
Previous Article
Partitioned difference families: The storm has not yet passed
 AMC Home
 This Issue

Next Article
Optimal antiblocking systems of information sets for the binary codes related to triangular graphs
Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.
Readers can access Online First articles via the “Online First” tab for the selected journal.
Formal security proof for a scheme on a topological network
1.  Department of Information Engineering, Computer Science, and Mathematics, University of L'Aquila, Via Vetoio, 67100 L'Aquila (AQ), Italy 
2.  Department of Mathematics, University of Trento, Via Sommarive 14, 38123 Povo (TN), Italy 
Key assignment and key maintenance in encrypted networks of resourcelimited devices may be a challenging task, due to the permanent need of replacing outofservice devices with new ones and to the consequent need of updating the key information. Recently, Aragona et al. proposed a new cryptographic scheme, ECTAKS, which provides a solution to this design problem by means of a DiffieHellmanlike key establishment protocol based on elliptic curves and on a prime field. Even if the authors proved some results related to the security of the scheme, the latter still lacks a formal security analysis. In this paper, we address this issue by providing a security proof for ECTAKS in the setting of computational security, assuming that no adversary can solve the underlying discrete logarithm problems with nonnegligible success probability.
References:
[1] 
R. Aragona, R. Civino, N. Gavioli and M. Pugliese, An authenticated key scheme over elliptic curves for topological networks, preprint, arXiv: 2006.02147. To appear in Journal of Discrete Mathematical Sciences & Cryptography Google Scholar 
[2] 
D. Boneh, The decision DiffieHellman problem, Algorithmic Number Theory (Portland, OR), Lecture Notes in Comput. Sci., 1423, Springer, (1998), 4863. doi: 10.1007/BFb0054851. Google Scholar 
[3] 
W. Diffie and M. E. Hellman, New directions in cryptography, IEEE Trans. Inform. Theory, 22 (1976), 644654. doi: 10.1109/tit.1976.1055638. Google Scholar 
[4] 
S. Marchesani, L. Pomante, M. Pugliese and F. Santucci, Definition and development of a topologybased cryptographic scheme for wireless sensor networks, in Sensor Systems and Software, Springer International Publishing, (2013), 4764. doi: 10.1007/9783319041667_4. Google Scholar 
[5] 
S. Marchesani, L. Pomante, F. Santucci and M. Pugliese, A cryptographic scheme for realworld wireless sensor networks applications, in Proceedings of the ACM/IEEE 4th International Conference on CyberPhysical Systems, Association for Computing Machinery, 2013. doi: 10.1145/2502524.2502568. Google Scholar 
[6] 
M. Pugliese, Managing Security Issues in Advanced Applications of Wireless Sensor Networks, Ph.D thesis, Department of Electrical Engineering and Computer Science, University of L'Aquila, 2008, available at https://mpugliese.webnode.it/_files/200000061a7608a760b/24.%20phd_thesis.pdf. Google Scholar 
[7] 
J. H. Silverman, The Arithmetic of Elliptic Curves, SpringerVerlag, New York, Graduate Texts in Mathematics, 2009. doi: 10.1007/9780387094946. Google Scholar 
show all references
References:
[1] 
R. Aragona, R. Civino, N. Gavioli and M. Pugliese, An authenticated key scheme over elliptic curves for topological networks, preprint, arXiv: 2006.02147. To appear in Journal of Discrete Mathematical Sciences & Cryptography Google Scholar 
[2] 
D. Boneh, The decision DiffieHellman problem, Algorithmic Number Theory (Portland, OR), Lecture Notes in Comput. Sci., 1423, Springer, (1998), 4863. doi: 10.1007/BFb0054851. Google Scholar 
[3] 
W. Diffie and M. E. Hellman, New directions in cryptography, IEEE Trans. Inform. Theory, 22 (1976), 644654. doi: 10.1109/tit.1976.1055638. Google Scholar 
[4] 
S. Marchesani, L. Pomante, M. Pugliese and F. Santucci, Definition and development of a topologybased cryptographic scheme for wireless sensor networks, in Sensor Systems and Software, Springer International Publishing, (2013), 4764. doi: 10.1007/9783319041667_4. Google Scholar 
[5] 
S. Marchesani, L. Pomante, F. Santucci and M. Pugliese, A cryptographic scheme for realworld wireless sensor networks applications, in Proceedings of the ACM/IEEE 4th International Conference on CyberPhysical Systems, Association for Computing Machinery, 2013. doi: 10.1145/2502524.2502568. Google Scholar 
[6] 
M. Pugliese, Managing Security Issues in Advanced Applications of Wireless Sensor Networks, Ph.D thesis, Department of Electrical Engineering and Computer Science, University of L'Aquila, 2008, available at https://mpugliese.webnode.it/_files/200000061a7608a760b/24.%20phd_thesis.pdf. Google Scholar 
[7] 
J. H. Silverman, The Arithmetic of Elliptic Curves, SpringerVerlag, New York, Graduate Texts in Mathematics, 2009. doi: 10.1007/9780387094946. Google Scholar 
[1] 
Rainer Steinwandt, Adriana Suárez Corona. Cryptanalysis of a 2party key establishment based on a semigroup action problem. Advances in Mathematics of Communications, 2011, 5 (1) : 8792. doi: 10.3934/amc.2011.5.87 
[2] 
Rainer Steinwandt, Adriana Suárez Corona. Attributebased group key establishment. Advances in Mathematics of Communications, 2010, 4 (3) : 381398. doi: 10.3934/amc.2010.4.381 
[3] 
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 
[4] 
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 
[5] 
JoanJosep Climent, Juan Antonio LópezRamos. Public key protocols over the ring $E_{p}^{(m)}$. Advances in Mathematics of Communications, 2016, 10 (4) : 861870. doi: 10.3934/amc.2016046 
[6] 
Yvo Desmedt, Niels Duif, Henk van Tilborg, Huaxiong Wang. Bounds and constructions for key distribution schemes. Advances in Mathematics of Communications, 2009, 3 (3) : 273293. doi: 10.3934/amc.2009.3.273 
[7] 
Giacomo Micheli. Cryptanalysis of a noncommutative key exchange protocol. Advances in Mathematics of Communications, 2015, 9 (2) : 247253. doi: 10.3934/amc.2015.9.247 
[8] 
Z. Reichstein and B. Youssin. Parusinski's "Key Lemma" via algebraic geometry. Electronic Research Announcements, 1999, 5: 136145. 
[9] 
Felipe Cabarcas, Daniel Cabarcas, John Baena. Efficient publickey operation in multivariate schemes. Advances in Mathematics of Communications, 2019, 13 (2) : 343371. doi: 10.3934/amc.2019023 
[10] 
Iris Anshel, Derek Atkins, Dorian Goldfeld, Paul E. Gunnells. Ironwood meta key agreement and authentication protocol. Advances in Mathematics of Communications, 2021, 15 (3) : 397413. doi: 10.3934/amc.2020073 
[11] 
Mohamed Baouch, Juan Antonio LópezRamos, Blas Torrecillas, Reto Schnyder. An active attack on a distributed Group Key Exchange system. Advances in Mathematics of Communications, 2017, 11 (4) : 715717. doi: 10.3934/amc.2017052 
[12] 
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 
[13] 
Mohammad Sadeq Dousti, Rasool Jalili. FORSAKES: A forwardsecure authenticated key exchange protocol based on symmetric keyevolving schemes. Advances in Mathematics of Communications, 2015, 9 (4) : 471514. doi: 10.3934/amc.2015.9.471 
[14] 
Yang Lu, Quanling Zhang, Jiguo Li. An improved certificateless strong keyinsulated signature scheme in the standard model. Advances in Mathematics of Communications, 2015, 9 (3) : 353373. doi: 10.3934/amc.2015.9.353 
[15] 
Jake Bouvrie, Boumediene Hamzi. Kernel methods for the approximation of some key quantities of nonlinear systems. Journal of Computational Dynamics, 2017, 4 (1&2) : 119. doi: 10.3934/jcd.2017001 
[16] 
Sikhar Patranabis, Debdeep Mukhopadhyay. Identitybased key aggregate cryptosystem from multilinear maps. Advances in Mathematics of Communications, 2019, 13 (4) : 759778. doi: 10.3934/amc.2019044 
[17] 
Diego F. Aranha, Ricardo Dahab, Julio López, Leonardo B. Oliveira. Efficient implementation of elliptic curve cryptography in wireless sensors. Advances in Mathematics of Communications, 2010, 4 (2) : 169187. doi: 10.3934/amc.2010.4.169 
[18] 
Riccardo Aragona, Marco Calderini, Roberto Civino. Some grouptheoretical results on Feistel Networks in a longkey scenario. Advances in Mathematics of Communications, 2020, 14 (4) : 727743. doi: 10.3934/amc.2020093 
[19] 
Xinwei Gao. Comparison analysis of Ding's RLWEbased key exchange protocol and NewHope variants. Advances in Mathematics of Communications, 2019, 13 (2) : 221233. doi: 10.3934/amc.2019015 
[20] 
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 
2020 Impact Factor: 0.935
Tools
Article outline
Figures and Tables
[Back to Top]