Asymmetric Encryption for Wiretap Channels

Since the definition of the wiretap channel by Wyner in 1975, there has been much research to investigate the communication security of this channel. This thesis presents some further investigations into the wiretap channel which improve the reliability of the communication security. The main results include the construction of best known equivocation codes which leads to an increase in the ambiguity of the wiretap channel by using different techniques based on syndrome coding. Best known codes (BKC) have been investigated, and two new design models which includes an inner code and outer code have been implemented. It is shown that best results are obtained when the outer code employs a syndrome coding scheme based on the (23; 12; 7) binary Golay code and the inner code employs the McEliece cryptosystem technique based on BKC0s. Three techniques of construction of best known equivocation codes (BEqC) for syndrome coding scheme are presented. Firstly, a code design technique to produce new (BEqC) codes which have better secrecy than the best error correcting codes is presented. Code examples (some 50 codes) are given for the case where the number of parity bits of the code is equal to 15. Secondly, a new code design technique is presented, which is based on the production of a new (BEqC) by adding two best columns to the parity check matrix(H) of a good (BEqC), [n; k] code. The highest minimum Hamming distance of a linear code is an important parameter which indicates the capability of detecting and correcting errors by the code. In general, (BEqC) have a respectable minimum Hamming distance, but are sometimes not as good as the best known codes with the same code parameters. This interesting point led to the production of a new code design technique which produces a (BEqC) code with the highest minimum Hamming distance for syndrome coding which has better secrecy than the corresponding (BKC). As many as 207 new best known equivocation codes which have the highest minimum distance have been found so far using this design technique.Ministry of Higher Education and Scientific Research, Kurdistan Regional Government, Erbil-Ira

Secure, reliable, and efficient communication over the wiretap channel

Secure wireless communication between devices is essential for modern communication systems. Physical-layer security over the wiretap channel may provide an additional level of secrecy beyond the current cryptographic approaches. Given a sender Alice, a legitimate receiver Bob, and a malicious eavesdropper Eve, the wiretap channel occurs when Eve experiences a worse signal-to-noise ratio than Bob. Previous study of the wiretap channel has tended to make assumptions that ignore the reality of wireless communication. This thesis presents a study of short block length codes with the aim of both reliability for Bob and confusion for Eve. The standard approach to wiretap coding is shown to be very inefficient for reliability. Quantifying Eve's confusion in terms of entropy is not solved in many cases, though it is possible for codes with a moderate complexity trellis representation. Using error rate arguments, error correcting codes with steep performance curves turn out to be desirable both for reliability and confusion.Masteroppgave i informatikkINF399MAMN-INFMAMN-PRO

New best equivocation codes for syndrome coding

In this paper we present a code design technique which produces codes for syndrome coding which have better secrecy than the best error correcting codes. Code examples are given for the case where the number of parity bits of the code is equal to 15. The code design technique presented is based on extensions of the parity check matrix of a set of good equivocation codes of shorter length. It is also shown that syndrome coding can be implemented without the traditional syndrome look up table, enabling any length codes to be used. An efficient recursive method to calculate the equivocation rate for the binary symmetric channel (BSC) and any linear binary code is also presented. The design results show that the best equivocation codes (BEC) that are produced have better equivocation rate for the syndrome coding scheme compared to all previously published codes, including the best known codes (BKC)

The Equivocation of Codes

EQUIVOCATION was introduced by Shannon in the late 1940’s in seminal papers that kick-started the whole field of information theory. Much ground has been covered on equivocation’s counterpart, channel capacity and in particular, its bounds. However, less work has been carried out on the evaluation of the equivocation of a code transmitted across a channel. The aim of the work covered in this thesis was to use a probabilistic approach to investigate and compare the equivocation of various codes across a range of channels. The probability and entropy of each output, given each input, can be used to calculate the equivocation. This gives a measure of the ambiguity and secrecy of a code when transmitted across a channel. The calculations increase exponentially in magnitude as both the message length and code length increase. In addition, the impact of factors such as erasures and deletions also serve to significantly complicate the process. In order to improve the calculation times offered by a conventional, linearly-programmed approach, an alternative strategy involving parallel processing with a CUDA-enabled (Compute Unified Device Architecture) graphical processor was employed. This enabled results to be obtained for codes of greater length than was possible with linear programming. However, the practical implementation of a CUDA driven, parallel processed solution gave rise to significant issues with both the software implementation and subsequent platform stability. By normalising equivocation results, it was possible to compare different codes under different conditions, making it possible to identify and select codes that gave a marked difference in the equivocation encountered by a legitimate receiver and an eavesdropper. The introduction of code expansion provided a novel method for enhancing equivocation differences still further. The work on parallel processing to calculate equivocation and the use of code expansion was published in the following conference: Schofield, M., Ahmed, M. & Tomlinson, M. (2015), Using parallel processing to calculate and improve equivocation, in ’IEEE Conference Publications - IEEE 16th International Conference on Communication Technology’. In addition to the novel use of a CUDA-enabled graphics process to calculated equivocation, equivocation calculations were also performed for expanded versions of the codes. Code expansion was shown to yield a dramatic increase in the achievable equivocation levels. Once methods had been developed with the Binary Symmetric Channel (BSC), they were extended to include work with intentional erasures on the BSC, intentional deletions on the BSC and work on the Binary Erasure Channel (BEC). The work on equivocation on the BSC with intentional erasures was published in: Schofield, M. et al, (2016), Intentional erasures and equivocation on the binary symmetric channel, in ’IEEE Conference Publications - International Computer Symposium’, IEEE, pp 233-235. The work on the BEC produced a novel outcome due to the erasure correction process employed. As the probability of an erasure occurring increases, the set of likely decoded outcomes diminishes. This directly impacts the output entropy of the system by decreasing it, thereby also affecting the equivocation value of the system. This aspect was something that had not been encountered previously. The work also extended to the consideration of intentional deletions on the BSC and the Binary Deletion Channel (BDC) itself. Although the methods used struggled to cope with the additional complexity brought by deletions, the use of Varshamov-Tenengolts codes on the BSC with intentional deletions showed that family of codes to be well suited to the channel arrangement as well as having the capability to be extended to enable the correction of multiple deletions.Plymouth Universit

Hiding Symbols and Functions: New Metrics and Constructions for Information-Theoretic Security

We present information-theoretic definitions and results for analyzing symmetric-key encryption schemes beyond the perfect secrecy regime, i.e. when perfect secrecy is not attained. We adopt two lines of analysis, one based on lossless source coding, and another akin to rate-distortion theory. We start by presenting a new information-theoretic metric for security, called symbol secrecy, and derive associated fundamental bounds. We then introduce list-source codes (LSCs), which are a general framework for mapping a key length (entropy) to a list size that an eavesdropper has to resolve in order to recover a secret message. We provide explicit constructions of LSCs, and demonstrate that, when the source is uniformly distributed, the highest level of symbol secrecy for a fixed key length can be achieved through a construction based on minimum-distance separable (MDS) codes. Using an analysis related to rate-distortion theory, we then show how symbol secrecy can be used to determine the probability that an eavesdropper correctly reconstructs functions of the original plaintext. We illustrate how these bounds can be applied to characterize security properties of symmetric-key encryption schemes, and, in particular, extend security claims based on symbol secrecy to a functional setting.Comment: Submitted to IEEE Transactions on Information Theor

Development of rate-compatible structured LDPC CODEC algorithms and hardware IP

Issued as final reportSamsung Advanced Institute of Technolog