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A filtering method for the hyperelliptic curve index calculus and its analysis
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] 
Andreas Klein. How to say yes, no and maybe with visual cryptography. Advances in Mathematics of Communications, 2008, 2 (3) : 249259. doi: 10.3934/amc.2008.2.249 
[14] 
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 
[15] 
Gérard Maze, Chris Monico, Joachim Rosenthal. Public key cryptography based on semigroup actions. Advances in Mathematics of Communications, 2007, 1 (4) : 489507. doi: 10.3934/amc.2007.1.489 
[16] 
Eitan Altman. Bioinspired paradigms in network engineering games. Journal of Dynamics & Games, 2014, 1 (1) : 115. doi: 10.3934/jdg.2014.1.1 
[17] 
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 
[18] 
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 
[19] 
Jintai Ding, Sihem Mesnager, LihChung Wang. Letters for postquantum cryptography standard evaluation. Advances in Mathematics of Communications, 2020, 14 (1) : ii. doi: 10.3934/amc.2020012 
[20] 
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 
2018 Impact Factor: 0.879
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