-
Previous Article
Subexponential time relations in the class group of large degree number fields
- AMC Home
- This Issue
-
Next Article
Trisection for supersingular genus $2$ curves in characteristic $2$
Comparison of scalar multiplication on real hyperelliptic curves
1. | Department of Computer Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4, Canada |
2. | Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4, Canada, Canada |
References:
[1] |
E. Barker, W. Barker, W. Polk and M. Smid, Recommendation for key management - part 1: General (revised),, NIST Special Publication 800-57, (2007), 800. Google Scholar |
[2] |
H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen and F. Vercouteren, Handbook of Elliptic and Hyperelliptic Curve Cryptography,, Chapman & Hall/CRC, (2006).
doi: 10.1201/9781420034981. |
[3] |
W. Diffie and M. Hellman, New directions in cryptography,, IEEE Trans. Inf. Theory, 22 (1976), 472.
doi: 10.1109/TIT.1976.1055638. |
[4] |
S. Erickson, M. J. Jacobson, Jr. and A. Stein, Explicit formulas for real hyperelliptic curves of genus $2$ in affine representation,, Adv. Math. Commun., 5 (2011), 623.
doi: 10.3934/amc.2011.5.623. |
[5] |
F. Fontein, Groups from cyclic infrastructures and Pohlig-Hellman in certain infrastructures,, Adv. Math. Commun., 2 (2008), 293.
doi: 10.3934/amc.2008.2.293. |
[6] |
F. Fontein, Holes in the infrastructure of global hyperelliptic function fields,, preprint, (). Google Scholar |
[7] |
E. Friedman and L. C. Washington, On the distribution of divisor class groups of curves over a finite field,, Théorie des Nombres (Québec, (1989), 227.
|
[8] |
S. D. Galbraith, M. Harrison and D. J. Mireles Morales, Efficient hyperelliptic curve arithmetic using balanced representation for divisors,, in Algorithmic Number Theory - ANTS 2008 (Berlin), (2008), 342.
doi: 10.1007/978-3-540-79456-1_23. |
[9] |
M. J. Jacobson, Jr., R. Scheidler and A. Stein, Cryptographic protocols on real hyperelliptic curves,, Adv. Math. Commun., 1 (2007), 197.
doi: 10.3934/amc.2007.1.197. |
[10] |
M. J. Jacobson, Jr., R. Scheidler and A. Stein, Fast arithmetic on hyperelliptic curves via continued fraction expansions,, in Advances in Coding Theory and Cryptology (eds. T. Shaska, (2007), 201.
doi: 10.1142/9789812772022_0013. |
[11] |
M. J. Jacobson, Jr., R. Scheidler and A. Stein, Cryptographic aspects of real hyperelliptic curves,, Tatra Mountains Math. Publ., 40 (2010), 1.
doi: 10.2478/v10127-010-0030-9. |
[12] |
N. Koblitz, Hyperelliptic cryptosystems,, J. Cryptology, 1 (1989), 139.
doi: 10.1007/BF02252872. |
[13] |
T. Lange, Formulae for arithmetic on genus 2 hyperelliptic curves,, Appl. Algebra Eng. Commun. Comput., 15 (2005), 295.
doi: 10.1007/s00200-004-0154-8. |
[14] |
D. J. Mireles Morales, An analysis of the infrastructure in real function fields,, Cryptology eprint archive no. 2008/299, (2008). Google Scholar |
[15] |
R. Scheidler, J. A. Buchmann and H. C. Williams, A key exchange protocol using real quadratic fields,, J. Cryptology, 7 (1994), 171.
doi: 10.1007/BF02318548. |
[16] |
R. Scheidler, A. Stein and H. C. Williams, Key-exchange in real quadratic congruence function fields,, Des. Codes Crypt., 7 (1996), 153.
doi: 10.1007/BF00125081. |
[17] |
V. Shoup, NTL: A Library for doing Number Theory (version 5.4.2),, , (2008). Google Scholar |
[18] |
A. Stein, Explicit infrastructure for real quadratic function fields and real hyperelliptic curves,, Glas. Mat. Ser. III, 44(64) (2009), 89.
doi: 10.3336/gm.44.1.05. |
show all references
References:
[1] |
E. Barker, W. Barker, W. Polk and M. Smid, Recommendation for key management - part 1: General (revised),, NIST Special Publication 800-57, (2007), 800. Google Scholar |
[2] |
H. Cohen, G. Frey, R. Avanzi, C. Doche, T. Lange, K. Nguyen and F. Vercouteren, Handbook of Elliptic and Hyperelliptic Curve Cryptography,, Chapman & Hall/CRC, (2006).
doi: 10.1201/9781420034981. |
[3] |
W. Diffie and M. Hellman, New directions in cryptography,, IEEE Trans. Inf. Theory, 22 (1976), 472.
doi: 10.1109/TIT.1976.1055638. |
[4] |
S. Erickson, M. J. Jacobson, Jr. and A. Stein, Explicit formulas for real hyperelliptic curves of genus $2$ in affine representation,, Adv. Math. Commun., 5 (2011), 623.
doi: 10.3934/amc.2011.5.623. |
[5] |
F. Fontein, Groups from cyclic infrastructures and Pohlig-Hellman in certain infrastructures,, Adv. Math. Commun., 2 (2008), 293.
doi: 10.3934/amc.2008.2.293. |
[6] |
F. Fontein, Holes in the infrastructure of global hyperelliptic function fields,, preprint, (). Google Scholar |
[7] |
E. Friedman and L. C. Washington, On the distribution of divisor class groups of curves over a finite field,, Théorie des Nombres (Québec, (1989), 227.
|
[8] |
S. D. Galbraith, M. Harrison and D. J. Mireles Morales, Efficient hyperelliptic curve arithmetic using balanced representation for divisors,, in Algorithmic Number Theory - ANTS 2008 (Berlin), (2008), 342.
doi: 10.1007/978-3-540-79456-1_23. |
[9] |
M. J. Jacobson, Jr., R. Scheidler and A. Stein, Cryptographic protocols on real hyperelliptic curves,, Adv. Math. Commun., 1 (2007), 197.
doi: 10.3934/amc.2007.1.197. |
[10] |
M. J. Jacobson, Jr., R. Scheidler and A. Stein, Fast arithmetic on hyperelliptic curves via continued fraction expansions,, in Advances in Coding Theory and Cryptology (eds. T. Shaska, (2007), 201.
doi: 10.1142/9789812772022_0013. |
[11] |
M. J. Jacobson, Jr., R. Scheidler and A. Stein, Cryptographic aspects of real hyperelliptic curves,, Tatra Mountains Math. Publ., 40 (2010), 1.
doi: 10.2478/v10127-010-0030-9. |
[12] |
N. Koblitz, Hyperelliptic cryptosystems,, J. Cryptology, 1 (1989), 139.
doi: 10.1007/BF02252872. |
[13] |
T. Lange, Formulae for arithmetic on genus 2 hyperelliptic curves,, Appl. Algebra Eng. Commun. Comput., 15 (2005), 295.
doi: 10.1007/s00200-004-0154-8. |
[14] |
D. J. Mireles Morales, An analysis of the infrastructure in real function fields,, Cryptology eprint archive no. 2008/299, (2008). Google Scholar |
[15] |
R. Scheidler, J. A. Buchmann and H. C. Williams, A key exchange protocol using real quadratic fields,, J. Cryptology, 7 (1994), 171.
doi: 10.1007/BF02318548. |
[16] |
R. Scheidler, A. Stein and H. C. Williams, Key-exchange in real quadratic congruence function fields,, Des. Codes Crypt., 7 (1996), 153.
doi: 10.1007/BF00125081. |
[17] |
V. Shoup, NTL: A Library for doing Number Theory (version 5.4.2),, , (2008). Google Scholar |
[18] |
A. Stein, Explicit infrastructure for real quadratic function fields and real hyperelliptic curves,, Glas. Mat. Ser. III, 44(64) (2009), 89.
doi: 10.3336/gm.44.1.05. |
[1] |
Akbar Mahmoodi Rishakani, Seyed Mojtaba Dehnavi, Mohmmadreza Mirzaee Shamsabad, Nasour Bagheri. Cryptographic properties of cyclic binary matrices. Advances in Mathematics of Communications, 2021, 15 (2) : 311-327. doi: 10.3934/amc.2020068 |
[2] |
José Madrid, João P. G. Ramos. On optimal autocorrelation inequalities on the real line. Communications on Pure & Applied Analysis, 2021, 20 (1) : 369-388. doi: 10.3934/cpaa.2020271 |
[3] |
Haiyu Liu, Rongmin Zhu, Yuxian Geng. Gorenstein global dimensions relative to balanced pairs. Electronic Research Archive, 2020, 28 (4) : 1563-1571. doi: 10.3934/era.2020082 |
[4] |
Yuxi Zheng. Absorption of characteristics by sonic curve of the two-dimensional Euler equations. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 605-616. doi: 10.3934/dcds.2009.23.605 |
[5] |
Takiko Sasaki. Convergence of a blow-up curve for a semilinear wave equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1133-1143. doi: 10.3934/dcdss.2020388 |
[6] |
Noah Stevenson, Ian Tice. A truncated real interpolation method and characterizations of screened Sobolev spaces. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5509-5566. doi: 10.3934/cpaa.2020250 |
[7] |
Djamel Aaid, Amel Noui, Özen Özer. Piecewise quadratic bounding functions for finding real roots of polynomials. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 63-73. doi: 10.3934/naco.2020015 |
[8] |
Masaharu Taniguchi. Axisymmetric traveling fronts in balanced bistable reaction-diffusion equations. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3981-3995. doi: 10.3934/dcds.2020126 |
[9] |
Joan Carles Tatjer, Arturo Vieiro. Dynamics of the QR-flow for upper Hessenberg real matrices. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1359-1403. doi: 10.3934/dcdsb.2020166 |
[10] |
Michiel Bertsch, Flavia Smarrazzo, Andrea Terracina, Alberto Tesei. Signed Radon measure-valued solutions of flux saturated scalar conservation laws. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3143-3169. doi: 10.3934/dcds.2020041 |
[11] |
Huanhuan Tian, Maoan Han. Limit cycle bifurcations of piecewise smooth near-Hamiltonian systems with a switching curve. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020368 |
[12] |
Kengo Nakai, Yoshitaka Saiki. Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1079-1092. doi: 10.3934/dcdss.2020352 |
[13] |
Gheorghe Craciun, Jiaxin Jin, Casian Pantea, Adrian Tudorascu. Convergence to the complex balanced equilibrium for some chemical reaction-diffusion systems with boundary equilibria. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1305-1335. doi: 10.3934/dcdsb.2020164 |
[14] |
Peter Frolkovič, Karol Mikula, Jooyoung Hahn, Dirk Martin, Branislav Basara. Flux balanced approximation with least-squares gradient for diffusion equation on polyhedral mesh. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 865-879. doi: 10.3934/dcdss.2020350 |
[15] |
Guoliang Zhang, Shaoqin Zheng, Tao Xiong. A conservative semi-Lagrangian finite difference WENO scheme based on exponential integrator for one-dimensional scalar nonlinear hyperbolic equations. Electronic Research Archive, 2021, 29 (1) : 1819-1839. doi: 10.3934/era.2020093 |
2019 Impact Factor: 0.734
Tools
Metrics
Other articles
by authors
[Back to Top]