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Protocols that depend on the use of trusted third parties are not well suited to the ad hoc network scenario The main reason is the lack of trusted infrastructure in ad hoc networks However, some proposals based on modi cations of this approach have been made Such proposals have been made, especially for asymmetric key systems in ad hoc networks We will explain this in detail later in Section 331 Another approach for key management in ad hoc networks that has been proposed prominently for symmetric key systems is based on the use of prior context In this case, it is assumed that nearly all the nodes share prior context at the same time before the network operation begins This prior context is generally in the form of an of ine secret key predistribution before network deployment This approach has received a lot of attention, especially in the context of sensor networks [14 18] Of course, the requirement that all nodes share a context prior to deployment might not always be practical A third approach which might be useful in such a situation is that based on selforganization In this case the nodes deployed in the network do not depend on any prior shared context There have been several proposals using this approach A basic assumption common in many of these proposals is related to the existence of an out-of-band authenticated communication channel [1, 19] Another approach is dependent on the use of identity-based public key systems [20 22] In this case, the public key of a node in the system is derived from the identity of the node We do not consider these solutions in this chapter We next explain the proposed solutions in detail, starting with solutions based on the use of asymmetric keys 331 Asymmetric Key-Based Approach
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The traditional approach towards developing an asymmetric key-based system is based on the use of a CA, as discussed earlier However, such an approach is not practical in ad hoc networks for several reasons Firstly, a CA will be a vulnerable point in the network, especially if it is not distributed Compromise of a CA will allow an adversary to sign any certi cate, thereby paving the way for impersonation of any node or for revocation of any certi cate More importantly, in order to carry out the key management operations, the CA will have to be accessible all the time If the CA is unavailable, then the nodes in the system might be unable to update/change keys New nodes will also not be able to obtain certi cates An approach to improving the availability would be to replicate the services of the CA, but a naive replication of the CA could lead to more problems Compromise of any single replica could lead to collapse of the entire system An approach to solving this problem is to distribute the trust reposed in a single CA over a set of nodes, thereby letting the nodes share the responsibility of key management This is the approach that we explain in the next few subsections We start by looking at approaches proposed to partially distribute the functionality of a CA in Section 3311 Approaches to fully distribute the functionality of the CA are explained in Section 3312 We also discuss self-issued certi cates in Section 3313 and some other schemes in Section 3314 Before that, we would like to remark brie y about the applicability of public key systems for resource constrained networks It is widely accepted that the limited resources associated with sensor nodes make it impossible to execute public-key cryptographic
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algorithms on them The authors in [23], however, show that this need not be the case In this paper the authors demonstrate the tractability of public key algorithms on sensor networks The authors make use of elliptic curve cryptography and show that public keys operations can be executed within 34 s While this is a tremendous improvement over earlier numbers, it is still a signi cant number A potential solution is to utilize asymmetric keys for setting up symmetric keys for subsequent communications Note though that, in a few years, the use of asymmetric techniques in sensor networks might become viable
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3311 Partially Distributed Authority We start this section by explaining brie y the concept of threshold cryptography (TC) A TC scheme makes it possible for n parties to share the ability to perform a cryptographic operation For example, consider the digital signature on a message We have seen techniques whereby a single user creates the digital signature A problem occurs, however, when this user is compromised or cannot be trusted A better approach then is to distribute the trust placed on a single user among multiple users This indeed is what threshold cryptography strives to achieve The objective of theshold cryptography is to protect information by distributing it among a set of n entities In addition, there is a threshold t associated with the TC schemes such that any t of the n parties can execute the cryptographic operation Such schemes are referred to as (n,t) TC schemes In case of an (n,t) TC scheme, fewer than t parties will not be able to execute the cryptographic operation successfully Thus, TC can be considered to be an approach for secure sharing of a secret We see from here that, even when some number of entities (less than the threshold t) in the network is compromised, the system is not at risk Nonavailability of certain number of nodes (at most n 2 t nodes, to be precise) in the network will also not have an impact on the working of the system Note that the TC schemes perform the cryptographic operation in a distributed manner In [24], the authors propose using a scheme based on the technique of threshold cryptography to distribute the private key of the certi cation authority Knowledge of this key is distributed over a subset of the nodes in the network The system, made up of the nodes in the network, is expected to have a public private key pair This key pair is created initially by a trusted authority before deployment of the nodes Following that, the private key is divided into n shares using an (n, t 1) threshold cryptography scheme These n shares are then allocated to n arbitrarily chosen nodes by the authority that created the public private key pair These chosen nodes are called servers Following this distribution of the shares of the private key to the servers, the central authority is no longer needed Thus, the central authority is only needed during the bootstrapping phase Each server also has its own key pair and stores the public keys of all the nodes in the network In particular, each server (chosen node) knows the public keys of other servers As a result, the servers can establish secure links among themselves We show the initial con guration of such a service in Figure 34 The service as a whole has a public private key pair K k The public key K is known to all nodes while the private k is divided into shares s1, , sn, with each server having one share Each server also has a public private key pair Ki ki Whenever a certi cate has to be signed using the private key of the system, the servers are contacted Each server generates a partial signature for the certi cate using the share of the private key that the server has The partial signature is then submitted to a combiner
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