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Efficient reduction of large divisors on hyperelliptic curves
1.  Fakultät für Mathematik, RuhrUniversität Bochum and Horst Gösrtz Institut für ITSicherheit, Universitätsstraße 150, D44780 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) : 389406. 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) : 703726. doi: 10.3934/amc.2020090 
[3] 
Deepak Kumar, Ahmad Jazlan, Victor Sreeram, Roberto Togneri. Partial fraction expansion based frequency weighted model reduction for discretetime systems. Numerical Algebra, Control and Optimization, 2016, 6 (3) : 329337. doi: 10.3934/naco.2016015 
[4] 
Svetlana Katok, Ilie Ugarcovici. Theory of $(a,b)$continued fraction transformations and applications. Electronic Research Announcements, 2010, 17: 2033. doi: 10.3934/era.2010.17.20 
[5] 
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) : 63096330. doi: 10.3934/dcds.2020281 
[6] 
Svetlana Katok, Ilie Ugarcovici. Structure of attractors for $(a,b)$continued fraction transformations. Journal of Modern Dynamics, 2010, 4 (4) : 637691. 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) : 485502. doi: 10.3934/amc.2013.7.485 
[8] 
Roberto Avanzi, Nicolas Thériault. A filtering method for the hyperelliptic curve index calculus and its analysis. Advances in Mathematics of Communications, 2010, 4 (2) : 189213. 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) : 673711. doi: 10.3934/dcds.2008.20.673 
[10] 
Pierre Arnoux, Thomas A. Schmidt. Commensurable continued fractions. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 43894418. 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) : 197221. 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: 5565. 
[13] 
Frank Trujillo. Uniqueness properties of the KAM curve. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 51655182. 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) : 13131332. 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) : 14771498. 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) : 307331. 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) : 170185. doi: 10.3934/steme.2021013 
[18] 
Sebastian J. Schreiber. Expansion rates and Lyapunov exponents. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 433438. doi: 10.3934/dcds.1997.3.433 
[19] 
Meina Gao. Smalldivisor equation with largevariable coefficient and periodic solutions of DNLS equations. Discrete and Continuous Dynamical Systems, 2015, 35 (1) : 173204. doi: 10.3934/dcds.2015.35.173 
[20] 
Koray Karabina, Berkant Ustaoglu. Invalidcurve attacks on (hyper)elliptic curve cryptosystems. Advances in Mathematics of Communications, 2010, 4 (3) : 307321. doi: 10.3934/amc.2010.4.307 
2020 Impact Factor: 0.935
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