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Efficient FPGA Implementations of Point Multiplication on Binary Edwards and Generalized Hessian Curves Using Gaussian Normal Basis

R. Azarderakhsh, A. Reyhani-Masoleh
2012 IEEE Transactions on Very Large Scale Integration (vlsi) Systems  
To the best of the authors' knowledge, this is the first FPGA implementation of point multiplication on binary Edwards and generalized Hessian curves represented by -coordinates.  ...  This paper presents the implementation results of an elliptic curve crypto-processor over binary fields (2 ) on binary Edwards and generalized Hessian curves using Gaussian normal basis (GNB).  ...  The authors would also like to thank Canadian Microelectronics Corporation (CMC) Microsystems for providing the required infrastructure and CAD tools that have been used in this work.  ... 
doi:10.1109/tvlsi.2011.2158595 fatcat:aixceifoazexxhrxagsla2vrjy

A Survey on Hardware Implementations of Elliptic Curve Cryptosystems [article]

Bahram Rashidi
2017 arXiv   pre-print
We first discuss different elliptic curves, point multiplication algorithms and underling finite field operations over binary fields F2m and prime fields Fp which are used in the literature for hardware  ...  High-speed implementation is an important factor in the ECC applications such as network servers.  ...  A high-speed hardware structures of the point multiplication based on Montgomery ladder algorithm for binary Edwards and generalized Hessian curves in GNB are presented in [114] .  ... 
arXiv:1710.08336v1 fatcat:g3gpz5lzgvc27fboa5tv4kdhze

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.  ...  Generic • • • • • • Binary Huff • Koblitz • • • Random • Generalized HessianBinary Edwards • Does not specify • • • The curves chosen by the authors vary due to the purpose of each implementation.  ... 
doi:10.3390/jsan10010003 fatcat:bjzznwtk7zhhvnxcc5yyf27mxq

A Survey Report On Elliptic Curve Cryptography

Samta Gajbhiye, Monisha Sharma, Samir Dashputre
2011 International Journal of Electrical and Computer Engineering (IJECE)  
Performance of ECC and HEC is also discussed based on scalar multiplication and DLP.  ...  The paper presents an extensive and careful study of elliptic curve cryptography (ECC) and its applications.  ...  The curve and its twists have the same j-invariant and is shown in [17] . Twisted Hessian curve [18] represents a generalization of Hessian curve.  ... 
doi:10.11591/ijece.v1i2.86 fatcat:etikame46ve2nkrio52rprs7ky

A Hybrid Cryptosystem to Enhance Security in IoT Health Care System

Kavitha. S, Department of Computer Applications, National Institute of Technology, Tiruchirapalli, TamilNadu, India, P.J. A.Alphonse
2019 International Journal of Wireless and Microwave Technologies  
Single cryptographic algorithm based solution suffered to provide efficient security as its high probability of attacks.  ...  Internet of Things (IoT) based health care system provides an essential interface between tiny devices and customers, who require customary checking by remedial focus.  ...  The analysis of different arithmetic formulas applied in binary representation of generalized hessian curve.  ... 
doi:10.5815/ijwmt.2019.01.01 fatcat:gxq3ttkuu5chtgqtupxc5tl3ay

An Optimized Architecture for Binary Huff Curves with Improved Security

Muhammad Rashid, Malik Imran, Muhammad Kashif, Asher Sajid
2021 IEEE Access  
ACKNOWLEDGEMENT We are thankful to the support of King Abdul-Aziz City for Science and Technology (KACST) and Science and Technology Unit (STU), MAKKAH, Saudi Arabia.  ...  The commonly used implementation models of ECC are Weierstrass [5] , Hessian [8] , Edward [9] and Huff [10] .  ...  The hardware implementation is carried out either using the prime GF (p) or binary GF (2 m ) field, with general affine or projective coordinate systems.  ... 
doi:10.1109/access.2021.3090216 fatcat:fyh5t3y24zgsddiw6eqqmpluqq

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

Mishall Al-Zubaidie, Zhongwei Zhang, Ji Zhang
2019 arXiv   pre-print
This paper presents detailed and a comprehensive survey of an update of the ECDSA algorithm in terms of performance, security, and applications.  ...  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

Survey: Vulnerability Analysis of Low-Cost ECC-Based RFID Protocols against Wireless and Side-Channel Attacks

Souhir Gabsi, Vincent Beroulle, Yann Kieffer, Hiep Manh Dao, Yassin Kortli, Belgacem Hamdi
2021 Sensors  
We compare the various lightweight ECC primitive implementations designed for RFID applications in terms of occupied area and power consumption.  ...  To reach the required security and confidentiality requirements for data transfer, elliptic curve cryptography (ECC) is a powerful solution, which ensures a tag/reader mutual authentication and guarantees  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/s21175824 pmid:34502714 pmcid:PMC8434319 fatcat:pkjqudq7mncfzeuwjocjfjrxfm

A Low-Complexity Edward-Curve Point Multiplication Architecture

Asher Sajid, Muhammad Rashid, Malik Imran, Atif Raza Jafri
2021 Electronics  
The Binary Edwards Curves (BEC) are becoming more and more important, as compared to other forms of elliptic curves, thanks to their faster operations and resistance against side channel attacks.  ...  The first contribution is the reduction of instruction-level complexity for unified point addition and point doubling laws by eliminating multiple operations in a single instruction format.  ...  Acknowledgments: We are thankful to the support of King Abdul-Aziz City for Science and Technology (KACST) and Science and Technology Unit (STU), MAKKAH, Saudi Arabia.  ... 
doi:10.3390/electronics10091080 doaj:e46bb95c5a9642ce877d2ab0aa0f559d fatcat:vioyqx4jwfbddeyhqgsdxy6hnm

High-Performance Pipelined Architecture of Elliptic Curve Scalar Multiplication Over GF(2m)

Lijuan Li, Shuguo Li
2016 IEEE Transactions on Very Large Scale Integration (vlsi) Systems  
We implement ECSM over the five binary fields recommended by the National Institute of Standard and Technology on Xilinx Virtex-4 and Virtex-5 field-programmable gate arrays.  ...  This paper proposes an efficient pipelined architecture of elliptic curve scalar multiplication (ECSM) over GF(2 m ).  ...  ACKNOWLEDGMENT The authors would like to thank the editors and reviewers for their contributive comments and suggestions.  ... 
doi:10.1109/tvlsi.2015.2453360 fatcat:t2w752xnjjhbnnzcfjdqiqslu4

Efficient Double Bases for Scalar Multiplication

Nicolas Meloni, M. Anwar Hasan
2015 IEEE transactions on computers  
We also propose an efficient algorithm for computing constrained expansions and finally provide a comprehensive comparison to double-base chain expansions, including a large variety of curve shapes and  ...  In this paper we present efficient algorithms to take advantage of the double-base number system in the context of elliptic curve scalar multiplication.  ...  Comments For high performance of cryptographic operations, many researchers have proposed dedicated hardware to accelerate the field arithmetic, especially multiplication.  ... 
doi:10.1109/tc.2014.2360539 fatcat:xzwkdldksjdclapwab67xurh5m

Design of elliptic curve cryptoprocessors over GF(2^163) using the Gaussian normal basis

Paulo Cesar Realpe, Vladimir Trujillo-Olaya, Jaime Velasco-Medina
2014 Ingeniería e Investigación  
In this case, the computation times of the multiplication kP using the Lopez-Dahab algorithm, 2-NAF halve-and-add algorithm and 16NAF method for Koblitz curves were 13.37 µs, 16.90 µs and 5.05 µs, respectively  ...  form (2-NAF) halve-and-add algorithm and the wNAF method for Koblitz curves.  ...  In this regard, hardware implementations of cryptographic algorithms have advantages, such as high speed, high security levels and low cost.  ... 
doi:10.15446/ing.investig.v34n2.40542 fatcat:dmv4pxiwgjdkrouy6zmu6j4ihy

How to Manipulate Curve Standards: A White Paper for the Black Hat [chapter]

Daniel J. Bernstein, Tung Chou, Chitchanok Chuengsatiansup, Andreas Hülsing, Eran Lambooij, Tanja Lange, Ruben Niederhagen, Christine van Vredendaal
2015 Lecture Notes in Computer Science  
This cost includes the cost of exploiting the vulnerability, but also the initial cost of computing a curve suitable for sabotaging the standard.  ...  For example, this paper shows that plausible models of the "Brainpool acceptability criteria" allow the attacker to target a one-in-a-million vulnerability and that plausible models of the "Microsoft NUMS  ...  For simplicity we do not discuss the possibility of choosing values other than −3. 2. Edwards curves, the speed leader in fixed-base scalar multiplication offering complete addition laws.  ... 
doi:10.1007/978-3-319-27152-1_6 fatcat:doqlmsvpdndfdmi5kolmdhfecu

PEC - An Alternate and More Efficient Public Key Cryptosystem

Rahul Krishnan
2018 International Journal on Cryptography and Information Security  
Elliptic Curve Cryptography (ECC) is the most commonly implemented PKC in use today.  ...  In an increasingly connected world, security is a top concern for Internet of Things (IoT).  ...  ACKNOWLEDGEMENTS I would like to acknowledge the thoughtful guidance of the Mass Academy faculty, Mr. Ellis and Mrs. Curran, for their helpful suggestions and pointers.  ... 
doi:10.5121/ijcis.2018.8101 fatcat:gmy4ycqtrvflrmohw4juvsvahe

Pec - An Alternate And More Efficient Public Key Cryptosystem

Rahul Krishnan
2018 Zenodo  
Elliptic Curve Cryptography (ECC) is the most commonly implemented PKC in use today.  ...  In an increasingly connected world, security is a top concern for Internet of Things (IoT).  ...  ACKNOWLEDGEMENTS I would like to acknowledge the thoughtful guidance of the Mass Academy faculty, Mr. Ellis and Mrs. Curran, for their helpful suggestions and pointers.  ... 
doi:10.5281/zenodo.1211124 fatcat:3rwtyhljvbfdjngnhnxqsoyza4
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