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@article{addchainreview,
title = "A Review on Heuristics for Addition Chain Problem: Towards Efficient Public Key Cryptosystems",
author = "Adamu Muhammad Noma and Abdullah Muhammed and Mohamad Afendee Mohamed and Zuriati Ahmad Zulkarnain",
url = "https://thescipub.com/pdf/10.3844/jcssp.2017.275.289.pdf",
journal = "Journal of Computer Science",
number = 8,
pages = "275-289",
volume = 13,
year = 2017,
}
@misc{aranha,
title = "A note on high-security general-purpose elliptic curves",
author = "Diego F. Aranha and Paulo S. L. M. Barreto and Geovandro C. C. F. Pereira and Jefferson E. Ricardini",
url = "https://eprint.iacr.org/2013/647",
howpublished = "Cryptology ePrint Archive, Report 2013/647",
year = 2013,
}
@inproceedings{boscoster,
title = "Addition Chain Heuristics",
author = "Bos, Jurjen and Coster, Matthijs",
url = "https://link.springer.com/content/pdf/10.1007/0-387-34805-0_37.pdf",
abstract = "Much current research focuses on fast evaluation of RSA, which consists of computing powers modulo a large number n. While some try to increase the speed of multiplica- tions, here we consider reducing the number of multiplications. In particular, we present a precomputation method that reduces the number of multiplications for the computation of a given power.",
address = "New York, NY",
booktitle = "Advances in Cryptology --- CRYPTO' 89 Proceedings",
editor = "Brassard, Gilles",
isbn = "978-0-387-34805-6",
pages = "400--407",
publisher = "Springer New York",
year = 1990,
}
@phdthesis{braueraddsubchains,
title = "Brauer addition-subtraction chains",
author = "Martin Otto",
url = "http://www.martin-otto.de/publications/docs/2001_MartinOtto_Diplom_BrauerAddition-SubtractionChains.pdf",
school = "Universitat Paderborn",
year = 2001,
}
@article{contfrac,
title = "Addition chains using continued fractions",
author = "F Bergeron and J Berstel and S Brlek and C Duboc",
url = "http://www-igm.univ-mlv.fr/~berstel/Articles/1989AdditionChainDuboc.pdf",
issn = "0196-6774",
journal = "Journal of Algorithms",
number = 3,
pages = "403 - 412",
volume = 10,
year = 1989,
}
@misc{crandallprime,
title = "Method and apparatus for public key exchange in a cryptographic system",
author = "Richard E. Crandall",
url = "https://patents.google.com/patent/US5159632A",
howpublished = "US Patent 5,159,632",
year = 1992,
}
@inproceedings{curve25519,
title = "Curve25519: New Diffie-Hellman Speed Records",
author = "Bernstein, Daniel J.",
url = "https://cr.yp.to/ecdh/curve25519-20060209.pdf",
abstract = "This paper explains the design and implementation of a high-security elliptic-curve-Diffie-Hellman function achieving record-setting speeds: e.g., 832457 Pentium III cycles (with several side benefits: free key compression, free key validation, and state-of-the-art timing-attack protection), more than twice as fast as other authors' results at the same conjectured security level (with or without the side benefits).",
address = "Berlin, Heidelberg",
booktitle = "Public Key Cryptography - PKC 2006",
editor = "Yung, Moti and Dodis, Yevgeniy and Kiayias, Aggelos and Malkin, Tal",
isbn = "978-3-540-33852-9",
pages = "207--228",
publisher = "Springer Berlin Heidelberg",
year = 2006,
}
@misc{curvechains,
title = "The Most Efficient Known Addition Chains for Field Element and Scalar Inversion for the Most Popular and Most Unpopular Elliptic Curves",
author = "Brian Smith",
url = "https://briansmith.org/ecc-inversion-addition-chains-01",
urldate = "2019-06-30",
year = 2017,
}
@article{efficientcompaddchain,
title = "Efficient computation of addition chains",
author = "Bergeron, F. and Berstel, J. and Brlek, S.",
url = "http://www.numdam.org/item/JTNB_1994__6_1_21_0",
journal = "Journal de theorie des nombres de Bordeaux",
language = "en",
mrnumber = 1305286,
number = 1,
pages = "21-38",
publisher = "Universite Bordeaux I",
volume = 6,
year = 1994,
zbl = "0812.11072",
}
@misc{elligator,
title = "Elligator: Elliptic-curve points indistinguishable from uniform random strings",
author = "Daniel J. Bernstein and Mike Hamburg and Anna Krasnova and Tanja Lange",
url = "https://eprint.iacr.org/2013/325",
howpublished = "Cryptology ePrint Archive, Report 2013/325",
year = 2013,
}
@misc{fips186-2,
title = "Digital Signature Standard (DSS)",
author = "NIST",
url = "https://csrc.nist.gov/csrc/media/publications/fips/186/2/archive/2000-01-27/documents/fips186-2.pdf",
howpublished = "Federal Information Processing Standards Publication 186-2",
year = 2000,
}
@misc{gencontfrac,
title = "Efficient computation of addition-subtraction chains using generalized continued Fractions",
author = "Amadou Tall and Ali Yassin Sanghare",
url = "https://eprint.iacr.org/2013/466",
howpublished = "Cryptology ePrint Archive, Report 2013/466",
year = 2013,
}
@article{genshortchains,
title = "New Methods for Generating Short Addition Chains",
author = "Kunihiro, Noboru and Yamamoto, Hirosuke",
url = "https://pdfs.semanticscholar.org/b398/d10faca35af9ce5a6026458b251fd0a5640c.pdf",
journal = "IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences",
month = 01,
volume = "E83A",
year = 2000,
}
@misc{github:kwantam/addchain,
title = "kwantam/addchain",
author = "Riad S. Wahby",
url = "https://github.com/kwantam/addchain",
howpublished = "Github Repository",
license = "Apache License, Version 2.0",
year = 2018,
}
@misc{goldilocks,
title = "Ed448-Goldilocks, a new elliptic curve",
author = "Mike Hamburg",
url = "https://eprint.iacr.org/2015/625",
howpublished = "Cryptology ePrint Archive, Report 2015/625",
year = 2015,
}
@misc{hashbls12-381,
title = "Fast and simple constant-time hashing to the BLS12-381 elliptic curve",
author = "Riad S. Wahby and Dan Boneh",
url = "https://eprint.iacr.org/2019/403",
howpublished = "Cryptology ePrint Archive, Report 2019/403",
year = 2019,
}
@inbook{hehcc:exp,
title = "Exponentiation",
author = "Christophe Doche",
url = "http://koclab.cs.ucsb.edu/teaching/ecc/eccPapers/Doche-ch09.pdf",
booktitle = "Handbook of Elliptic and Hyperelliptic Curve Cryptography",
chapter = 9,
publisher = "Chapman and Hall",
year = 2006,
}
@inbook{knuth,
title = "Evaluation of Powers",
author = "Knuth, Donald E.",
url = "https://www-cs-faculty.stanford.edu/~knuth/taocp.html",
booktitle = "The Art of Computer Programming, Volume 2 (Third Edition): Seminumerical Algorithms",
chapter = "4.6.3",
publisher = "Addison-Wesley Longman Publishing Co., Inc.",
year = 1997,
}
@mastersthesis{modboscoster,
title = "Modifications of Bos and Coster’s Heuristics in search of a shorter addition chain for faster exponentiation",
author = "Ayan Nandy",
url = "http://library.isical.ac.in:8080/jspui/bitstream/10263/6441/1/DISS-285.pdf",
school = "Indian Statistical Institute Kolkata",
year = 2011,
}
@techreport{mpnt,
title = "MpNT: A Multi-Precision Number Theory Package, Number Theoretical Algorithms (I)",
author = "F. L. Ţiplea and S. Iftene and C. Hriţcu and I. Goriac and R. Gordân and E. Erbiceanu",
url = "https://profs.info.uaic.ro/~tr/tr03-02.pdf",
institution = {Faculty of Computer Science, "Alexandru Ioan Cuza" University, Iasi},
number = "TR03-02",
year = 2003,
}
@misc{nistdanger,
title = "Security dangers of the NIST curves",
author = "Daniel J. Bernstein and Tanja Lange",
url = "https://cr.yp.to/talks/2013.09.16/slides-djb-20130916-a4.pdf",
year = 2013,
}
@misc{pairingsfinalexp,
title = "On the final exponentiation for calculating pairings on ordinary elliptic curves",
author = "Michael Scott and Naomi Benger and Manuel Charlemagne and Luis J. Dominguez Perez and Ezekiel J. Kachisa",
url = "https://eprint.iacr.org/2008/490",
howpublished = "Cryptology ePrint Archive, Report 2008/490",
year = 2008,
}
@misc{safecurves,
title = "SafeCurves: choosing safe curves for elliptic-curve cryptography",
author = "Daniel J. Bernstein and Tanja Lange",
url = "https://safecurves.cr.yp.to",
}
@misc{sec2,
title = "SEC 2: Recommended Elliptic Curve Domain Parameters, Version 2.0",
author = "Certicom Research",
url = "https://safecurves.cr.yp.to/www.secg.org/sec2-v2.pdf",
howpublished = "Standards for Efficient Cryptography 2",
year = 2010,
}
@techreport{solinasprime,
title = "Generalized Mersenne Primes",
author = "Jerome A. Solinas",
url = "http://cacr.uwaterloo.ca/techreports/1999/corr99-39.pdf",
institution = "Centre for Applied Cryptographic Research (CACR) at the University of Waterloo",
number = "CORR 99-39",
year = 1999,
}
@phdthesis{speedsubgroup,
title = "Speeding up subgroup cryptosystems",
author = "Stam, Martijn",
url = "https://cr.yp.to/bib/2003/stam-thesis.pdf",
school = "Technische Universiteit Eindhoven",
year = 2003,
}
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