mylib.bib

@String{LNCS = {Lecture Notes in Computer Science}
}

@InProceedings{Cohen_heuristics_1984,
author="Cohen, H.
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editor="Jager, Hendrik",
title="Heuristics on class groups of number fields",
booktitle="Number Theory Noordwijkerhout 1983",
year="1984",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="33--62",
isbn="978-3-540-38906-4"
}

@inproceedings{flynn2019genus,
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  year={2019},
  organization={Springer}
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@ARTICLE{Sutherland_sato_2016,
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         year = "2016",
        month = "Apr",
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        pages = {arXiv:1604.01256},
archivePrefix = {arXiv},
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 primaryClass = {math.NT},
}

@article{Flynn_empirical_2001,
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}


@InProceedings{Joye_montladder_2003,
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    pages={291--302},
    year={2002},
    organization={Springer},
}

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@article{fong2004field,
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@InProceedings{halfadd,
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@misc{hyperelliptic,
author = {Burnstein, D.J. and Lange, T.},
title = {Explicit Formulas Database},
year = {2016},
note = {\url{http://hyperelliptic.org/}},
}

@mastersthesis{Lindner_Msc_2014,
author = {S.A. Lindner},
school = {University of Calgary},
title = {Fast Divisor Tripling},
year = {2014},
note = {\url{https://prism.ucalgary.ca/handle/11023/1723}},
}

@mastersthesis{Balamohan_MSc_2009,
author = {B. Balamohan},
school = {University of Ottawa},
title = {Accelerating the scalar multiplication on genus 2 hyperelliptic curve cryptosystems},
year = {2009},
}

@article{BauerJaulmesProuffWild_horizontalecc_2015,
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  number={1},
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  year={2015},
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@misc{BelenkyGeyzelKaraEntelis_cross_2012,
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@article{Bos_constant_2014,
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  year={2014},
  publisher={Springer},
}

@inproceedings{BosCostelloHisilLauter_fastg2_2013,
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booktitle = {EUROCRYPT},
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title = {Fast cryptography in genus 2},
volume = {7881 of Lecture Notes in Computer Science},
year = {2013},
editor = {T. Johansson and P.Q. Nguyen},
publisher = {Springer},
}


@inproceedings{BrierJoye_unified_2002,
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  booktitle={Public Key Cryptography},
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  year={2002},
  organization={Springer},
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@article{Byrne_comparison_2007,
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@article{paulus1999real,
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@article{Cantor_compjac_1987,
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year = {1987},
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@book{CasselsFlynn_g2arithmetic_1996,
address = {Cambridge},
author = {J.W.S. Cassels and E.V. Flynn},
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year = {1996},
}

@inproceedings{ChabrierTisserand_multibase_2013,
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  booktitle={Computer Arithmetic (ARITH), 2013 21st IEEE Symposium on},
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  year={2013},
  organization={IEEE},
}

@article{ChevallierCietJoye_atomicity_2004,
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  volume={53},
  number={6},
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  year={2004},
  publisher={IEEE},
}

@inproceedings{Coron_resistance_1999,
  title={Resistance against differential power analysis for elliptic curve cryptosystems},
  author={Coron, J.S.},
  booktitle={Cryptographic Hardware and Embedded Systems},
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  year={1999},
  organization={Springer},
}

@incollection{CostelloLonga_fourq_2015,
  title={Fourℚ: Four-Dimensional Decompositions on a ℚ-curve over the Mersenne Prime},
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  booktitle={Advances in Cryptology--ASIACRYPT 2015},
  pages={214--235},
  year={2015},
  publisher={Springer},
}

@inproceedings{CostelloLauter_geo_2011,
author = {C. Costello and K. Lauter},
booktitle = {Selected areas in Cryptography},
pages = {92-117},
title = {Group Law Computations on Jacobians of Hyperelliptic Curves},
volume = {7118 of Lecture Notes in Computer Science},
year = {2011},
editor = {Miri and S. Vaudenay},
publisher = {Springer},
}

@article{ChungCostelloSmith_uniform_2015,
  title={Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes},
  author={Chung, P.N. and Costello, C. and Smith, B.},
  journal={arXiv preprint arXiv:1510.03174},
  year={2015},
}

@incollection{ClavierFeixGagnerotRousselletVerneuil_horizontal_2010,
  title={Horizontal correlation analysis on exponentiation},
  author={Clavier, C. and Feix, B. and Gagnerot, G. and Roussellet, M. and Verneuil, V.},
  booktitle={Information and Communications Security},
  pages={46--61},
  year={2010},
  publisher={Springer},
}

@misc{DangerGuilleyHoogvorstMurdicaNaccache_eccbigmac_2015,
title={Improving the Big Mac Attack on Elliptic Curve Cryptography},
  author={Danger, J.L. and Guilley, S. and Hoogvorst, P. and Murdica, C. and Naccache, D.},
   howpublished = {Cryptology ePrint Archive, Report 2015/819},
   year         = {2015},
   note         = {\url{http://eprint.iacr.org/}},
}

@inproceedings{DimitrovImbertMishra_dbchains_2005,
author = {V.Dimitrov and L. Imbert and P.K. Mishra},
title = { Efficient and secure elliptic curve point multiplication using double-base chains},
booktitle = {Advances in Cryptology, ASIACRYPT'05},
volume = {3788 of Lecture Notes in Computer Science},
pages = {59-78},
publisher = {Springer},
year = {2005},
}

@INPROCEEDINGS{DimitrovImbertMishra_DBNS_2008,
    author = {V. Dimitrov and L. Imbert and P.K. Mishra},
    title = {The Double-base Number System and its Application to Elliptic Curve Cryptography},
    booktitle = {Mathematics of Computation},
    year = {2008},
    number = {262},
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}

@INPROCEEDINGS{RozenhartJacobsonScheidler_Tabulation,
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}

@incollection{Doche_DIK_2006,
  title={Efficient scalar multiplication by isogeny decompositions},
  author={Doche, C. and Icart, T. and Kohel, D.R.},
  booktitle={Public Key Cryptography-PKC 2006},
  pages={191--206},
  year={2006},
  publisher={Springer}
}

@incollection{Doche_enumeration_2014,
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  booktitle={Advances in Cryptology--ASIACRYPT 2014},
  pages={297--316},
  year={2014},
  publisher={Springer},
}

@article{EricksonJacobsonStein_realg2_2011,
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    number = {4},
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}

@inproceedings{FanGong_DBLADD_2007,
author = {X. Fan and G. Gong},
booktitle = {Selected Areas in Cryptography},
pages = {155-172},
title = {Efficient explicit formulae for genus 2 hyperelliptic curves over prime fields and their implementations},
volume = {4876 of Lecture Notes in Computer Science},
year = {2007},
publisher = {Springer-Verlag},
}

@InProceedings{FanGuoMulSchPreVer2010,
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  booktitle = {Proceedings of the 2010 {IEEE} International Symposium on Hardware-Oriented Security and Trust, {HOST 2010}},
  pages = 	 {76--87},
  year = 	 2010,
  publisher =    {IEEE},
  doi =          {10.1109/HST.2010.5513110}
}


@incollection{FouqueValette_doubling_2003,
  title={The doubling attack--why upwards is better than downwards},
  author={Fouque, P.A. and Valette, F.},
  booktitle={Cryptographic Hardware and Embedded Systems-CHES 2003},
  pages={269--280},
  year={2003},
  publisher={Springer},
}

@article{GalbraithLinScott_GLV_2011,
author = {S.D. Galbraith and X. Lin and M. Scott},
title = {Endomorphisms for faster elliptic curve cryptography on a large class of curves},
journal = {J. Cryptography},
volume = {24},
number ={3},
pages = {446-469},
year = {2011},
}

@inproceedings{GallantLambertVanstone_GLV_2001,
author = {R.P. Gallant and R.J. Lambert and S.A. Vanstone},
title = {Faster point multiplication on elliptic curves with efficient endomorphisms},
booktitle = {Eurocrypt},
volume = {2139 of Lecture Notes in Computer Science},
editor = {J. Kilian},
pages = {190-210},
year = {2001},
publisher = {Springer},
}

@INPROCEEDINGS{GaudryHarley_pointcount_2000,
    author = {P. Gaudry and R. Harley},
    title = {Counting Points on Hyperelliptic Curves over Finite Fields},
    booktitle = {ANTS IV},
    year = {2000},
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}

@article{Gaudry_kummer_2007,
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}

@incollection{HanleyKimTunstall_addchain_2015,
  title={Exploiting collisions in addition chain-based exponentiation algorithms using a single trace},
  author={Hanley, N. and Kim, H. and Tunstall, M.},
  booktitle={Topics in Cryptology---CT-RSA 2015},
  pages={431--448},
  year={2015},
  publisher={Springer},
}


@unpublished{Harley_explicit_2000,
author = {Harley, R.},
year = {2000},
title = {Fast Arithmetic on Genus Two Curves},
note = {Available at \url{http://cristal.inria.fr/~harley/hyper}},
journal = {ACM Transactions in Embedded Computing Systems - TECS},
}


@unpublished{Lange_explicitformulas_2017,
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    note = { Available at \url{https://hyperelliptic.org/EFD/}},
    title = {Explicit-formulas database},
    year = {2017},
}

@unpublished{Lindner_g2arithmetic_2017,
    author = {S.A. Lindner},
    note = { Available at \url{https://github.com/salindne/g2Arithmetic}},
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    year = {2017},
}

@phdthesis{Hisil_linalgtrick_2010,
author = {H. Hisil},
school = {Queensland University of Technology},
title = {Elliptic curves, group law, and efficient computation},
year = {2010},
}


@incollection{HisilCostello_jaccoord_2014,
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  author={Hisil, H. and Costello, C.},
  booktitle={Advances in Cryptology--ASIACRYPT 2014},
  pages={338--357},
  year={2014},
  publisher={Springer},
}

@incollection{HommaMiyamotoAokiSatohShamir_collision_2008,
  title={Collision-based power analysis of modular exponentiation using chosen-message pairs},
  author={Homma, N. and Miyamoto, A. and Aoki, T. and Satoh, A. and Shamir, A.},
  booktitle={Cryptographic Hardware and Embedded Systems--CHES 2008},
  pages={15--29},
  year={2008},
  publisher={Springer},
}

@inproceedings{ImbertJacobsonSchmidt_NUCOMP_2010,
author = {L. Imbert and M. J. Jacobson and A. Schmidt},
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booktitle = {Advances in Mathematics of Communications},
year = {2010},
number = {2},
series = {4},
pages = {237-260},
}

@inproceedings{Joye_regmaryladder_2009,
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  author={Joye, M.},
  booktitle={Selected Areas in Cryptography},
  pages={350-363},
  year={2009},
  organization={Springer},
}

@incollection{Joye_recoding_2009,
  title={Exponent recoding and regular exponentiation algorithms},
  author={Joye, M. and Tunstall, M.},
  booktitle={Progress in Cryptology--AFRICACRYPT 2009},
  pages={334--349},
  year={2009},
  publisher={Springer},
}

@inproceedings{Joye_rtlalg_2007,
  title={Highly regular right-to-left algorithms for scalar multiplication},
  author={Joye, M.},
  volume={4727},
  booktitle={LNCS},
  pages={135-147},
  year={2007},
  organization={CHES 2007},
}

@article{KaratsubaOfman_polymul_1963,
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year = {1963},
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@article{Koblitz_ecc_1987,
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@article{Lange_explicit_2005,
author = {T. Lange},
journal = {Applicable Algebra in Engineering, Communications and Computing},
title = {Formulae for Arithmetic on Genus 2 Hyperelliptic Cruves},
volume = {15},
year = {2005},
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publisher = {Spring-Verlag},
}

@article{Lauter_geo_2003,
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volume = {324},
year = {2003},
publisher = {American Mathematicl Society},
}

@article{Lauter_wireless_2004,
author = {K. Lauter},
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title = {The advantages of elliptic curve cryptography for wireless security},
year = {2004},
}

@article{LongaSica_4DGLV_2014,
  title={Four-dimensional Gallant--Lambert--Vanstone scalar multiplication},
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  number={2},
  pages={248--283},
  year={2014},
  publisher={Springer},
}

@misc{Meloni_addchains_2006,
   author       = {N. Meloni},
   title        = {Fast and secure elliptic curve scalar multiplication over prime fields using special addition chains},
   howpublished = {Cryptology ePrint Archive, Report 2006/216},
   year         = {2006},
   note         = {\url{http://eprint.iacr.org/}},
}

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author = {A. Menezes and Y. Wu and R. Zuccherato},
title = {An Elementary Introduction to Hyperelliptic Curves},
institution = {Center for Applied Cryptorgraphy Research (CACR)},
number = {CORR 1996-19},
year={1996},
note = {Available at \url{http://www.cacr.math.uwaterloo.ca/}},
}

@inproceedings{Miller_ecc_1986,
author = {V. S. Miller},
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pages = {417-426},
title = {Use of elliptic curves in cryptography},
year = {1986},
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volume = {218 0f Lecture Notes in Computer Science},
publisher = {Springer, Heidleberg},
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@incollection{Moller_SCA_2001,
  title={Securing elliptic curve point multiplication against side-channel attacks},
  author={M{\"o}ller, B.},
  booktitle={Information Security},
  pages={324--334},
  year={2001},
  publisher={Springer},
}


@inproceedings{Nagao_highprob_2000,
author = {K. Nagao},
title = { Improving Group Law Algorithms for Jacobians of Hyperelliptic Curves},
booktitle = {ANTS IV},
volume = {ser. LNCS 1838},
pages = {439-448},
editor = {W. Bosma},
address = {Berlin},
publisher = {Springer-Verlag},
year = {2000},
}

@misc{RenesCostelloBatina_complete_2015,
  title={Complete addition formulas for prime order elliptic curves},
  author={Renes, J. and Costello, C. and Batina, L.},
   howpublished = {Cryptology ePrint Archive, Report 2015/1060},
   year         = {2015},
   note         = {\url{http://eprint.iacr.org/}},
}

@inproceedings{Takahashi_inversiontrick_2002,
author = {M. Takahashi},
publisher = {IEICE Japan},
booktitle = {Proceedings of {SCIS 2002}},
note = {In Japanese},
title = "Improving {H}arley Algorithms for Jacobians of Genus 2 Hyperelliptic Curves",
year = 2002,
pages = {497--502}
}

@inproceedings{Walter_bigmac_2001,
  title={Sliding windows succumbs to Big Mac attack},
  author={Walter, C.D.},
  booktitle={Cryptographic Hardware and Embedded Systems, {CHES 2001}},
  pages={286--299},
  year={2001},
  organization={Springer},
}

@article{WollingerPelzlPaar_g2explicit_2005,
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journal = {IEEE, Transactions on Computers},
pages = {861-872},
title = {Cantor versus Harley: Optimization and Analysis of Explicit Formulae for Hyperelliptic Curve Cryptosystems},
volume = {54},
year = {2005},
}

@inproceedings{WollingerKovtun_proj_2007,
author = {T. Wollinger and V. Kovtun},
booktitle = {Fourth International Conference on Information Technology},
pages = {893-897},
title = {Fast explicit formulae for genus 2 hyperelliptic curves using projective coordinates},
year = {2007},
}

@phdthesis{Wollinger_PhD_2004,
author = {T. Wollinger},
school = {Bochum Germany},
title = {Software and hardware implementation of hyperelliptic curve cryptosystems},
year = {2004},
}

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year = {2006},
}

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@book{MCA_2003,
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}

@InProceedings{Coron99,
  author = 	 {J.S. Coron},
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@Article{YenJoy00,
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  number = 	 9,
  pages = 	 {967--970}
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@Article{Montgomery87,
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@InProceedings{JoyYen02,
  author = 	 {M. Joye and S.M. Yen},
  title = 	 {The {Montgomery} Powering Ladder},
  booktitle =	 {Cryptographic Hardware and Embedded Systems, {CHES'02}},
  pages =	 {291--302},
  year =	 2002,
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  series =	 LNCS
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@Book{Knuth:vol2,
  author =	 {D.E. Knuth},
  title =	 {The Art of Computer Programming, Vol. 2: Seminumerical Algorithms},
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@InProceedings{BruTuv11:Remote_Timing_Still_Practical,
  author = 	 {B.B. Brumley and N. Tuveri},
  title = 	 {Remote Timing Attacks are Still Practical},
  booktitle = {Computer Security, {ESORICS 2011}},
  pages = 	 {355--371},
  year = 	 2011,
  volume = 	 6879,
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  publisher = {Springer},
  doi={10.1007/978-3-642-23822-2_20}
}

@InCollection{FanVer12,
  author = 	 {J. Fan and I. Verbauwhede},
  title = 	 {An Updated Survey on Secure {ECC} Implementations: Attacks, Countermeasures and Cost},
  booktitle = 	 {Cryptography and Security: From Theory to Applications},
  pages = 	 {265--282},
  publisher =    {Springer},
  year = 	 2012,
  volume = 	 6805,
  series = 	 LNCS,
  doi =          {10.1007/978-3-642-28368-0_18}
}

@article{fan_g3_2006,
  title={Efficient explicit formulae for genus 3 hyperelliptic curve cryptosystems over binary fields},
  author={X. Fan and  T. Wollinger and G. Gong},
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  number={2},
  pages={65--81},
  year={2007},
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@book{HandbookFF_2013,
  title={Handbook of finite fields},
  author={Mullen, G.L. and Panario, D.},
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}


@ARTICLE{Sutherland_g3_2019,
   AUTHOR = "Sutherland, A.V.",
   TITLE = "Fast {J}acobian arithmetic for hyperelliptic curves of genus 3",
   BOOKTITLE = "Algorithmic Number Theory - ANTS-XIII",
   ADDRESS = "Madison, USA",
   JOURNAL = "The Open Book Series",
   VOLUME = "2",
   NUMBER = "1",
   PUBLISHER = "Mathematical Sciences Publishers",
   YEAR = "2018",
   PAGES = "425-442" }

@phdthesis{Morales_balanced_2009,
  title={Efficient arithmetic on hyperelliptic curves with real representation},
  author={Mireles-Morales, D.J.M.},
  year={2009},
  school={University of London}
}

@article{Monireh_comp_2014,
  title={Comparison of scalar multiplication on real hyperelliptic curves.},
  author={Jacobson, M.J. and Rad, M.R. and Scheidler, R.},
  journal={Advances in Mathematics of Communication},
  volume={8},
  number={4},
  pages={389--406},
  year={2014}
}

@incollection{jacobson_fast_2007,
  title={Fast arithmetic on hyperelliptic curves via continued fraction expansions},
  author={Jacobson, M.J. and Scheidler, R. and Stein, A.},
  booktitle={Advances in coding theory and cryptography},
  pages={200--243},
  year={2007},
  publisher={World Scientific}
}



@article{Jacobson_real_2007,
  title={Cryptographic protocols on real hyperelliptic curves},
  author={Jacobson, M.J. and Scheidler, R. and Stein, A.},
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  volume={1},
  number={2},
  pages={197},
  year={2007},
  publisher={AMERICAN INSTITUTE OF MATHEMATICAL SCIENCES}
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@inproceedings{Kedlaya_lseries_2008,
  title={Computing L-series of hyperelliptic curves},
  author={Kedlaya, K.S. and Sutherland, A.V.},
  booktitle={International Algorithmic Number Theory Symposium},
  pages={312--326},
  year={2008},
  organization={Springer}
}


@book{Galbraith_PKC_2012,
  author    = {Galbraith, S.D.},
  title     = {Mathematics of Public Key Cryptography},
  publisher = {Cambridge University Press},
  year      = {2012},
}

@Article{ImbJac13:amc,
  author = 	 {L. Imbert and {Jacobson Jr.}, M. J.},
  title = 	 {Empirical optimization of divisor arithmetic on hyperelliptic curves over
 $\mathbb{F}_{2^m}$},
  journal = 	 {Advances in Mathematics of Communication},
  year = 	 2013,
  volume = 	 7,
  number = 	 4,
  pages = 	 {485--502},
  doi =          {doi:10.3934/amc.2013.7.485}
}

@article{khuri_Jac_2018,
  title={On Jacobian group arithmetic for typical divisors on curves},
  author={Khuri-Makdisi, Kamal},
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  volume={4},
  number={1},
  pages={3},
  year={2018},
  publisher={Springer}
}


@INPROCEEDINGS{ShanksNUCOMP,
  AUTHOR = "D. Shanks",
  TITLE = "On {G}auss and composition {I}, {II}",
  BOOKTITLE = "Proc. NATO ASI on Number Theory and Applications",
  PUBLISHER = "Kluwer Academic Press",
  EDITOR = "R.A. Mollin",
  YEAR = "1989",
  PAGES = "163-179" 
}


@INPROCEEDINGS{jacobson_nucomp_2002,
   AUTHOR = "Jacobson, Jr., M. J. and A. J. van der Poorten",
   TITLE = "Computational Aspects of {NUCOMP}",
   BOOKTITLE = "Algorithmic Number Theory - ANTS-V",
   ADDRESS = "Sydney, Australia",
   SERIES = "Lecture Notes in Computer Science",
   VOLUME = "2369",
   PUBLISHER = "Springer-Verlag, Berlin",
   YEAR = "2002",
   PAGES = "120-133" }
   
@INPROCEEDINGS{Galbraith_balanced_2008,
   AUTHOR = "Galbraith, S. D. and Harrison, M. and Mireles-Morales, D. J.",
   TITLE = "Efficient hyperelliptic arithmetic using balanced representation for divisors",
   BOOKTITLE = "Algorithmic Number Theory - ANTS-VIII",
   ADDRESS = "Banff, Canada",
   SERIES = "Lecture Notes in Computer Science",
   VOLUME = "5011",
   PUBLISHER = "Springer-Verlag, Berlin",
   YEAR = "2008",
   PAGES = "342-356" }
   

@BOOK{JWPellBook,
   AUTHOR = "Jacobson, Jr., M. J. and H. C. Williams",
   TITLE = "Solving the {P}ell Equation",
   PUBLISHER = "Springer-Verlag",
   SERIES = "CMS Books in Mathematics",
   NOTE = "ISBN 978-0-387-84922-5",
   YEAR = "2009"  
}

@unpublished{LindnerBal20:ANTS,
author = "S. A. Lindner and L. Imbert and Jacobson, Jr., M. J.",
title = "Balanced NUCOMP",
note = "submitted",
}

@unpublished{LindnerBal20:CASC,
author = "S. A. Lindner and L. Imbert and Jacobson, Jr., M. J.",
title = "Balanced NUCOMP",
note = "submitted",
}

@inproceedings{rad2019jacobian,
  title={Jacobian Versus Infrastructure in Split Hyperelliptic Curves},
  author={M. Rezai Rad and M. J. Jacobson and R. Scheidler},
  booktitle={Algebra, Codes and Cryptology},
  series={Communications in Computer and Information Science},
  volume={1133},
  pages={183--203},
  year={2019},
  organization={Springer}
}

@inproceedings{harasawa2000fast,
  title={Fast Jacobian group arithmetic on $C_{ab}$ curves},
  author={Harasawa, Ryuichi and Suzuki, Joe},
  BOOKTITLE = "Algorithmic Number Theory - ANTS-IV",
  ADDRESS = "Leiden, Netherlands",
  SERIES = "Lecture Notes in Computer Science",
  VOLUME = "1838",
  PUBLISHER = "Springer-Verlag, Berlin",
  YEAR = "2000",
  PAGES = "359-376" }

@ARTICLE{shaska_2019,
       author = "Shashka, T. and Kopeliovich, Y.",
        title = "{The addition on Jacobian varieties from a geometric viewpoint}",
      journal = {arXiv e-prints},
     keywords = {Mathematics - Number Theory, 14H05, 14H40 (Primary), 14H55, 94A60 (Secondary)},
         year = "2019",
        month = "Oct",
          eid = {arXiv:1907.11070v2},
        pages = {arXiv:1907.11070v2},
archivePrefix = {arXiv},
       eprint = {1907.11070v2},
 primaryClass = {math.NT}
}

@ARTICLE{evan_g3,
   AUTHOR = "MacNeil, E. and Jacobson Jr., M.J. and  Scheidler, R.",
   TITLE = "Divisor class group arithmetic on non-hyperelliptic genus 3 curves",
   BOOKTITLE = "Algorithmic Number Theory - ANTS-XIV",
   ADDRESS = "Aukland, New Zealand",
   JOURNAL = "The Open Book Series",
   VOLUME ="2",
   PUBLISHER = "Mathematical Sciences Publishers",
   YEAR = "2020",
}

@inproceedings{basiri2004implementing,
  title={Implementing the arithmetic of C 3, 4 curves},
  author={Basiri, Abdolali and Enge, Andreas and Faugere, Jean-Charles and G{\"u}rel, Nicolas},
  booktitle={International Algorithmic Number Theory Symposium},
  pages={87--101},
  year={2004},
  organization={Springer}
}