Differential addition in Edwards coordinates revisited and a short note on doubling in twisted Edwards form

Srinivasa Rao Subramanya Rao

doi:10.5220/0005970603360343

Differential addition in Edwards coordinates revisited and a short note on doubling in twisted Edwards form

Srinivasa Rao Subramanya Rao^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Cryptographic algorithms in smart cards and other constrained environments increasingly rely on Elliptic Curves and thus it is desirable to have fast algorithms for elliptic curve arithmetic. In this paper, we provide (i) faster differential addition formulae for elliptic curve arithmetic on Generalized Edwards' Curves improving upon the currently known formulae in the literature, proposed by Justus and Loebenberger at IWSEC 2010, (ii) more efficient affine differential addition formulae for a new model of Binary Edwards Curves proposed by Wu, Tang and Feng at INDOCRYPT 2012 and (iii) an algorithm for point doubling on Twisted Edwards Curves with a smaller footprint when the implementation is desired to work across Homogeneous Projective, Inverted and Extended Homogeneous Projective Coordinates.

Original language	English
Title of host publication	ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications
Editors	Christian Callegari, Marten van Sinderen, Enrique Cabello, Pierangela Samarati, Pascal Lorenz, Mohammad S. Obaidat, Panagiotis Sarigiannidis
Publisher	SciTePress
Pages	336-343
Number of pages	8
ISBN (Electronic)	9789897581960
DOIs	https://doi.org/10.5220/0005970603360343
Publication status	Published - 2016
Event	13th International Conference on Security and Cryptography, SECRYPT 2016 - Part of the 13th International Joint Conference on e-Business and Telecommunications, ICETE 2016 - Lisbon, Portugal Duration: 26 Jul 2016 → 28 Jul 2016

Publication series

Name	ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications
Volume	4

Conference

Conference	13th International Conference on Security and Cryptography, SECRYPT 2016 - Part of the 13th International Joint Conference on e-Business and Telecommunications, ICETE 2016
Country/Territory	Portugal
City	Lisbon
Period	26/07/16 → 28/07/16

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10.5220/0005970603360343

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Rao, S. R. S. (2016). Differential addition in Edwards coordinates revisited and a short note on doubling in twisted Edwards form. In C. Callegari, M. van Sinderen, E. Cabello, P. Samarati, P. Lorenz, M. S. Obaidat, & P. Sarigiannidis (Eds.), ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications (pp. 336-343). (ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications; Vol. 4). SciTePress. https://doi.org/10.5220/0005970603360343

Rao, Srinivasa Rao Subramanya. / Differential addition in Edwards coordinates revisited and a short note on doubling in twisted Edwards form. ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications. editor / Christian Callegari ; Marten van Sinderen ; Enrique Cabello ; Pierangela Samarati ; Pascal Lorenz ; Mohammad S. Obaidat ; Panagiotis Sarigiannidis. SciTePress, 2016. pp. 336-343 (ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications).

@inproceedings{330d09d5fb6241e190e7420e448f23ef,

title = "Differential addition in Edwards coordinates revisited and a short note on doubling in twisted Edwards form",

abstract = "Cryptographic algorithms in smart cards and other constrained environments increasingly rely on Elliptic Curves and thus it is desirable to have fast algorithms for elliptic curve arithmetic. In this paper, we provide (i) faster differential addition formulae for elliptic curve arithmetic on Generalized Edwards' Curves improving upon the currently known formulae in the literature, proposed by Justus and Loebenberger at IWSEC 2010, (ii) more efficient affine differential addition formulae for a new model of Binary Edwards Curves proposed by Wu, Tang and Feng at INDOCRYPT 2012 and (iii) an algorithm for point doubling on Twisted Edwards Curves with a smaller footprint when the implementation is desired to work across Homogeneous Projective, Inverted and Extended Homogeneous Projective Coordinates.",

keywords = "Binary Edwards curves, Differential addition, Edwards curves, Extended homogeneous projective coordinates, Homogeneous projective, Inverted coordinates, Montgomery curves, Scalar multiplication, Twisted Edwards curves, w-coordinate differential addition",

author = "Rao, {Srinivasa Rao Subramanya}",

note = "Publisher Copyright: Copyright {\textcopyright} 2016 by SCITEPRESS - Science and Technology Publications, Lda. All rights reserved.; 13th International Conference on Security and Cryptography, SECRYPT 2016 - Part of the 13th International Joint Conference on e-Business and Telecommunications, ICETE 2016 ; Conference date: 26-07-2016 Through 28-07-2016",

year = "2016",

doi = "10.5220/0005970603360343",

language = "English",

series = "ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications",

publisher = "SciTePress",

pages = "336--343",

editor = "Christian Callegari and {van Sinderen}, Marten and Enrique Cabello and Pierangela Samarati and Pascal Lorenz and Obaidat, {Mohammad S.} and Panagiotis Sarigiannidis",

booktitle = "ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications",

}

Rao, SRS 2016, Differential addition in Edwards coordinates revisited and a short note on doubling in twisted Edwards form. in C Callegari, M van Sinderen, E Cabello, P Samarati, P Lorenz, MS Obaidat & P Sarigiannidis (eds), ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications. ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications, vol. 4, SciTePress, pp. 336-343, 13th International Conference on Security and Cryptography, SECRYPT 2016 - Part of the 13th International Joint Conference on e-Business and Telecommunications, ICETE 2016, Lisbon, Portugal, 26/07/16. https://doi.org/10.5220/0005970603360343

Differential addition in Edwards coordinates revisited and a short note on doubling in twisted Edwards form. / Rao, Srinivasa Rao Subramanya.
ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications. ed. / Christian Callegari; Marten van Sinderen; Enrique Cabello; Pierangela Samarati; Pascal Lorenz; Mohammad S. Obaidat; Panagiotis Sarigiannidis. SciTePress, 2016. p. 336-343 (ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications; Vol. 4).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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PY - 2016

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N2 - Cryptographic algorithms in smart cards and other constrained environments increasingly rely on Elliptic Curves and thus it is desirable to have fast algorithms for elliptic curve arithmetic. In this paper, we provide (i) faster differential addition formulae for elliptic curve arithmetic on Generalized Edwards' Curves improving upon the currently known formulae in the literature, proposed by Justus and Loebenberger at IWSEC 2010, (ii) more efficient affine differential addition formulae for a new model of Binary Edwards Curves proposed by Wu, Tang and Feng at INDOCRYPT 2012 and (iii) an algorithm for point doubling on Twisted Edwards Curves with a smaller footprint when the implementation is desired to work across Homogeneous Projective, Inverted and Extended Homogeneous Projective Coordinates.

AB - Cryptographic algorithms in smart cards and other constrained environments increasingly rely on Elliptic Curves and thus it is desirable to have fast algorithms for elliptic curve arithmetic. In this paper, we provide (i) faster differential addition formulae for elliptic curve arithmetic on Generalized Edwards' Curves improving upon the currently known formulae in the literature, proposed by Justus and Loebenberger at IWSEC 2010, (ii) more efficient affine differential addition formulae for a new model of Binary Edwards Curves proposed by Wu, Tang and Feng at INDOCRYPT 2012 and (iii) an algorithm for point doubling on Twisted Edwards Curves with a smaller footprint when the implementation is desired to work across Homogeneous Projective, Inverted and Extended Homogeneous Projective Coordinates.

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KW - Differential addition

KW - Edwards curves

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KW - Homogeneous projective

KW - Inverted coordinates

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M3 - Conference contribution

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BT - ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications

A2 - Callegari, Christian

A2 - van Sinderen, Marten

A2 - Cabello, Enrique

A2 - Samarati, Pierangela

A2 - Lorenz, Pascal

A2 - Obaidat, Mohammad S.

A2 - Sarigiannidis, Panagiotis

PB - SciTePress

T2 - 13th International Conference on Security and Cryptography, SECRYPT 2016 - Part of the 13th International Joint Conference on e-Business and Telecommunications, ICETE 2016

Y2 - 26 July 2016 through 28 July 2016

ER -

Rao SRS. Differential addition in Edwards coordinates revisited and a short note on doubling in twisted Edwards form. In Callegari C, van Sinderen M, Cabello E, Samarati P, Lorenz P, Obaidat MS, Sarigiannidis P, editors, ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications. SciTePress. 2016. p. 336-343. (ICETE 2016 - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications). doi: 10.5220/0005970603360343

Differential addition in Edwards coordinates revisited and a short note on doubling in twisted Edwards form

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