Four-dimensional gallant-lambert-vanstone scalar multiplication
The GLV method of Gallant, Lambert and Vanstone (CRYPTO 2001) computes any multiple
kP of a point P of prime order n lying on an elliptic curve with a low-degree endomorphism Φ …
kP of a point P of prime order n lying on an elliptic curve with a low-degree endomorphism Φ …
Four-dimensional gallant–lambert–vanstone scalar multiplication
The GLV method of Gallant, Lambert, and Vanstone (CRYPTO 2001) computes any multiple
kP of a point P of prime order n lying on an elliptic curve with a low-degree endomorphism Φ …
kP of a point P of prime order n lying on an elliptic curve with a low-degree endomorphism Φ …
Implementing the 4-dimensional GLV method on GLS elliptic curves with j-invariant 0
Z Hu, P Longa, M Xu - Designs, Codes and Cryptography, 2012 - Springer
Abstract The Gallant–Lambert–Vanstone (GLV) method is a very efficient technique for
accelerating point multiplication on elliptic curves with efficiently computable …
accelerating point multiplication on elliptic curves with efficiently computable …
[PDF][PDF] Integer matrix size 2× 2 sub-decomposition method for elliptic curve cryptography
RKK Ajeena - Computer Science, 2023 - ijmcs.future-in-tech.net
This work proposes a new version of integer sub-decomposition of a scalar k in an elliptic
curve scalar multiplication kP which is a core operation for elliptic curve cryptography (ECC) …
curve scalar multiplication kP which is a core operation for elliptic curve cryptography (ECC) …
Montgomery algorithm over a prime field
W Yu, K Wang, B Li, S Tian - Chinese Journal of Electronics, 2019 - Wiley Online Library
New formulae for point addition and point doubling on elliptic curves over prime fields are
presented. Based on these formulae, an improved Montgomery algorithm is proposed. The …
presented. Based on these formulae, an improved Montgomery algorithm is proposed. The …
The -curve Construction for Endomorphism-Accelerated Elliptic Curves
B Smith - Journal of cryptology, 2016 - Springer
We give a detailed account of the use of Q Q-curve reductions to construct elliptic curves
over F _ p^ 2 F p 2 with efficiently computable endomorphisms, which can be used to …
over F _ p^ 2 F p 2 with efficiently computable endomorphisms, which can be used to …
Families of fast elliptic curves from ℚ-curves
B Smith - International Conference on the Theory and …, 2013 - Springer
We construct new families of elliptic curves over F_p^2 with efficiently computable
endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the …
endomorphisms, which can be used to accelerate elliptic curve-based cryptosystems in the …
Constructing multidimensional differential addition chains and their applications
A Hutchinson, K Karabina - Journal of Cryptographic Engineering, 2019 - Springer
We propose new algorithms for constructing multidimensional differential addition chains
and for performing multidimensional scalar point multiplication based on these chains. Our …
and for performing multidimensional scalar point multiplication based on these chains. Our …
A special scalar multiplication algorithm on Jacobi quartic curves
J Weng, A Chen, T Huang, W Ji - Applicable Algebra in Engineering …, 2023 - Springer
At present, GLV/GLS scalar multiplication mainly focuses on elliptic curves in Weierstrass
form, attempting to find and construct more and more efficiently computable endomorphism …
form, attempting to find and construct more and more efficiently computable endomorphism …
[PDF][PDF] Jacobi Quartic 曲线上GLV/GLS 标量乘算法
翁江， 姬伟峰， 吴玄， 李映岐， 张林锋， 孟浩 - 电子学报, 2021 - ejournal.org.cn
目前GLV/GLS (Gallant, Lambert, Vanstone/Galbraith, Lin, Scott) 标量乘算法的研究主要集中
在Weierstrass 曲线上, 尝试寻找和构造更多或者更高次数的可有效计算的自同态 …
在Weierstrass 曲线上, 尝试寻找和构造更多或者更高次数的可有效计算的自同态 …