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Abstract
We propose a new authenticated key agreement scheme based on Blom’s scheme, but using multiple master keys and public keys in permutations to compute the private keys in each node. The computations are over a small prime field, and by storing them in a random order in the node, the private-public-master-key associations (PPMka) of the private keys are lost. If a node is captured, the PPMka of the private keys cannot be determined with certainty, making it difficult to begin to attack the scheme. We obtained analytical results to show that, using suitable keying parameters, the probability of discovering the correct PPMka can be made so small, that a very powerful adversary needs to capture the entire network of tens of thousands of nodes or expend an infeasible amount of effort to try all of the possible solutions. We verified our results using computer-simulated attacks on the scheme. The unknown PPMka enables our scheme to break free from the capture threshold of the original Blom’s scheme, so that it can be used in large networks of low-resource devices, such as sensor nodes.
Highlights
Wireless sensor devices are physically small electronic devices equipped with the appropriate sensors, a micro-controller, a limited amount of memory and a radio transceiver for communicating with other devices
Our multiple-key Blom’s scheme [1,2], called the Blom–Yang key agreement (BYka) scheme, uses the Blom’s scheme as the cryptographic primitive, but with multiple master keys and public keys used in permutations in a single key space
When a traitor node is found, a new implementation is made using a new set of master keys and this is repeated for 1000 runs
Summary
Wireless sensor devices are physically small electronic devices equipped with the appropriate sensors, a micro-controller, a limited amount of memory and a radio transceiver for communicating with other devices They are designed to be inexpensive, so that they can be deployed in large numbers. A better solution is to use a key agreement scheme where pairs of nodes would compute their pairwise keys after exchanging some information over the insecure channel Such schemes, such as those by Diffie-Hellman (DH), by Rivest, Shamir and Adleman (RSA) and by El-Gamal, are already widely used in computer networks. These use public key cryptographic (PKC) algorithms involving complex mathematical operations on large integers and require substantial computational, memory and energy resources that are not readily available in sensor nodes. This paper, an extension of our previous works in [1,2,3], presents a symmetric key scheme, which retains the advantages of the symmetric key scheme and is able to overcome these limitations
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