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Speeding Up the Fixed-Base Comb Method for Faster Scalar Multiplication on Koblitz Curves [chapter]

Christian Hanser, Christian Wagner
2013 Lecture Notes in Computer Science  
One of the fastest methods for fixed-base scalar multiplications is the so-called fixed-base comb scalar multiplication method, which is due to Lim and Lee.  ...  For single scalar multiplications, we are able to achieve performance improvements over the WTNAF method of up to 25% and of up to 42% over the conventional comb methods.  ...  The authors of [15] proposed a new, fast fixed-base comb method, which combines the Lim-Lee and the Tsaur-Chou method [19] .  ... 
doi:10.1007/978-3-642-40588-4_12 fatcat:nkqi5olrrfddnh6p5maf4evyte

An Improved Algorithm of Elliptic Curve Cryptograph

Kai Zhang, Tao Yan
2013 International Journal of Security and Its Applications  
The limitation of the traditional fixed point comb method is analyzed, and on the basis of the study improvement strategy of fixed-base comb algorithm of this proposed, thus the speed of the whole system  ...  The fast implementation of elliptic curve cryptosystem key algorithms, namely, Scalar Multiplication, is studied in this paper.  ...  Currently, for scalar multiplication operation based on fix base point, the best methods are fix base window method and fix base comb method. The latter one is proposed by Lim and Lee.  ... 
doi:10.14257/ijsia.2013.7.5.22 fatcat:q6hhddzambe45fgfrgrtfycnui

Short Memory Scalar Multiplication on Koblitz Curves [chapter]

Katsuyuki Okeya, Tsuyoshi Takagi, Camille Vuillaume
2005 Lecture Notes in Computer Science  
We present a new method for computing the scalar multiplication on Koblitz curves. Our method is as fast as the fastest known technique but requires much less memory.  ...  Thus, with much smaller memory usage, the proposed method yields the same efficiency as the fastest scalar multiplication schemes on Koblitz curves.  ...  Techniques based on normal basis representations have been proposed to speed-up the scalar multiplication on Koblitz curves, with known point and large memory [4] .  ... 
doi:10.1007/11545262_7 fatcat:d3hmuhhgnjgptdiorrd5phpuwq

Software Implementation of Binary Elliptic Curves: Impact of the Carry-Less Multiplier on Scalar Multiplication [chapter]

Jonathan Taverne, Armando Faz-Hernández, Diego F. Aranha, Francisco Rodríguez-Henríquez, Darrel Hankerson, Julio López
2011 Lecture Notes in Computer Science  
levels, and a new speed record for side-channel resistant scalar multiplication in a random curve at the 128-bit security level.  ...  The contributions are illustrated with experimental results improving the state-of-the-art performance of halving and doubling-based scalar multiplication on NIST curves at the 112-and 192-bit security  ...  Acknowledgments We wish to thank the University of Waterloo and especially, Professor Alfred Menezes for useful discussions related to this work during a visit by three of the authors, where the idea of  ... 
doi:10.1007/978-3-642-23951-9_8 fatcat:fgygdub5t5gkfjqqacobpq7xuu

A Review of Techniques for Implementing Elliptic Curve Point Multiplication on Hardware

Arielle Verri Lucca, Guilherme Augusto Mariano Sborz, Valderi Reis Quietinho Leithardt, Marko Beko, Cesar Albenes Zeferino, Wemerson Delcio Parreira
2020 Journal of Sensor and Actuator Networks  
Elliptic Curve Point Multiplication (ECPM) is the main function in ECC, and is the component with the highest hardware cost.  ...  The obtained results show which methods and technologies have been used to implement ECPM on hardware and present some findings of the choices available to the hardware designers.  ...  , and the fixed-base comb for ECPM.  ... 
doi:10.3390/jsan10010003 fatcat:bjzznwtk7zhhvnxcc5yyf27mxq

Software Implementation of Elliptic Curve Cryptography over Binary Fields [chapter]

Darrel Hankerson, Julio López Hernandez, Alfred Menezes
2000 Lecture Notes in Computer Science  
This paper presents an extensive and careful study of the software implementation on workstations of the NIST-recommended elliptic curves over binary fields.  ...  We also present the results of our implementation in C on a Pentium II 400 MHz workstation.  ...  Acknowledgements The authors would like to thank Mike Brown, Donny Cheung, Eric Fung, and Mike Kirkup for numerous fruitful discussions and for help with the implementation and timings.  ... 
doi:10.1007/3-540-44499-8_1 fatcat:6vlenmp6dzexzpvrhrzp7skvmi

Ultra Low-Power implementation of ECC on the ARM Cortex-M0+

Ruan de Clercq, Leif Uhsadel, Anthony Van Herrewege, Ingrid Verbauwhede
2014 Proceedings of the The 51st Annual Design Automation Conference on Design Automation Conference - DAC '14  
To aid in the elliptic curve parameter selection, the energy consumption of different instructions on the ARM Cortex-M0+ was measured and it was found that there is a variation of up to 22.5% between different  ...  A software implementation that uses the proposed algorithm was made in C and assembly, and on average our implementation of a random point multiplication requires 34.16 µJ, whereas our fixed point multiplication  ...  For the fixed point multiplication, the point can be seen as a constant, and therefore some precomputations can be done on this point in order to speed up the multiplication. IV.  ... 
doi:10.1145/2593069.2593238 dblp:conf/dac/ClercqUHV14 fatcat:ndeym5xkv5cl7gjuyaznoql4ti

Software Implementation of Curve based Cryptography for Constrained Devices

Kakali Chatterjee, Asok De, Daya Gupta
2011 International Journal of Computer Applications  
So ECC and HECC are more suitable in constrained environment such as smart cards if we can select suitable curves and efficient scalar multiplication technique to speed up arithmetic on the curve.  ...  Curve based cryptography are preferred for embedded hardware since they require shorter operand size than RSA to attain the same security level.  ...  Different efficient scalar multiplication methods in elliptic curves like Windows-NAF, Fixed-Base comb, Montgomery point multiplication etc are available.  ... 
doi:10.5120/2942-3914 fatcat:6cuca7q2ivdhrnkzclwjfly54y

Efficient and Secure ECDSA Algorithm and its Applications: A Survey [article]

Mishall Al-Zubaidie, Zhongwei Zhang, Ji Zhang
2019 arXiv   pre-print
Public-key cryptography algorithms, especially elliptic curve cryptography (ECC) and elliptic curve digital signature algorithm (ECDSA) have been attracting attention from many researchers in different  ...  of the constrained source and large systems.  ...  Acknowledgements We would like to acknowledge and thank the efforts of Dr. Barbara Harmes, and Hawa Bahedh as well as the valuable feedback of the reviewers.  ... 
arXiv:1902.10313v1 fatcat:7k44pfghujbzdmoxpkynavzone

Secure Binary Field Multiplication [chapter]

Hwajeong Seo, Chien-Ning Chen, Zhe Liu, Yasuyuki Nogami, Taehwan Park, Jongseok Choi, Howon Kim
2016 Lecture Notes in Computer Science  
Both bit-wise scanning and Look-Up Table ( LUT) based methods are commonly used for binary field multiplication.  ...  In this paper, we conduct the SCA on the LUT based binary field multiplication. The attack exploits the horizontal Correlation Power Analysis (CPA) on weights of LUT.  ...  Our future works are attacking the other algorithms based on LUT such as window methods for exponentiation and scalar multiplication.  ... 
doi:10.1007/978-3-319-31875-2_14 fatcat:tqps3u4bqzd57d3cjgag6ic7ay

Random Euclidean Addition Chain Generation and Its Application to Point Multiplication [chapter]

Fabien Herbaut, Pierre-Yvan Liardet, Nicolas Méloni, Yannick Téglia, Pascal Véron
2010 Lecture Notes in Computer Science  
We also propose a new scheme in the context of fixed base point scalar multiplication.  ...  Many schemes have been proposed in order to speed up or secure its computation, usually thanks to efficient scalar representation [30, 10, 24] , faster point operation formulae [8, 25, 13] or new curve  ...  In the context of a fixed base point we propose a new scalar multiplication scheme based on our chains generation method.  ... 
doi:10.1007/978-3-642-17401-8_18 fatcat:6bj6dwcl5zhnpmgq3eb7lf47u4

Energy-Efficient Implementation of ECDH Key Exchange for Wireless Sensor Networks [chapter]

Christian Lederer, Roland Mader, Manuel Koschuch, Johann Großschädl, Alexander Szekely, Stefan Tillich
2009 Lecture Notes in Computer Science  
A scalar multiplication using a random base point takes about 12.33 · 10 6 cycles.  ...  Our implementation uses a 192-bit prime field specified by the NIST as underlying algebraic structure and requires only 5.20 · 10 6 clock cycles to compute a scalar multiplication if the base point is  ...  The information in this document reflects only the authors' views, is provided as is, and no guarantee or warranty is given that the information is fit for any particular purpose.  ... 
doi:10.1007/978-3-642-03944-7_9 fatcat:a7fs5vel7zhafejmd57b4hn274

Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication

Hwajeong Seo, Hyunjin Kim, Taehwan Park, Yeoncheol Lee, Zhe Liu, Howon Kim
2013 Sensors  
To this end, we must focus on scalar multiplication, which is the most expensive operation in ECC.  ...  This method can be applied to ordinary group scalar multiplication, but it requires large pre-computation table, so we combined the previous method with ours for practical purposes.  ...  Conflict of Interest The authors declare no conflict of interest. Sensors 2013, 13  ... 
doi:10.3390/s130709483 pmid:23881143 pmcid:PMC3758659 fatcat:yqxigg7xh5fvforavbctls5ldq

Lightweight Coprocessor for Koblitz Curves: 283-Bit ECC Including Scalar Conversion with only 4300 Gates [chapter]

Sujoy Sinha Roy, Kimmo Järvinen, Ingrid Verbauwhede
2015 Lecture Notes in Computer Science  
Koblitz curves offer fast point multiplications if the scalars are given as specific τ -adic expansions, which results in a need for conversions between integers and τ -adic expansions.  ...  We propose the first lightweight variant of the conversion algorithm and, by using it, introduce the first lightweight implementation of Koblitz curves that includes the scalar conversion.  ...  One field addition requires 60 cycles. -Field multiplication uses word-serial comb method [13] .  ... 
doi:10.1007/978-3-662-48324-4_6 fatcat:5qkqsrpepva3hogrfqitma7wma

Four $$\mathbb {Q}$$ NEON: Faster Elliptic Curve Scalar Multiplications on ARM Processors [chapter]

Patrick Longa
2017 Lecture Notes in Computer Science  
For example, one single variable-base scalar multiplication is computed in about 235,000 Cortex-A8 cycles or 132,000 Cortex-A15 cycles which, compared to the fastest genus 2 Kummer and Curve25519 implementations  ...  We present a high-speed, high-security implementation of the recently proposed elliptic curve FourQ (ASIACRYPT 2015) for 32-bit ARM processors with NEON support.  ...  We thank Craig Costello for his valuable comments. References  ... 
doi:10.1007/978-3-319-69453-5_27 fatcat:vmwyodf6bfddbekh7n3fhnjc3m
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