f5c0b6245d
* Productionize multipairings for BLS12-381 * typo * arg order + benchmark * Introduce mul_3way_sparse_sparse * cleanup MultiMiller loop * fix init sparse optimization in multimiller loop [skip ci]
Pairing-Based Cryptography primitives
References
Normative references
- Pairing-Friendly Curves
IETF Draft Specification (expires May 2020)
https://tools.ietf.org/html/draft-irtf-cfrg-pairing-friendly-curves-00#ref-KB16
Research
-
Compressed Pairings
Scott, Barreto, 2004
https://eprint.iacr.org/2004/032.pdf -
On the Implementation of Pairing-based Cryptosystems
PhD Thesis
Ben Lynn, 2007
https://crypto.stanford.edu/pbc/thesis.pdf -
On the final exponentiation for calculating
pairings on ordinary elliptic curves
Scott, Benger, Charlemagne, Perez, Kachisa, 2008
https://eprint.iacr.org/2008/490.pdf -
Faster Squaring in the Cyclotomic Subgroup of Sixth Degree Extensions
Granger, Scott, 2009
https://eprint.iacr.org/2009/565.pdf -
Faster Pairing Computations on Curves with High-Degree Twists Craig Costello, Tanja Lange, and Michael Naehrig, 2009 https://eprint.iacr.org/2009/615.pdf
-
High-Speed Software Implementation of the Optimal Ate Pairing over Barreto-Naehrig Curves
Jean-Luc Beuchat and Jorge Enrique González Díaz and Shigeo Mitsunari and Eiji Okamoto and Francisco Rodríguez-Henríquez and Tadanori Teruya, 2010
https://eprint.iacr.org/2010/354 -
An Analysis of Affine Coordinates for Pairing Computation
Kristin Lauter, Peter L. Montgomery, and Michael Naehrig, 2010
https://eprint.iacr.org/2010/363.pdf -
Faster Explicit Formulas for Computing Pairings over Ordinary Curves
Diego F. Aranha and Koray Karabina and Patrick Longa and Catherine H. Gebotys and Julio López, 2010
https://eprint.iacr.org/2010/526.pdf
https://www.iacr.org/archive/eurocrypt2011/66320047/66320047.pdf -
Avoiding Full Extension Field Arithmetic in Pairing Computations Craig Costello, Colin Boyd, Juan Manuel Gonzalez Nieto, and Kenneth Koon-Ho Wong, 2010 https://eprint.iacr.org/2010/104.pdf
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Faster hashing to G2
Laura Fuentes-Castañeda, Edward Knapp,
Francisco Jose Rodríguez-Henríquez, 2011
https://link.springer.com/content/pdf/10.1007%2F978-3-642-28496-0_25.pdf -
Pairings for beginners
Craig Costello, 2012 (?)
http://www.craigcostello.com.au/pairings/PairingsForBeginners.pdf -
Fast Formulas for Computing Cryptographic Pairings
PhD Thesis
Craig Costello, 2012
https://eprints.qut.edu.au/61037/1/Craig_Costello_Thesis.pdf -
Efficient Implementation of Bilinear Pairings on ARM Processors Gurleen Grewal, Reza Azarderakhsh, Patrick Longa, Shi Hu, and David Jao, 2012 https://eprint.iacr.org/2012/408.pdf
-
The Realm of the Pairings
Diego F. Aranha and Paulo S. L. M. Barreto
and Patrick Longa and Jefferson E. Ricardini, 2013
https://eprint.iacr.org/2013/722.pdf
http://sac2013.irmacs.sfu.ca/slides/s1.pdf -
Efficient Implementations of Pairing-Based Cryptography on Embedded Systems
Master Thesis
Rajeev Verma, 2015
https://scholarworks.rit.edu/cgi/viewcontent.cgi?referer=&httpsredir=1&article=10083&context=theses https://github.com/rajeevakarv/FiniteFieldComputations -
Memory-saving computation of the pairing final exponentiation on BN curves
Sylvain Duquesne and Loubna Ghammam, 2015
https://eprint.iacr.org/2015/192 -
Software Implementation, Aranha, Dominguez Perez, A. Mrabet, Schwabe, Guide to Pairing-Based Cryptography, 2015
-
Physical Attacks, N. El Mrabet, Goubin, Guilley, Fournier, Jauvart, Moreau, Rauzy, Rondepierre, Guide to Pairing-Based Cryptography, 2015
-
A taxonomy of pairings, their security, their complexity
Razvan Barbulescu, Nadia El Mrabet, and Loubna Ghammam, 2019
https://hal.archives-ouvertes.fr/hal-02129868/file/2019-485.pdf -
Pairing Implementation Revisited
Mike Scott, 2019
https://eprint.iacr.org/2019/077.pdf -
A short-list of pairing-friendly curves resistant to Special TNFS at the 128-bit security level
Aurore Guillevic, 2019
https://eprint.iacr.org/2019/1371.pdf -
Improving the computation of the optimal ate pairing for a high security level. Loubna Ghammam, Emmanuel Fouotsa J. Appl. Math. Comput.59, 21–36 (2019)
-
Efficient Final Exponentiation via Cyclotomic Structure for Pairings over Families of Elliptic Curves Daiki Hayashida and Kenichiro Hayasaka and Tadanori Teruya, 2020 https://eprint.iacr.org/2020/875.pdf
Presentations
- Introduction to pairings
ECC Summer School
Diego F. Aranha, 2017
https://ecc2017.cs.ru.nl/slides/ecc2017school-aranha.pdf