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Efficient reduction of large divisors on hyperelliptic curves
1. | Fakultät für Mathematik, Ruhr-Universität Bochum and Horst Gösrtz Institut für IT-Sicherheit, Universitätsstraße 150, D-44780 Bochum |
2. | Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4, Canada |
3. | Department of Mathematics & Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4, Canada |
[1] |
Michael J. Jacobson, Jr., Monireh Rezai Rad, Renate Scheidler. Comparison of scalar multiplication on real hyperelliptic curves. Advances in Mathematics of Communications, 2014, 8 (4) : 389-406. doi: 10.3934/amc.2014.8.389 |
[2] |
Kwang Ho Kim, Junyop Choe, Song Yun Kim, Namsu Kim, Sekung Hong. Speeding up regular elliptic curve scalar multiplication without precomputation. Advances in Mathematics of Communications, 2020, 14 (4) : 703-726. doi: 10.3934/amc.2020090 |
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Deepak Kumar, Ahmad Jazlan, Victor Sreeram, Roberto Togneri. Partial fraction expansion based frequency weighted model reduction for discrete-time systems. Numerical Algebra, Control and Optimization, 2016, 6 (3) : 329-337. doi: 10.3934/naco.2016015 |
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Svetlana Katok, Ilie Ugarcovici. Theory of $(a,b)$-continued fraction transformations and applications. Electronic Research Announcements, 2010, 17: 20-33. doi: 10.3934/era.2010.17.20 |
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Charlene Kalle, Niels Langeveld, Marta Maggioni, Sara Munday. Matching for a family of infinite measure continued fraction transformations. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 6309-6330. doi: 10.3934/dcds.2020281 |
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Svetlana Katok, Ilie Ugarcovici. Structure of attractors for $(a,b)$-continued fraction transformations. Journal of Modern Dynamics, 2010, 4 (4) : 637-691. doi: 10.3934/jmd.2010.4.637 |
[7] |
Laurent Imbert, Michael J. Jacobson, Jr.. Empirical optimization of divisor arithmetic on hyperelliptic curves over $\mathbb{F}_{2^m}$. Advances in Mathematics of Communications, 2013, 7 (4) : 485-502. doi: 10.3934/amc.2013.7.485 |
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Roberto Avanzi, Nicolas Thériault. A filtering method for the hyperelliptic curve index calculus and its analysis. Advances in Mathematics of Communications, 2010, 4 (2) : 189-213. doi: 10.3934/amc.2010.4.189 |
[9] |
Laura Luzzi, Stefano Marmi. On the entropy of Japanese continued fractions. Discrete and Continuous Dynamical Systems, 2008, 20 (3) : 673-711. doi: 10.3934/dcds.2008.20.673 |
[10] |
Pierre Arnoux, Thomas A. Schmidt. Commensurable continued fractions. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4389-4418. doi: 10.3934/dcds.2014.34.4389 |
[11] |
M. J. Jacobson, R. Scheidler, A. Stein. Cryptographic protocols on real hyperelliptic curves. Advances in Mathematics of Communications, 2007, 1 (2) : 197-221. doi: 10.3934/amc.2007.1.197 |
[12] |
D. Novikov and S. Yakovenko. Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems. Electronic Research Announcements, 1999, 5: 55-65. |
[13] |
Frank Trujillo. Uniqueness properties of the KAM curve. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 5165-5182. doi: 10.3934/dcds.2021072 |
[14] |
Claudio Bonanno, Carlo Carminati, Stefano Isola, Giulio Tiozzo. Dynamics of continued fractions and kneading sequences of unimodal maps. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1313-1332. doi: 10.3934/dcds.2013.33.1313 |
[15] |
Élise Janvresse, Benoît Rittaud, Thierry de la Rue. Dynamics of $\lambda$-continued fractions and $\beta$-shifts. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 1477-1498. doi: 10.3934/dcds.2013.33.1477 |
[16] |
Bertrand Lods. Variational characterizations of the effective multiplication factor of a nuclear reactor core. Kinetic and Related Models, 2009, 2 (2) : 307-331. doi: 10.3934/krm.2009.2.307 |
[17] |
Christopher C. Tisdell. Reimagining multiplication as diagrammatic and dynamic concepts via cutting, pasting and rescaling actions. STEM Education, 2021, 1 (3) : 170-185. doi: 10.3934/steme.2021013 |
[18] |
Sebastian J. Schreiber. Expansion rates and Lyapunov exponents. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 433-438. doi: 10.3934/dcds.1997.3.433 |
[19] |
Meina Gao. Small-divisor equation with large-variable coefficient and periodic solutions of DNLS equations. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 173-204. doi: 10.3934/dcds.2015.35.173 |
[20] |
Koray Karabina, Berkant Ustaoglu. Invalid-curve attacks on (hyper)elliptic curve cryptosystems. Advances in Mathematics of Communications, 2010, 4 (3) : 307-321. doi: 10.3934/amc.2010.4.307 |
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