Physical-Layer Security, Quantum Key Distribution and Post-quantum Cryptography

The growth of data-driven technologies, 5G, and the Internet place enormous pressure on underlying information infrastructure. There exist numerous proposals on how to deal with the possible capacity crunch. However, the security of both optical and wireless networks lags behind reliable and spectrally efficient transmission. Significant achievements have been made recently in the quantum computing arena. Because most conventional cryptography systems rely on computational security, which guarantees the security against an efficient eavesdropper for a limited time, with the advancement in quantum computing this security can be compromised. To solve these problems, various schemes providing perfect/unconditional security have been proposed including physical-layer security (PLS), quantum key distribution (QKD), and post-quantum cryptography. Unfortunately, it is still not clear how to integrate those different proposals with higher level cryptography schemes. So the purpose of the Special Issue entitled “Physical-Layer Security, Quantum Key Distribution and Post-quantum Cryptography” was to integrate these various approaches and enable the next generation of cryptography systems whose security cannot be broken by quantum computers. This book represents the reprint of the papers accepted for publication in the Special Issue

Efficient simultaneous encryption and compression of digital videos in computationally constrained applications

This thesis is concerned with the secure video transmission over open and wireless network channels. This would facilitate adequate interaction in computationally constrained applications among trusted entities such as in disaster/conflict zones, secure airborne transmission of videos for intelligence/security or surveillance purposes, and secure video communication for law enforcing agencies in crime fighting or in proactive forensics. Video content is generally too large and vulnerable to eavesdropping when transmitted over open network channels so that compression and encryption become very essential for storage and/or transmission. In terms of security, wireless channels, are more vulnerable than other kinds of mediums to a variety of attacks and eavesdropping. Since wireless communication is the main mode in the above applications, protecting video transmissions from unauthorized access through such network channels is a must. The main and multi-faceted challenges that one faces in implementing such a task are related to competing, and to some extent conflicting, requirements of a number of standard control factors relating to the constrained bandwidth, reasonably high image quality at the receiving end, the execution time, and robustness against security attacks. Applying both compression and encryption techniques simultaneously is a very tough challenge due to the fact that we need to optimize the compression ratio, time complexity, security and the quality simultaneously. There are different available image/video compression schemes that provide reasonable compression while attempting to maintain image quality, such as JPEG, MPEG and JPEG2000. The main approach to video compression is based on detecting and removing spatial correlation within the video frames as well as temporal correlations across the video frames. Temporal correlations are expected to be more evident across sequences of frames captured within a short period of time (often a fraction of a second). Correlation can be measured in terms of similarity between blocks of pixels. Frequency domain transforms such as the Discrete Cosine Transform (DCT) and the Discrete Wavelet Transform (DWT) have both been used restructure the frequency content (coefficients) to become amenable for efficient detection. JPEG and MPEG use DCT while JPEG2000 uses DWT. Removing spatial/temporal correlation encodes only one block from each class of equivalent (i.e. similar) blocks and remembering the position of all other block within the equivalence class. JPEG2000 compressed images achieve higher image quality than JPEG for the same compression ratios, while DCT based coding suffer from noticeable distortion at high compression ratio but when applied to any block it is easy to isolate the significant coefficients from the non-significant ones. Efficient video encryption in computationally constrained applications is another challenge on its own. It has long been recognised that selective encryption is the only viable approach to deal with the overwhelming file size. Selection can be made in the spatial or frequency domain. Efficiency of simultaneous compression and encryption is a good reason for us to apply selective encryption in the frequency domain. In this thesis we develop a hybrid of DWT and DCT for improved image/video compression in terms of image quality, compression ratio, bandwidth, and efficiency. We shall also investigate other techniques that have similar properties to the DCT in terms of representation of significant wavelet coefficients. The statistical properties of wavelet transform high frequency sub-bands provide one such approach, and we also propose phase sensing as another alternative but very efficient scheme. Simultaneous compression and encryption, in our investigations, were aimed at finding the best way of applying these two tasks in parallel by selecting some wavelet sub-bands for encryptions and applying compression on the other sub-bands. Since most spatial/temporal correlation appear in the high frequency wavelet sub-bands and the LL sub-bands of wavelet transformed images approximate the original images then we select the LL-sub-band data for encryption and the non-LL high frequency sub-band coefficients for compression. We also follow the common practice of using stream ciphers to meet efficiency requirements of real-time transmission. For key stream generation we investigated a number of schemes and the ultimate choice will depend on robustness to attacks. The still image (i.e. RF’s) are compressed with a modified EZW wavelet scheme by applying the DCT on the blocks of the wavelet sub-bands, selecting appropriate thresholds for determining significance of coefficients, and encrypting the EZW thresholds only with a simple 10-bit LFSR cipher This scheme is reasonably efficient in terms of processing time, compression ratio, image quality, as well was security robustness against statistical and frequency attack. However, many areas for improvements were identified as necessary to achieve the objectives of the thesis. Through a process of refinement we developed and tested 3 different secure efficient video compression schemes, whereby at each step we improve the performance of the scheme in the previous step. Extensive experiments are conducted to test performance of the new scheme, at each refined stage, in terms of efficiency, compression ratio, image quality, and security robustness. Depending on the aspects of compression that needs improvement at each refinement step, we replaced the previous block coding scheme with a more appropriate one from among the 3 above mentioned schemes (i.e. DCT, Edge sensing and phase sensing) for the reference frames or the non-reference ones. In subsequent refinement steps we apply encryption to a slightly expanded LL-sub-band using successively more secure stream ciphers, but with different approaches to key stream generation. In the first refinement step, encryption utilized two LFSRs seeded with three secret keys to scramble the significant wavelet LL-coefficients multiple times. In the second approach, the encryption algorithm utilises LFSR to scramble the wavelet coefficients of the edges extracted from the low frequency sub-band. These edges are mapped from the high frequency sub-bands using different threshold. Finally, use a version of the A5 cipher combined with chaotic logistic map to encrypt the significant parameters of the LL sub-band. Our empirical results show that the refinement process achieves the ultimate objectives of the thesis, i.e. efficient secure video compression scheme that is scalable in terms of the frame size at about 100 fps and satisfying the following features; high compression, reasonable quality, and resistance to the statistical, frequency and the brute force attack with low computational processing. Although image quality fluctuates depending on video complexity, in the conclusion we recommend an adaptive implementation of our scheme. Although this thesis does not deal with transmission tasks but the efficiency achieved in terms of video encryption and compression time as well as in compression ratios will be sufficient for real-time secure transmission of video using commercially available mobile computing devices

Homomorphic encryption in algebraic settings

PhD ThesisCryptography methods have been around for a long time to protect sensitive data. With data sets becoming increasingly large we wish to not only store sensitive data in public clouds but in fact, analyse and compute there too. The idea behind homomorphic encryption is that encryption preserves the structure and allows us to perform the same operations on ciphertext as we would on the plaintext. A lot of the work so far restricts the operations that can be performed correctly on ciphertexts. The goal of this thesis is to explore methods for encryption which should greatly increase the amount of analysis and computation that can be performed on ciphertexts. First of all, we will consider the implications of quantum computers on cryptography. There has already been research conducted into quantum-resistant encryption methods. The particular method we will be interested in is still classical. We are assuming these schemes are going to be used in a post-quantum world anyway, we look at how we can use the quantum properties to improve the cryptosystem. More speci cally, we aim to remove a restriction that naturally comes with the scheme restricting how many operations we can perform on ciphertexts. Secondly, we propose a key exchange protocol that works in a polynomial ideal setting. We do this so that the key can be used for a homomorphic cryptography protocol. The advantage of using key exchange over a public key system is that a large proportion of the process needs to be carried out only once instead of needing a more complicated encryption function to use for each piece of data. Polynomial rings are an appropriate choice of structure for this particular type of scheme as they allow us to do everything we need. We will examine how we can perform computation correctly on ciphertexts and address some of the potential weaknesses of such a process. Finally after establishing a fully homomorphic encryption system we will take a more in-depth look at complexity. Measuring the complexity of mathematical problems is, of course, crucial in cryptography, but the choice of measure is something we need to consider seriously. In the nal chapter we will look at generic complexity as its gives us a good feel for how di cult the typical instances of a problem are to solve.Engineering and Physical Sciences Research Council, Centre for Doctoral Training in Cloud Computing for Big Dat

Metodi Matriciali per l'Acquisizione Efficiente e la Crittografia di Segnali in Forma Compressa

The idea of balancing the resources spent in the acquisition and encoding of natural signals strictly to their intrinsic information content has interested nearly a decade of research under the name of compressed sensing. In this doctoral dissertation we develop some extensions and improvements upon this technique's foundations, by modifying the random sensing matrices on which the signals of interest are projected to achieve different objectives. Firstly, we propose two methods for the adaptation of sensing matrix ensembles to the second-order moments of natural signals. These techniques leverage the maximisation of different proxies for the quantity of information acquired by compressed sensing, and are efficiently applied in the encoding of electrocardiographic tracks with minimum-complexity digital hardware. Secondly, we focus on the possibility of using compressed sensing as a method to provide a partial, yet cryptanalysis-resistant form of encryption; in this context, we show how a random matrix generation strategy with a controlled amount of perturbations can be used to distinguish between multiple user classes with different quality of access to the encrypted information content. Finally, we explore the application of compressed sensing in the design of a multispectral imager, by implementing an optical scheme that entails a coded aperture array and Fabry-Pérot spectral filters. The signal recoveries obtained by processing real-world measurements show promising results, that leave room for an improvement of the sensing matrix calibration problem in the devised imager