordinates.
UR - https://ijnaa.semnan.ac.ir/article_3090.html
L1 - https://ijnaa.semnan.ac.ir/article_3090_0f826058d0ae814be01864ee304396ac.pdf
ER -