We describe two new public key broadcast encryption systems for stateless receivers. Both systems are fully secure against any number of colluders. In our first construction both ciphertexts and private keys are of constant size (only two group elements), for any subset of receivers. The public key size in this system is linear in the total number of receivers. Our second system is a generalization of the first that provides a tradeoff between ciphertext size and public key size. For example, we achieve a collusion resistant broadcast system for n users where both ciphertexts and public keys are of size $O(\sqrt{N})$ for any subset of receivers. We discuss several applications of these systems.

/pdf/collusion-resistant-broadcast-encryption-with-short-31dhzqvvof.pdf

Collusion resistant broadcast encryption with short ciphertexts and private keys

Secure communications in wireless sensor networks operating under adversarial conditions require providing pairwise (symmetric) keys to sensor nodes. In large scale deployment scenarios, there is no priory knowledge of post deployment network configuration since nodes may be randomly scattered over a hostile territory. Thus, shared keys must be distributed before deployment to provide each node a key-chain. For large sensor networks it is infeasible to store a unique key for all other nodes in the key-chain of a sensor node. Consequently, for secure communication either two nodes have a key in common in their key-chains and they have a wireless link between them, or there is a path, called key-path, among these two nodes where each pair of neighboring nodes on this path have a key in common. Length of the key-path is the key factor for efficiency of the design. This paper presents novel deterministic and hybrid approaches based on Combinatorial Design for deciding how many and which keys to assign to each key-chain before the sensor network deployment. In particular, Balanced Incomplete Block Designs (BIBD) and Generalized Quadrangles (GQ) are mapped to obtain efficient key distribution schemes. Performance and security properties of the proposed schemes are studied both analytically and computationally. Comparison to related work shows that the combinatorial approach produces better connectivity with smaller key-chain sizes.

/pdf/combinatorial-design-of-key-distribution-mechanisms-for-1nwbfdilv8.pdf

Combinatorial design of key distribution mechanisms for wireless sensor networks

In order to protect copyrighted material, codes may be embedded in the content or codes may be associated with the keys used to recover the content. Codes can offer protection by providing some form of traceability (TA) for pirated data. Several researchers have studied different notions of TA and related concepts in previous years. "Strong" versions of TA allow at least one member of a coalition that constructs a "pirate decoder" to be traced. Weaker versions of this concept ensure that no coalition can "frame" a disjoint user or group of users. All these concepts can be formulated as codes having certain combinatorial properties. We study the relationships between the various notions, and we discuss equivalent formulations using structures such as perfect hash families. We use methods from combinatorics and coding theory to provide bounds (necessary conditions) and constructions (sufficient conditions) for the objects of interest.

Combinatorial properties of frameproof and traceability codes

In this paper, we study the application of universal hashing to the construction of unconditionally secure authentication codes without secrecy. This idea is most useful when the number of authenticators is exponentially small compared to the number of possible source states (plaintext messages). We formally define some new classes of hash functions and then prove some new bounds and give some general constructions for these classes of hash functions. Then we discuss the implications to authentication codes.

/pdf/universal-hashing-and-authentication-codes-5422mwobag.pdf

Universal hashing and authentication codes

We consider re-keying protocols for secure multicasting in a dynamic multicast group with a center. There is a variety of different scenarios using multicast, presenting a wide range of efficiency requirements with respect to several parameters. We give an upper bound on the tradeoff between storage and communication parameters. In particular, we suggest an improvement of the schemes by Wallner et al. and Wong et al. [13,14] with sub-linear center storage, without a significant loss in other parameters.

Correctly selecting the parameters of our scheme we can efficiently accommodate a wide range of scenarios. This is demonstrated by Applying the protocol to some known benchmark scenarios.

We also show lower bounds on the tradeoff between communication and user storage, and show that our scheme is almost optimal with respect to these lower bounds.

/pdf/efficient-communication-storage-tradeoffs-for-multicast-2e2t53z9ew.pdf

Efficient communication-storage tradeoffs for multicast encryption

Secure frameproof codes, key distribution patterns, group testing algorithms and related structures

This paper concerns methods by which a trusted authority can distribute keys and/or broadcast a message over a network, so that each member of a privileged subset of users can compute a specified key or decrypt the broadcast message. Moreover, this is done in such a way that no coalition is able to recover any information on a key or broadcast message they are not supposed to know. The problems are studied using the tools of information theory, so the security provided is unconditional (i.e., not based on any computational assumption).

In a recent paper st95a, Stinson described a method of constructing key predistribution schemes by combining Mitchell-Piper key distribution patterns with resilient functions; and also presented a construction method for broadcast encryption schemes that combines Fiat-Naor key predistribution schemes with ideal secret sharing schemes. In this paper, we further pursue these two themes, providing several nice applications of these techniques by using combinatorial structures such as orthogonal arrays, perpendicular arrays, Steiner systems and universal hash families.

Some New Results on Key Distribution Patterns and BroadcastEncryption

This paper concerns construction methods for t-covering arrays. Firstly, a construction method using perfect hash families is discussed by combining with recursion techniques and error-correcting codes. In particular, by using algebraic-geometric codes for this method we obtain infinite families of t-covering arrays which are proved to be better than currently known probabilistic bounds for covering arrays. Secondly, inspired from a result of Roux l16r and also from a recent result of Chateauneuf and Kreher l6r for 3-covering arrays, we present several explicit constructions for t-covering arrays, which can be viewed as generalizations of their results for t-covering arrays.

On t -Covering Arrays

A covering array CA(N;t,k,v) is an N × k array such that every N × t sub-array contains all t-tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t-sets of component interactions. Recursive constructions for covering arrays of strengths 3 and 4 are developed, generalizing many "Roux-type" constructions. A numerical comparison with current construction techniques is given through existence tables for covering arrays.

Tran van Trung

Papers

Secure frameproof codes, key distribution patterns, group testing algorithms and related structures

Some New Results on Key Distribution Patterns and BroadcastEncryption

On t -Covering Arrays

Roux-type constructions for covering arrays of strengths three and four

Resolvable and Near Resolvable Designs