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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 
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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 
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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 
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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 
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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 
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