# Differential Addition in Edwards Coordinates Revisited and a Short Note on Doubling in Twisted Edwards Form

### Srinivasa Rao Subramanya Rao

#### 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 Edwardsâ€™ 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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#### Paper Citation

#### in Harvard Style

Subramanya Rao S. (2016). **Differential Addition in Edwards Coordinates Revisited and a Short Note on Doubling in Twisted Edwards Form** . In *Proceedings of the 13th International Joint Conference on e-Business and Telecommunications - Volume 4: SECRYPT, (ICETE 2016)* ISBN 978-989-758-196-0, pages 336-343. DOI: 10.5220/0005970603360343

#### in Bibtex Style

@conference{secrypt16,

author={Srinivasa Rao Subramanya Rao},

title={Differential Addition in Edwards Coordinates Revisited and a Short Note on Doubling in Twisted Edwards Form},

booktitle={Proceedings of the 13th International Joint Conference on e-Business and Telecommunications - Volume 4: SECRYPT, (ICETE 2016)},

year={2016},

pages={336-343},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005970603360343},

isbn={978-989-758-196-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Joint Conference on e-Business and Telecommunications - Volume 4: SECRYPT, (ICETE 2016)

TI - Differential Addition in Edwards Coordinates Revisited and a Short Note on Doubling in Twisted Edwards Form

SN - 978-989-758-196-0

AU - Subramanya Rao S.

PY - 2016

SP - 336

EP - 343

DO - 10.5220/0005970603360343