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Explicit 2power torsion of genus 2 curves over finite fields
Efficient implementation of elliptic curve cryptography in wireless sensors
1.  University of Campinas (UNICAMP), Campinas  SP, CEP 13083970, Brazil, Brazil, Brazil, Brazil 
[1] 
Gerhard Frey. Relations between arithmetic geometry and public key cryptography. Advances in Mathematics of Communications, 2010, 4 (2) : 281305. doi: 10.3934/amc.2010.4.281 
[2] 
Haibo Yi. Efficient systolic multiplications in composite fields for cryptographic systems. Discrete & Continuous Dynamical Systems  S, 2019, 12 (4&5) : 11351145. doi: 10.3934/dcdss.2019078 
[3] 
Florian Luca, Igor E. Shparlinski. On finite fields for pairing based cryptography. Advances in Mathematics of Communications, 2007, 1 (3) : 281286. doi: 10.3934/amc.2007.1.281 
[4] 
Huaiyu Jian, Hongjie Ju, Wei Sun. Traveling fronts of curve flow with external force field. Communications on Pure & Applied Analysis, 2010, 9 (4) : 975986. doi: 10.3934/cpaa.2010.9.975 
[5] 
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 
[6] 
Anton Stolbunov. Constructing publickey cryptographic schemes based on class group action on a set of isogenous elliptic curves. Advances in Mathematics of Communications, 2010, 4 (2) : 215235. doi: 10.3934/amc.2010.4.215 
[7] 
Steven D. Galbraith, Ping Wang, Fangguo Zhang. Computing elliptic curve discrete logarithms with improved babystep giantstep algorithm. Advances in Mathematics of Communications, 2017, 11 (3) : 453469. doi: 10.3934/amc.2017038 
[8] 
Richard Hofer, Arne Winterhof. On the arithmetic autocorrelation of the Legendre sequence. Advances in Mathematics of Communications, 2017, 11 (1) : 237244. doi: 10.3934/amc.2017015 
[9] 
Andrew P. Sage. Risk in system of systems engineering and management. Journal of Industrial & Management Optimization, 2008, 4 (3) : 477487. doi: 10.3934/jimo.2008.4.477 
[10] 
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 
[11] 
Tanja Eisner, Rainer Nagel. Arithmetic progressions  an operator theoretic view. Discrete & Continuous Dynamical Systems  S, 2013, 6 (3) : 657667. doi: 10.3934/dcdss.2013.6.657 
[12] 
Mehdi Pourbarat. On the arithmetic difference of middle Cantor sets. Discrete & Continuous Dynamical Systems  A, 2018, 38 (9) : 42594278. doi: 10.3934/dcds.2018186 
[13] 
Qichun Wang, Chik How Tan, Pantelimon Stănică. Concatenations of the hidden weighted bit function and their cryptographic properties. Advances in Mathematics of Communications, 2014, 8 (2) : 153165. doi: 10.3934/amc.2014.8.153 
[14] 
Eitan Altman. Bioinspired paradigms in network engineering games. Journal of Dynamics & Games, 2014, 1 (1) : 115. doi: 10.3934/jdg.2014.1.1 
[15] 
Ruinian Li, Yinhao Xiao, Cheng Zhang, Tianyi Song, Chunqiang Hu. Cryptographic algorithms for privacypreserving online applications. Mathematical Foundations of Computing, 2018, 1 (4) : 311330. doi: 10.3934/mfc.2018015 
[16] 
Pascale Charpin, Jie Peng. Differential uniformity and the associated codes of cryptographic functions. Advances in Mathematics of Communications, 2019, 13 (4) : 579600. doi: 10.3934/amc.2019036 
[17] 
Joseph H. Silverman. Localglobal aspects of (hyper)elliptic curves over (in)finite fields. Advances in Mathematics of Communications, 2010, 4 (2) : 101114. doi: 10.3934/amc.2010.4.101 
[18] 
WolfJüergen Beyn, Janosch Rieger. Galerkin finite element methods for semilinear elliptic differential inclusions. Discrete & Continuous Dynamical Systems  B, 2013, 18 (2) : 295312. doi: 10.3934/dcdsb.2013.18.295 
[19] 
Lijuan Wang, Jun Zou. Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems. Discrete & Continuous Dynamical Systems  B, 2010, 14 (4) : 16411670. doi: 10.3934/dcdsb.2010.14.1641 
[20] 
Christos V. Nikolopoulos, Georgios E. Zouraris. Numerical solution of a nonlocal elliptic problem modeling a thermistor with a finite element and a finite volume method. Conference Publications, 2007, 2007 (Special) : 768778. doi: 10.3934/proc.2007.2007.768 
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