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New Composite Operations and Precomputation Scheme for Elliptic Curve Cryptosystems over Prime Fields
[chapter]

*
Public Key Cryptography – PKC 2008
*

We present a

doi:10.1007/978-3-540-78440-1_14
dblp:conf/pkc/LongaM08
fatcat:6hlgjw44lrg3talbfs6sgmskce
*new*methodology to derive faster*composite**operations*of the form dP+Q, where d is a small integer ≥ 2,*for*generic ECC scalar multiplications*over**prime**fields*. ... By combining the benefits of our*precomputation**scheme**and*the*new*DA*operation*, we can save up to 6.2% in the scalar multiplication using fractional wNAF. ...*over**prime**fields*. ...##
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Elliptical Curve Digital Signatures Algorithm

2015
*
International Journal on Recent and Innovation Trends in Computing and Communication
*

The survey of ECDSA involves major issues like security of

doi:10.17762/ijritcc2321-8169.1503180
fatcat:5ncm73qzy5et3mdtm5qullwnsq
*cryptosystem*, RFID-tag authentication, Montgomery multiplication*over*binary*fields*, Scaling techniques, Signature generation ,signature verification ...*Elliptical*digital signatures algorithm provides security services*for*resource constrained embedded devices. ... Case of both*elliptic**curved**over*F 2 P C*and**over**composite**fields*F 2 2 P are investigated. This type of implementation made RFID tags suitable*for*anti-counterfeiting even in the offline setting. ...##
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Fast Algorithms for Elliptic Curve Cryptosystems over Binary Finite Field
[chapter]

1999
*
Lecture Notes in Computer Science
*

We present two novel algorithms

doi:10.1007/978-3-540-48000-6_8
fatcat:vi4dh7enrvcpbgppypb6o24c3q
*for*efficient implementation of*field*multiplication*and*modular reduction used frequently in an*elliptic**curve**cryptosystem*defined*over*GF (2 n ). ... In the underlying finite*field*arithmetic of an*elliptic**curve**cryptosystem*,*field*multiplication is the next computational costly*operation*other than*field*inversion. ... We consider only nonsupersingular*and*non-anomalous*elliptic**curves**over*non-*composite**field*in the paper. ...##
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Elliptic Curve Cryptography on Smart Cards without Coprocessors
[chapter]

2000
*
Smart Card Research and Advanced Applications
*

This contribution describes how an

doi:10.1007/978-0-387-35528-3_5
fatcat:epuxwk5jkvfoffko3hdcfdk56q
*elliptic**curve**cryptosystem*can be implemented on very low cost microprocessors with reasonable performance. ... We show that an*elliptic**curve*scalar multiplication with a fixed point, which is the core*operation**for*a signature generation, can be performed in a group of order approximately 2 134 in less than 2 ... ACKNOWLEDGEMENTS The authors would like to thank Jorge Guajardo*and*Pedro Soria-Rodriguez*for*their contribution of the even*composite**field*multiplication implementation. ...##
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On the Performance of Hyperelliptic Cryptosystems
[chapter]

1999
*
Lecture Notes in Computer Science
*

This paper presents a practical comparison between the performance of

doi:10.1007/3-540-48910-x_12
fatcat:qt76qbabqfc7bfgzs6vdfhzaty
*elliptic**curve*based digital signature*schemes**and**schemes*based on hyperelliptic*curves*. ... In particular we cover the implementation of the group law of such*curves**and*how to generate suitable*curves**for*use in cryptography. ... This paper presents a practical comparison between the performance of*elliptic**curve*based digital signature*schemes**and**schemes*based on hyperelliptic*curves*. ...##
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Efficient algorithms for elliptic curve cryptosystems
[chapter]

1997
*
Lecture Notes in Computer Science
*

*Elliptic*

*curves*are the basis

*for*a relative

*new*class of public-key

*schemes*. It is predicted that

*elliptic*

*curves*will replace many existing

*schemes*in the near future. ... This thesis describes three

*new*algorithms

*for*efficient implementations of

*elliptic*

*curve*

*cryptosystems*. ...

*over*

*prime*

*fields*. ...

##
###
A Group Law on the Projective Plane with Applications in Public Key Cryptography

2020
*
Mathematics
*

We present an experimental setup in order to show real computation times along a comparison with the group

doi:10.3390/math8050734
fatcat:y5ywbaforbghllbbuwgcjxaucu
*operation*in the group of points of an*elliptic**curve*. ... plane F P 2*over*an arbitrary*field*F , which lends itself to applications in Public Key Cryptography*and*turns out to be more efficient in terms of computational resources. ... In order to overcome these limitations, Menezes*and*Vanstone proposed in [8] the*Elliptic**Curve*Menezes-Vanstone*cryptosystem*(ECMV)*for**elliptic**curves**over*finite*fields*F q . ...##
###
Elliptic Curve Array Ballots for Homomorphic Tallying Elections
[chapter]

2015
*
Lecture Notes in Computer Science
*

In this paper, we propose a

doi:10.1007/978-3-319-22389-6_24
fatcat:5ov5k6rupzcozcaznw3ntmvo5i
*new*homomorphic tallying remote voting system that makes use of*elliptic**curve*cryptography. The proposed system is suitable*for*multiple choice elections. ... Detailed security*and*performance analysis are provided. ... Research of the authors was supported in part by grants MTM2013-46949-P (Spanish Ministerio de Ciencia e Innovación), 2014SGR-1666 (Generalitat de Catalunya)*and*IPT-2012-0603-430000 (Spanish Ministerio ...##
###
Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation
[chapter]

2003
*
Lecture Notes in Computer Science
*

We give applications to simultaneous multiple scalar multiplication

doi:10.1007/3-540-36563-x_24
fatcat:ygkwiehajzgjjjaie4eyonssmi
*and*to the*Elliptic**Curve*Method of factorization. ... We present an algorithm which speeds scalar multiplication on a general*elliptic**curve*by an estimated 3.8% to 8.5%*over*the best known general methods when using affine coordinates. ... Scalar multiplication on*elliptic**curves*is used by*cryptosystems**and*signature*schemes*based on*elliptic**curves*. ...##
###
Improved algorithms for an efficient arithmetic on some categories of elliptic curves

2016
*
International Journal of Computational Complexity and Intelligent Algorithms
*

The Frobenius endomorphism τ is known to be useful

doi:10.1504/ijccia.2016.077465
fatcat:r3aoplqh4ngspcadle5mlawsju
*for*an efficient scalar multiplication on*elliptic**curves*E(Fqm ) defined either*over**fields*with small characteristics or*over*optimal extension*fields*... Finally, we show that there are a lot of*curves*which are well suited*for*cryptography,*and**for*which the proposed methods can be applied. ... The GHS attack on*elliptic**curves**over**composite*binary*fields*was fully analysed by Mauer et al. (2001) . ...##
###
Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation
[article]

2003
*
arXiv
*
pre-print

We give applications to simultaneous multiple scalar multiplication

arXiv:math/0208038v2
fatcat:3slwpkz6trhohibjzvixwy3pcy
*and*to the*Elliptic**Curve*Method of factorization. ... We present an algorithm which speeds scalar multiplication on a general*elliptic**curve*by an estimated 3.8 % to 8.5 %*over*the best known general methods when using affine coordinates. ... Scalar multiplication on*elliptic**curves*is used by*cryptosystems**and*signature*schemes*based on*elliptic**curves*. ...##
###
NICE - New Ideal Coset Encryption -
[chapter]

1999
*
Lecture Notes in Computer Science
*

We discuss the reasons

doi:10.1007/3-540-48059-5_28
fatcat:4qd4k6gegrabxb6sffgojyayeu
*for*this*and*indicate requirements*for*smartcard designers to achieve fast implementation on smartcards. ... Recently, a novel public-key*cryptosystem*constructed on number*fields*is presented. ...*Elliptic**curves*are somewhat more complicated,*and*the best known algorithms to break*elliptic**curve**cryptosystems*are much slower, in the order of exponential complexity. ...##
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Efficient Algorithms for Pairing-Based Cryptosystems
[chapter]

2002
*
Lecture Notes in Computer Science
*

We describe fast

doi:10.1007/3-540-45708-9_23
fatcat:j5lpacqpmbfrvmb7vhexk3oox4
*new*algorithms to implement recent*cryptosystems*based on the Tate pairing. ... Mathematical Preliminaries Let p be a*prime*number, m a positive integer*and*F p m the finite*field*with p m elements; p is said to be the characteristic of F p m ,*and*m is its extension ... The contributions of this paper are: -The definition of point tripling*for*supersingular*elliptic**curves**over*F 3 m , that is,*over**fields*of characteristic 3. ...##
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Memory-Efficient Algorithm for Scalar Multiplications on Twisted Edwards Curves for Isogeny-Based Cryptosystems

2022
*
Mathematical Problems in Engineering
*

The efficiency of scalar multiplication depends on the equation of the underlying

doi:10.1155/2022/3846369
fatcat:x533uonphzffho2ategkig74iy
*elliptic**curves**and*the addition chain employed. ...*curves*in the setting of isogeny-based*cryptosystem*. ... Let E 1*and*E 2 be two*elliptic**curves**over*a finite*field*F q . ...##
###
:{unav)

2012
*
Designs, Codes and Cryptography
*

integers modulo a

doi:10.1023/a:1008354106356
fatcat:zeumo2bjbffabkvqohtru7j62m
*prime*, this idea can be extended to arbitrary groups*and*, in particular, to*elliptic**curve*groups. ... This paper surveys the development of*elliptic**curve**cryptosystems*from their inception in 1985 by Koblitz*and*Miller to present day implementations. ... A*new*record*for**elliptic**curve*point counting*over**prime**fields*was established in 1995 by Lercier*and*Morain [44] , who computed the order of a*curve**over*a 499-decimal digit (1658-bit)*prime**field*; ...
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