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### Improving the Efficiency of Elliptic Curve Scalar Multiplication Using Binary Huff Curves [chapter]

Gerwin Gsenger, Christian Hanser
2013 Lecture Notes in Computer Science
In 2010, Joye et. al brought the so-called Huff curve model, which was originally proposed in 1948 for the studies of diophantine equations, into the context of elliptic curve cryptography.  ...  a side-channel attack resistant scalar multiplication algorithm.  ...  As defined in [5] , binary Huff curves are a new class of elliptic curves.  ...

### Efficient Software Implementation of Laddering Algorithms Over Binary Elliptic Curves [chapter]

Diego F. Aranha, Reza Azarderakhsh, Koray Karabina
2017 Lecture Notes in Computer Science
In this paper, we study the efficient implementation of laddering algorithms for variable-base scalar multiplication under different models of elliptic curves defined over binary extension fields.  ...  In this paper, we keep pushing in this direction and study efficient implementation of regular scalar multiplication algorithms for binary curves equipped with efficient endomorphisms.  ...  In Section 2, Weierstraß, Huff and Edwards elliptic curve models are introduced, together with efficient formulae and algorithms for converting from binary GLS curves in the Weierstraßmodel.  ...

### On the Implementation of Unified Arithmetic on Binary Huff Curves [chapter]

Santosh Ghosh, Amit Kumar, Amitabh Das, Ingrid Verbauwhede
2013 Lecture Notes in Computer Science
Joye, "Binary huff curves," CT-RSA 2011 , LNCS 6558, pp. 340-355, Springer-Verlag, 2011 .  ...  Unified Binary Huff Curve (UBHC) Let, P = (X 1 , Y 1 , Z 1 ) and Q = (X 2 , Y 2 , Z 2 ) then P+Q: This is computed as: • J. Devigne and M.  ...  .: High-speed unified elliptic curve cryptosystem on FPGAs using binary Huff curves. VDAT 2012.  ...

### Differential Addition on Binary Elliptic Curves [chapter]

Reza Rezaeian Farashahi, Seyed Gholamhossein Hosseini
2016 Lecture Notes in Computer Science
., the addition of two points with the known difference) and doubling formulas, as the core step in Montgomery scalar multiplication, for various forms of elliptic curves over binary fields.  ...  The formulas are provided for binary Edwards, binary Hessian and binary Huff elliptic curves with cost of 5M + 4S + 1D when the given difference point is in affine form.  ...  The authors would like to thank anonymous reviewers for their useful comments. This research was in part supported by a grant from IPM (No. 93050416).  ...

### Binary Huff Curves [chapter]

Julien Devigne, Marc Joye
2011 Lecture Notes in Computer Science
While studying a diophantine problem, Huff introduced a new model for elliptic curves [7] (see also [18] ). Huff's model was recently revisited in [9] . The case of  ...  This paper describes the addition law for a new form for elliptic curves over fields of characteristic 2.  ...  Acknowledgments We are very grateful to the anonymous referees for their useful comments and suggestions.  ...

### 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.  ...  Among various existent algorithms on asymmetric cryptography, we may cite Elliptic Curve Cryptography (ECC), which has been widely used due to its security level and reduced key sizes.  ...  Elliptic Curve Point Multiplication To generate the public key, cryptosystems based on elliptic curves must perform point multiplication, also called scalar multiplication.  ...

### 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  ...  In the past two decades, Elliptic Curve Cryptography (ECC) have become increasingly advanced.  ...  The efficient and popular curves are include binary Weierstrass curves, Koblitz curves, binary Edwards curves, generalized Hessian curves and binary Huff curves. • FPGA implementations of the binary Weierstrass  ...

### 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
The radio frequency identification (RFID) system is one of the most important technologies of the Internet of Things (IoT) that tracks single or multiple objects.  ...  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.  ...

### How to (Pre-)Compute a Ladder [chapter]

Thomaz Oliveira, Julio López, Hüseyin Hışıl, Armando Faz-Hernández, Francisco Rodríguez-Henríquez
2017 Lecture Notes in Computer Science
To our knowledge, this is the first proposal of a Montgomery ladder procedure for prime elliptic curves that admits the extensive use of pre-computation.  ...  In the RFC 7748 memorandum, the Internet Research Task Force specified a Montgomery-ladder scalar multiplication function based on two recently adopted elliptic curves, "curve25519" and "curve448".  ...  Although this primitive can be performed at a low computational cost in binary elliptic curves, in general there are no known procedures to compute it efficiently for elliptic curves defined over odd prime  ...

### Protecting ECC Against Fault Attacks: The Ring Extension Method Revisited

Marc Joye
2020 Journal of Mathematical Cryptology
This paper revisits the ring extension method and its adaptation to the elliptic curve setting.  ...  AbstractDue to its shorter key size, elliptic curve cryptography (ECC) is gaining more and more popularity.  ...  BOS countermeasure As aforementioned, the main operation for elliptic curve cryptography is the scalar multiplication.  ...

### AREEBA: An Area Efficient Binary Huff-Curve Architecture

Asher Sajid, Muhammad Rashid, Sajjad Shaukat Jamal, Malik Imran, Saud S. Alotaibi, Mohammed H. Sinky
2021 Electronics
Therefore, this article has provided a low area hardware architecture for point multiplication computation of Binary Huff curves over GF(2163) and GF(2233).  ...  Elliptic curve cryptography is the most widely employed class of asymmetric cryptography algorithm.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ...

### An Optimized Architecture for Binary Huff Curves with Improved Security

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.  ...  BINARY HUFF CURVES The Huff model for elliptic curves was initially presented in 2010 [26] .  ...  Rivest Shamir Adleman (RSA) [4] and Elliptic Curve Cryptography (ECC) [5] are the frequently used asymmetric algorithms.  ...

### Innovative Dual-Binary-Field Architecture for Point Multiplication of Elliptic Curve Cryptography

Jiakun Li, Weijiang Wang, Jingqi Zhang, Yixuan Luo, Shiwei Ren
2021 IEEE Access
INDEX TERMS Elliptic curve cryptography (ECC), dual-field point multiplication, montgomery ladder, field-programmable gate array (FPGA) implementation.  ...  High-performance Elliptic Curve Cryptography (ECC) implementation in encryption authentication severs has become a challenge due to the explosive growth of e-commerce's demand for speed and security.  ...  Some works applied PM over special elliptic curves to improve the performance of ECC.  ...

### 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.  ...  This work provides a low-complexity architecture for point multiplication computations using BEC over GF(2233). There are three major contributions in this article.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ...

### COSMIC SHEAR RESULTS FROM THE DEEP LENS SURVEY. I. JOINT CONSTRAINTS ON ΩMAND σ8WITH A TWO-DIMENSIONAL ANALYSIS

M. James Jee, J. Anthony Tyson, Michael D. Schneider, David Wittman, Samuel Schmidt, Stefan Hilbert
2013 Astrophysical Journal
We expect that a future DLS weak-lensing tomographic study will further tighten these constraints because explicit treatment of the redshift dependence of cosmic shear more efficiently breaks the Omega_M-sigma  ...  We use cosmology-dependent covariances for the Markov Chain Monte Carlo analysis and find that the role of this varying covariance is critical in our parameter estimation.  ...  We thank Russell Ryan and Ami Choi for useful discussions. We thank Perry Gee for relentless efforts to carefully manage the DLS database.  ...
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