A key pre-distribution scheme is a method by which initially an off-line trusted authority distributes pieces of information among a set of users. Later, each member of a group of users can compute a common key for secure communication. In this paper we present an asymmetric key pre-distribution scheme. Instead of assuming that the network is comprised entirely of identical users in conventional key pre-distribution schemes, the network now consists of a mix of users with different missions, i.e., ordinary users and keying material servers. A group of users, using secret keys preloaded in their memory and public keying material retrieved from one keying material server, can compute a session key. The properties of this method are that, the compromise of keying material servers does not reveal any information about users' secret keys and the session keys of privileged subset of users; if computational assumptions are considered, each user has very low storage requirement. These properties make it attractive for sensor networks. We first formally define the asymmetric key pre-distribution scheme in terms of the entropy and give lower bounds on user's storage requirement and the public keying material size. Then, we present its constructions and applications for sensor networks.

In this paper, a collusion-resistant matrix system (CRMS) for group key managements is presented. The CRMS is defined as a collection of subsets of users, and the keys held by users in CRMS are organized in a hierarchical matrix manner. After describing the join and leave protocols, we prove that CRMS has lceil2N/trceil-collusion resistant capability. Moreover, the suggestion of how to select the parameters in CRMS is given. The simulated experiments show that CRMS is a practical group key management in wireless networks.

A key pre-distribution scheme is a method by which initially an off-line trusted authority T A distributes pieces of information among a set of users. Later, each member of a group of users can compute a common key for secure communication. In this paper we present a Keying Material Based Key Pre-distribution Scheme, i.e., a group of users, using secret information preloaded in their memory and some public information retrieved from a keying material server, can compute a common key. We first formally define the keying material based key pre-distribution scheme in terms of the entropy, and give lower bounds on the amount of information each user has to keep secret. Then, we describe its applications for sensor networks.

This article considers the problem of how to prevent RSA signature and decryption computation with a residue number system (CRT-based approach) speedup from a hardware fault cryptanalysis in a highly reliable and efficient approach. CRT-based speedup for an RSA signature has been widely adopted as an implementation standard ranging from large servers to very tiny smart IC cards. However, given a single erroneous computation result, hardware fault cryptanalysis can totally break the RSA system by factoring the public modulus. Countermeasures using a simple verification function (e.g., raising a signature to the power of a public key) or fault detection (e.g., an expanded modulus approach) have been reported in the literature; however, it is pointed out that very few of these existing solutions are both sound and efficient. Unreasonably, in these methods, they assume that a comparison instruction will always be fault-free when developing countermeasures against hardware fault cryptanalysis. Research shows that the expanded modulus approach proposed by Shamir (1997, 1999) is superior to the approach using a simple verification function when another physical cryptanalysis (e.g., timing cryptanalysis) is considered. So, we intend to improve Shamir's method. In this paper, the new concepts of fault infective CRT computation and fault infective CRT recombination are proposed. Based on the new concepts, two novel protocols are developed with a rigorous proof of security. Two possible parameter settings are provided for the protocols. One setting selects a small public key and the proposed protocols can have comparable performance to Shamir's scheme. The other setting has better performance than Shamir's scheme (i.e., having comparable performance to conventional CRT speedup), but with a large public key. Most importantly, we wish to emphasize the importance of developing and proving the security of physically secure protocols without relying on unreliable or unreasonable assumptions, e.g., always fault-free instructions. In this paper, related protocols are also considered and carefully examined to point out possible weaknesses.