Formal security proof for a scheme on a topological network

Roberto Civino; Riccardo Longo

doi:10.3934/amc.2021009

Article Contents

2023, Volume 17, Issue 3: 562-571. Doi: 10.3934/amc.2021009

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Formal security proof for a scheme on a topological network

Roberto Civino^1, , and
Riccardo Longo^2,

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

^* Corresponding author
^* Corresponding author

Received: November 2020

Revised: February 2021

Early access: April 2021

Published online: April 2021

The authors are members of INdAM-GNSAGA (Italy). This work was partially supported by the Centre of EXcellence on Connected, Geo-Localized and Cybersecure Vehicles (EX-Emerge), funded by Italian Government under CIPE resolution n. 70/2017 (Aug. 7, 2017).

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Abstract

Key assignment and key maintenance in encrypted networks of resource-limited devices may be a challenging task, due to the permanent need of replacing out-of-service 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 Diffie-Hellman-like 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 non-negligible success probability.

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Mathematics Subject Classification: 94A60, 94A62, 94C15, 68P25.

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Figure 1. An example of $ {\rm{ANT}} $, where red nodes represent $ {\rm{ANT}}_{{i}} $

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Figure 2. Target ANT

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References

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