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

2013
*
Lecture Notes in Computer Science
*

In 2010, Joye et. al brought

doi:10.1007/978-3-642-40588-4_11
fatcat:trqirocxkranfgcrdff2pnowli
*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]

2017
*
Lecture Notes in Computer Science
*

In this paper, we study

doi:10.1007/978-3-319-71501-8_5
fatcat:dfet5za735ge5piomgp5tzejsi
*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]

2013
*
Lecture Notes in Computer Science
*

Joye, "

doi:10.1007/978-3-642-40349-1_20
fatcat:g47ii7pqh5eztkiej6eyqwayma
*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]

2016
*
Lecture Notes in Computer Science
*

.,

doi:10.1007/978-3-319-55227-9_2
fatcat:hcb6pmdq55gnzcufniqj2khjtm
*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]

2011
*
Lecture Notes in Computer Science
*

While studying a diophantine problem,

doi:10.1007/978-3-642-19074-2_22
fatcat:moec46h4dzeo5bmn37qd6tc2ci
*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

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]

2017
*
arXiv
*
pre-print

We first discuss different

arXiv:1710.08336v1
fatcat:g3gpz5lzgvc27fboa5tv4kdhze
*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

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]

2017
*
Lecture Notes in Computer Science
*

To our knowledge, this is

doi:10.1007/978-3-319-72565-9_9
fatcat:w4hwppqbnzhfpbbmggkts6mtce
*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

2020
*
Journal of Mathematical Cryptology
*

This paper revisits

doi:10.1515/jmc-2019-0030
fatcat:ymsslt5qtngwlggbem7aknci5m
*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

2021
*
Electronics
*

Therefore, this article has provided a low area hardware architecture for point

doi:10.3390/electronics10121490
fatcat:sn64oisbabcebenwxtjlrkmjdu
*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

doi:10.1109/access.2021.3090216
fatcat:fyh5t3y24zgsddiw6eqqmpluqq
*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

2021
*
IEEE Access
*

INDEX TERMS

doi:10.1109/access.2021.3051282
fatcat:rybe4uvimjdrhl6fbcd3tzwmwu
*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

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

2013
*
Astrophysical Journal
*

We expect that a future DLS weak-lensing tomographic study will further tighten these constraints because explicit treatment

doi:10.1088/0004-637x/765/1/74
fatcat:kmbeeu75lvbcjbjd45usvuidpa
*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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