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

Patrick Longa, Ali Miri
Public Key Cryptography – PKC 2008  
We present a 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.  ... 
doi:10.1007/978-3-540-78440-1_14 dblp:conf/pkc/LongaM08 fatcat:6hlgjw44lrg3talbfs6sgmskce

Elliptical Curve Digital Signatures Algorithm

Prajna D
2015 International Journal on Recent and Innovation Trends in Computing and Communication  
The survey of ECDSA involves major issues like security of 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.  ... 
doi:10.17762/ijritcc2321-8169.1503180 fatcat:5ncm73qzy5et3mdtm5qullwnsq

Fast Algorithms for Elliptic Curve Cryptosystems over Binary Finite Field [chapter]

Yongfei Han, Peng-Chor Leong, Peng-Chong Tan, Jiang Zhang
1999 Lecture Notes in Computer Science  
We present two novel algorithms 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.  ... 
doi:10.1007/978-3-540-48000-6_8 fatcat:vi4dh7enrvcpbgppypb6o24c3q

Elliptic Curve Cryptography on Smart Cards without Coprocessors [chapter]

Adam D. Woodbury, Daniel V. Bailey, Christof Paar
2000 Smart Card Research and Advanced Applications  
This contribution describes how an 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.  ... 
doi:10.1007/978-0-387-35528-3_5 fatcat:epuxwk5jkvfoffko3hdcfdk56q

On the Performance of Hyperelliptic Cryptosystems [chapter]

Nigel P. Smart
1999 Lecture Notes in Computer Science  
This paper presents a practical comparison between the performance of 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.  ... 
doi:10.1007/3-540-48910-x_12 fatcat:qt76qbabqfc7bfgzs6vdfhzaty

Efficient algorithms for elliptic curve cryptosystems [chapter]

Jorge Guajardo, Christof Paar
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.  ... 
doi:10.1007/bfb0052247 fatcat:i26ofxwhyrdqzc6j7sip4r4clq

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

Raúl Durán Díaz, Luis Hernández Encinas, Jaime Muñoz Masqué
2020 Mathematics  
We present an experimental setup in order to show real computation times along a comparison with the group 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 .  ... 
doi:10.3390/math8050734 fatcat:y5ywbaforbghllbbuwgcjxaucu

Elliptic Curve Array Ballots for Homomorphic Tallying Elections [chapter]

Maria dels Àngels Cerveró, Víctor Mateu, Santi Martínez, Josep Maria Miret, Francesc Sebé
2015 Lecture Notes in Computer Science  
In this paper, we propose a 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  ... 
doi:10.1007/978-3-319-22389-6_24 fatcat:5ov5k6rupzcozcaznw3ntmvo5i

Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation [chapter]

Kirsten Eisenträger, Kristin Lauter, Peter L. Montgomery
2003 Lecture Notes in Computer Science  
We give applications to simultaneous multiple scalar multiplication 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.  ... 
doi:10.1007/3-540-36563-x_24 fatcat:ygkwiehajzgjjjaie4eyonssmi

Improved algorithms for an efficient arithmetic on some categories of elliptic curves

Mustapha Hedabou
2016 International Journal of Computational Complexity and Intelligent Algorithms  
The Frobenius endomorphism τ is known to be useful 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) .  ... 
doi:10.1504/ijccia.2016.077465 fatcat:r3aoplqh4ngspcadle5mlawsju

Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation [article]

Kirsten Eisentraeger, Kristin Lauter, Peter L. Montgomery
2003 arXiv   pre-print
We give applications to simultaneous multiple scalar multiplication 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.  ... 
arXiv:math/0208038v2 fatcat:3slwpkz6trhohibjzvixwy3pcy

NICE - New Ideal Coset Encryption - [chapter]

Michael Hartmann, Sachar Paulus, Tsuyoshi Takagi
1999 Lecture Notes in Computer Science  
We discuss the reasons 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.  ... 
doi:10.1007/3-540-48059-5_28 fatcat:4qd4k6gegrabxb6sffgojyayeu

Efficient Algorithms for Pairing-Based Cryptosystems [chapter]

Paulo S. L. M. Barreto, Hae Y. Kim, Ben Lynn, Michael Scott
2002 Lecture Notes in Computer Science  
We describe fast 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.  ... 
doi:10.1007/3-540-45708-9_23 fatcat:j5lpacqpmbfrvmb7vhexk3oox4

Memory-Efficient Algorithm for Scalar Multiplications on Twisted Edwards Curves for Isogeny-Based Cryptosystems

Sookyung Eom, Hyang-Sook Lee, Kyunghwan Song, Salvatore Alfonzetti
2022 Mathematical Problems in Engineering  
The efficiency of scalar multiplication depends on the equation of the underlying 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 .  ... 
doi:10.1155/2022/3846369 fatcat:x533uonphzffho2ategkig74iy

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Neal Koblitz, Alfred Menezes, Scott Vanstone
2012 Designs, Codes and Cryptography  
integers modulo a 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;  ... 
doi:10.1023/a:1008354106356 fatcat:zeumo2bjbffabkvqohtru7j62m
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