Lists that are smaller than their parts: A coding approach to tunable secrecy

We present a new information-theoretic definition and associated results, based on list decoding in a source coding setting. We begin by presenting list-source codes, which naturally map a key length (entropy) to list size. We then show that such codes can be analyzed in the context of a novel information-theoretic metric, \epsilon-symbol secrecy, that encompasses both the one-time pad and traditional rate-based asymptotic metrics, but, like most cryptographic constructs, can be applied in non-asymptotic settings. We derive fundamental bounds for \epsilon-symbol secrecy and demonstrate how these bounds can be achieved with MDS codes when the source is uniformly distributed. We discuss applications and implementation issues of our codes.Comment: Allerton 2012, 8 page

Performance Analysis and Design of Two Edge Type LDPC Codes for the BEC Wiretap Channel

We consider transmission over a wiretap channel where both the main channel and the wiretapper's channel are Binary Erasure Channels (BEC). We propose a code construction method using two edge type LDPC codes based on the coset encoding scheme. Using a standard LDPC ensemble with a given threshold over the BEC, we give a construction for a two edge type LDPC ensemble with the same threshold. If the given standard LDPC ensemble has degree two variable nodes, our construction gives rise to degree one variable nodes in the code used over the main channel. This results in zero threshold over the main channel. In order to circumvent this problem, we numerically optimize the degree distribution of the two edge type LDPC ensemble. We find that the resulting ensembles are able to perform close to the boundary of the rate-equivocation region of the wiretap channel. There are two performance criteria for a coding scheme used over a wiretap channel: reliability and secrecy. The reliability measure corresponds to the probability of decoding error for the intended receiver. This can be easily measured using density evolution recursion. However, it is more challenging to characterize secrecy, corresponding to the equivocation of the message for the wiretapper. M\'easson, Montanari, and Urbanke have shown how the equivocation can be measured for a broad range of standard LDPC ensembles for transmission over the BEC under the point-to-point setup. By generalizing the method of M\'easson, Montanari, and Urbanke to two edge type LDPC ensembles, we show how the equivocation for the wiretapper can be computed. We find that relatively simple constructions give very good secrecy performance and are close to the secrecy capacity. However finding explicit sequences of two edge type LDPC ensembles which achieve secrecy capacity is a more difficult problem. We pose it as an interesting open problem.Comment: submitted to IEEE Transactions on Information Theory. Updated versio

Security for correlated sources across wiretap network

A thesis submitted in ful llment of the requirements for the degree of Doctor of Philosophy in the School of Electrical and Information Engineering Faculty of Engineering University of the Witwatersrand July 2015This thesis presents research conducted for the security aspects of correlated sources across a wiretap network. Correlated sources are present in communication systems where protocols ensure that there is some predetermined information for sources to transmit. Systems that contain correlated sources are for example broadcast channels, smart grid systems, wireless sensor networks and social media networks. In these systems there exist common information between the nodes in a network, which gives rise to security risks as common information can be determined about more than one source. In this work the security aspects of correlated sources are investigated. Correlated source coding in terms of the Slepian-Wolf theorem is investigated to determine the amount of information leakage for various correlated source models. The perfect secrecy approach developed by Shannon has also been incorporated as a security approach. In order to explore these security aspects the techniques employed range from typical sequences used to prove Slepian-Wolf's theorem to coding methods incorporating matrix partitions for correlated sources. A generalized correlated source model is presented and the procedure to determine the information leakage is initially illustrated using this model. A novel scenario for two correlated sources across a channel with eavesdroppers is also investigated. It is a basic model catering for the correlated source applications that have been detailed. The information leakage quanti cation is provided, where bounds specify the quantity of information leaked for various cases of eavesdropped channel information. The required transmission rates for perfect secrecy when some channel information has been wiretapped is further determined, followed by a method to reduce the key length required for perfect secrecy. The implementation thereafter provided shows how the information leakage is determined practically. In the same way using the information leakage quanti cation, Shannon's cipher system approach and practical implementation a novel two correlated source model where channel information and some source data symbols (predetermined information) are wiretapped is investigated. The adversary in this situation has access to more information than if a link is wiretapped only and can thus determine more about a particular source. This scenario caters for an application where the eavesdropper has access to some predetermined information. The security aspects and coding implementation have further been developed for a novel correlated source model with a heterogeneous encoding method. The model caters for situations where a wiretapper is able to easily access a particular source. iii The interesting link between information theory and coding theory is explored for the novel models presented in this research. A matrix partition method is utilized and the information leakage for various cases of wiretapped syndromes are presented. The research explores the security for correlated sources in the presence of wiretappers. Both the information leakage and Shannon's cipher system approach are used to achieve these security aspects. The implementation shows the practicality of using these security aspects in communications systems. The research contained herein is signi cant as evident from the various applications it may be used for and to the author's knowledge is novel