Fast Scalar Multiplication for Elliptic Curves over Binary Fields by Efficiently Computable Formulas

2017 ◽  
pp. 206-226
Author(s):  
Saud Al Musa ◽  
Guangwu Xu
Keyword(s):  
Elliptic Curves ◽  
Scalar Multiplication ◽  
Binary Fields

Efficient scalar multiplication for elliptic curves over binary fields

2008 ◽  
Vol 13 (6) ◽  
pp. 717-720
Author(s):  
Haihua Gu ◽  
Dawu Gu ◽  
Ya Liu
Keyword(s):  
Elliptic Curves ◽  
Scalar Multiplication ◽  
Binary Fields

scholarly journals Efficient scalar multiplication of ECC using SMBR and fast septuple formula for IoT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Chong Guo ◽  
Bei Gong
Keyword(s):  
Internet Of Things ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Elliptic Curve Cryptography ◽  
Computational Cost ◽  
Scalar Multiplication ◽  
Lightweight Cryptography ◽  
Multiplication Algorithm ◽  
Binary Fields ◽  
Division Polynomial

AbstractIn order to solve the problem between low power of Internet of Things devices and the high cost of cryptography, lightweight cryptography is required. The improvement of the scalar multiplication can effectively reduce the complexity of elliptic curve cryptography (ECC). In this paper, we propose a fast formula for point septupling on elliptic curves over binary fields using division polynomial and multiplexing of intermediate values to accelerate the computation by more than 14%. We also propose a scalar multiplication algorithm based on the step multi-base representation using point halving and the septuple formula we proposed, which significantly reduces the computational cost. The experimental results show that our method is more efficient over binary fields and contributes to reducing the complexity of ECC.

Compression on the Twisted Jacobi Intersection

2021 ◽  
Vol 181 (4) ◽  
pp. 303-312
Author(s):  
Robert Dryło
Keyword(s):  
Elliptic Curves ◽  
Scalar Multiplication ◽  
Not Given ◽  
Montgomery Ladder ◽  
Standard Models

Formulas for doubling, differential addition and point recovery after compression were given for many standard models of elliptic curves, and allow for scalar multiplication after compression using the Montgomery ladder algorithm and point recovery on a curve after this multiplication. In this paper we give such formulas for the twisted Jacobi intersection au2 + v2 = 1, bu2 + w2 = 1. To our knowledge such formulas were not given for this model or for the Jacobi intersection. In projective coordinates these formulas have cost 2M +2S +6D for doubling and 5M + 2S + 6D for differential addition, where M; S; D are multiplication, squaring and multiplication by constants in a field, respectively, choosing suitable curve parameters cost of D may be small.

Scalar Multiplication on Elliptic Curves by Frobenius Expansions

ETRI Journal ◽  
1999 ◽  
Vol 21 (1) ◽  
pp. 28-39 ◽  
Author(s):  
Jung Hee Cheon ◽  
Sangjoon Park ◽  
Choonsik Park ◽  
Sang Geun Hahn
Keyword(s):  
Elliptic Curves ◽  
Scalar Multiplication
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