An authenticated key scheme over elliptic curves for topological networks

Abstract

Nodes of sensor networks may be resource-constrained devices, often having a limited lifetime, making sensor networks remarkably dynamic environments. Managing a cryptographic protocol on such setups may require a disproportionate effort when it comes to update the secret parameters of new nodes that enter the network in place of dismantled sensors. For this reason, the designers of schemes for sensor network are always concerned with the need of scalable and adaptable solutions. In this work, we present a novel elliptic-curve based solution, derived from the previously released cryptographic protocol TAKS, which addresses this issue. We give a formal description of the scheme, built on a two-dimensional vector space over a prime field and over elliptic curves, where node topology is more relevant than node identity, allowing a dynamic handling of the network and reducing the cost of network updates. We compare our solution with classical Diffie-Hellman-like protocols and we also study some security concerns and their relation to the related discrete logarithm problem over elliptic curves.

Subject Classification: (2010):

• 94A60
• 94A62
• 94C15

Keywords:

• Key establishment protocols
• Elliptic curve cryptography
• Discrete logarithm problem
• Authenticated networks
• Directed graphs