d-MUL: Optimizing and Implementing a Multidimensional Scalar Multiplication Algorithm over Elliptic Curves

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.

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Cache timing attacks countermeasures and error detection in Euclidean addition chains based scalar multiplication algorithm for elliptic curves

2017 IEEE 23rd International Symposium on On-Line Testing and Robust System Design (IOLTS) ◽

10.1109/iolts.2017.8046212 ◽

2017 ◽

Author(s):

Fangan-Yssouf Dosso ◽

Pascal Veron

Keyword(s):

Elliptic Curves ◽

Error Detection ◽

Scalar Multiplication ◽

Multiplication Algorithm ◽

Addition Chains ◽

Timing Attacks

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An improved wNAF scalar-multiplication algorithm with low computational complexity by using prime precomputation

IEEE Access ◽

10.1109/access.2021.3061124 ◽

2021 ◽

pp. 1-1

Author(s):

Huang Hai ◽

Na Ning ◽

Xing Lin ◽

Liu Zhiwei ◽

Yu Bin ◽

...

Keyword(s):

Computational Complexity ◽

Scalar Multiplication ◽

Low Computational Complexity ◽

Multiplication Algorithm

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Compression on the Twisted Jacobi Intersection

Fundamenta Informaticae ◽

10.3233/fi-2021-2060 ◽

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.

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