Contributions to Confidentiality and Integrity Algorithms for 5G

The confidentiality and integrity algorithms in cellular networks protect the transmission of user and signaling data over the air between users and the network, e.g., the base stations. There are three standardised cryptographic suites for confidentiality and integrity protection in 4G, which are based on the AES, SNOW 3G, and ZUC primitives, respectively. These primitives are used for providing a 128-bit security level and are usually implemented in hardware, e.g., using IP (intellectual property) cores, thus can be quite efficient. When we come to 5G, the innovative network architecture and high-performance demands pose new challenges to security. For the confidentiality and integrity protection, there are some new requirements on the underlying cryptographic algorithms. Specifically, these algorithms should: 1) provide 256 bits of security to protect against attackers equipped with quantum computing capabilities; and 2) provide at least 20 Gbps (Gigabits per second) speed in pure software environments, which is the downlink peak data rate in 5G. The reason for considering software environments is that the encryption in 5G will likely be moved to the cloud and implemented in software. Therefore, it is crucial to investigate existing algorithms in 4G, checking if they can satisfy the 5G requirements in terms of security and speed, and possibly propose new dedicated algorithms targeting these goals. This is the motivation of this thesis, which focuses on the confidentiality and integrity algorithms for 5G. The results can be summarised as follows.1. We investigate the security of SNOW 3G under 256-bit keys and propose two linear attacks against it with complexities 2172 and 2177, respectively. These cryptanalysis results indicate that SNOW 3G cannot provide the full 256-bit security level. 2. We design some spectral tools for linear cryptanalysis and apply these tools to investigate the security of ZUC-256, the 256-bit version of ZUC. We propose a distinguishing attack against ZUC-256 with complexity 2236, which is 220 faster than exhaustive key search. 3. We design a new stream cipher called SNOW-V in response to the new requirements for 5G confidentiality and integrity protection, in terms of security and speed. SNOW-V can provide a 256-bit security level and achieve a speed as high as 58 Gbps in software based on our extensive evaluation. The cipher is currently under evaluation in ETSI SAGE (Security Algorithms Group of Experts) as a promising candidate for 5G confidentiality and integrity algorithms. 4. We perform deeper cryptanalysis of SNOW-V to ensure that two common cryptanalysis techniques, guess-and-determine attacks and linear cryptanalysis, do not apply to SNOW-V faster than exhaustive key search. 5. We introduce two minor modifications in SNOW-V and propose an extreme performance variant, called SNOW-Vi, in response to the feedback about SNOW-V that some use cases are not fully covered. SNOW-Vi covers more use cases, especially some platforms with less capabilities. The speeds in software are increased by 50% in average over SNOW-V and can be up to 92 Gbps.Besides these works on 5G confidentiality and integrity algorithms, the thesis is also devoted to local pseudorandom generators (PRGs). 6. We investigate the security of local PRGs and propose two attacks against some constructions instantiated on the P5 predicate. The attacks improve existing results with a large gap and narrow down the secure parameter regime. We also extend the attacks to other local PRGs instantiated on general XOR-AND and XOR-MAJ predicates and provide some insight in the choice of safe parameters

The dynamics of complex systems. Studies and applications in computer science and biology

Our research has focused on the study of complex dynamics and on their use in both information security and bioinformatics. Our first work has been on chaotic discrete dynamical systems, and links have been established between these dynamics on the one hand, and either random or complex behaviors. Applications on information security are on the pseudorandom numbers generation, hash functions, informationhiding, and on security aspects on wireless sensor networks. On the bioinformatics level, we have applied our studies of complex systems to theevolution of genomes and to protein folding

Pseudorandom Functions: Three Decades Later

In 1984, Goldreich, Goldwasser and Micali formalized the concept of pseudorandom functions and proposed a construction based on any length-doubling pseudorandom generator. Since then, pseudorandom functions have turned out to be an extremely influential abstraction, with applications ranging from message authentication to barriers in proving computational complexity lower bounds. In this tutorial we survey various incarnations of pseudorandom functions, giving self-contained proofs of key results from the literature. Our main focus is on feasibility results and constructions, as well as on limitations of (and induced by) pseudorandom functions. Along the way we point out some open questions that we believe to be within reach of current techniques

Security, Scalability and Privacy in Applied Cryptography

In the modern digital world, cryptography finds its place in countless applications. However, as we increasingly use technology to perform potentially sensitive tasks, our actions and private data attract, more than ever, the interest of ill-intentioned actors. Due to the possible privacy implications of cryptographic flaws, new primitives’ designs need to undergo rigorous security analysis and extensive cryptanalysis to foster confidence in their adoption. At the same time, implementations of cryptographic protocols should scale on a global level and be efficiently deployable on users’ most common devices to widen the range of their applications. This dissertation will address the security, scalability and privacy of cryptosystems by presenting new designs and cryptanalytic results regarding blockchain cryptographic primitives and public-key schemes based on elliptic curves. In Part I, I will present the works I have done in regards to accumulator schemes. More precisely, in Chapter 2, I cryptanalyze Au et al. Dynamic Universal Accumulator, by showing some attacks which can completely take over the authority who manages the accumulator. In Chapter 3, I propose a design for an efficient and secure accumulator-based authentication mechanism, which is scalable, privacy-friendly, lightweight on the users’ side, and suitable to be implemented on the blockchain. In Part II, I will report some cryptanalytical results on primitives employed or considered for adoption in top blockchain-based cryptocurrencies. In particular, in Chapter 4, I describe how the zero-knowledge proof system and the commitment scheme adopted by the privacy-friendly cryptocurrency Zcash, contain multiple subliminal channels which can be exploited to embed several bytes of tagging information in users’ private transactions. In Chapter 5, instead, I report the cryptanalysis of the Legendre PRF, employed in a new consensus mechanism considered for adoption by the blockchain-based platform Ethereum, and attacks for further generalizations of this pseudo-random function, such as the Higher-Degree Legendre PRF, the Jacobi Symbol PRF, and the Power-Residue PRF. Lastly, in Part III, I present my line of research on public-key primitives based on elliptic curves. In Chapter 6, I will describe a backdooring procedure for primes so that whenever they appear as divisors of a large integer, the latter can be efficiently factored. This technique, based on elliptic curves Complex Multiplication theory, enables to eventually generate non-vulnerable certifiable semiprimes with unknown factorization in a multi-party computation setting, with no need to run a statistical semiprimality test common to other protocols. In Chapter 7, instead, I will report some attack optimizations and specific implementation design choices that allow breaking a reduced-parameters instance, proposed by Microsoft, of SIKE, a post-quantum key-encapsulation mechanism based on isogenies between supersingular elliptic curves

Cryptographic primitives on reconfigurable platforms.

Tsoi Kuen Hung.Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.Includes bibliographical references (leaves 84-92).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Objectives --- p.3Chapter 1.3 --- Contributions --- p.3Chapter 1.4 --- Thesis Organization --- p.4Chapter 2 --- Background and Review --- p.6Chapter 2.1 --- Introduction --- p.6Chapter 2.2 --- Cryptographic Algorithms --- p.6Chapter 2.3 --- Cryptographic Applications --- p.10Chapter 2.4 --- Modern Reconfigurable Platforms --- p.11Chapter 2.5 --- Review of Related Work --- p.14Chapter 2.5.1 --- Montgomery Multiplier --- p.14Chapter 2.5.2 --- IDEA Cipher --- p.16Chapter 2.5.3 --- RC4 Key Search --- p.17Chapter 2.5.4 --- Secure Random Number Generator --- p.18Chapter 2.6 --- Summary --- p.19Chapter 3 --- The IDEA Cipher --- p.20Chapter 3.1 --- Introduction --- p.20Chapter 3.2 --- The IDEA Algorithm --- p.21Chapter 3.2.1 --- Cipher Data Path --- p.21Chapter 3.2.2 --- S-Box: Multiplication Modulo 216 + 1 --- p.23Chapter 3.2.3 --- Key Schedule --- p.24Chapter 3.3 --- FPGA-based IDEA Implementation --- p.24Chapter 3.3.1 --- Multiplication Modulo 216 + 1 --- p.24Chapter 3.3.2 --- Deeply Pipelined IDEA Core --- p.26Chapter 3.3.3 --- Area Saving Modification --- p.28Chapter 3.3.4 --- Key Block in Memory --- p.28Chapter 3.3.5 --- Pipelined Key Block --- p.30Chapter 3.3.6 --- Interface --- p.31Chapter 3.3.7 --- Pipelined Design in CBC Mode --- p.31Chapter 3.4 --- Summary --- p.32Chapter 4 --- Variable Radix Montgomery Multiplier --- p.33Chapter 4.1 --- Introduction --- p.33Chapter 4.2 --- RSA Algorithm --- p.34Chapter 4.3 --- Montgomery Algorithm - Ax B mod N --- p.35Chapter 4.4 --- Systolic Array Structure --- p.36Chapter 4.5 --- Radix-2k Core --- p.37Chapter 4.5.1 --- The Original Kornerup Method (Bit-Serial) --- p.37Chapter 4.5.2 --- The Radix-2k Method --- p.38Chapter 4.5.3 --- Time-Space Relationship of Systolic Cells --- p.38Chapter 4.5.4 --- Design Correctness --- p.40Chapter 4.6 --- Implementation Details --- p.40Chapter 4.7 --- Summary --- p.41Chapter 5 --- Parallel RC4 Engine --- p.42Chapter 5.1 --- Introduction --- p.42Chapter 5.2 --- Algorithms --- p.44Chapter 5.2.1 --- RC4 --- p.44Chapter 5.2.2 --- Key Search --- p.46Chapter 5.3 --- System Architecture --- p.47Chapter 5.3.1 --- RC4 Cell Design --- p.47Chapter 5.3.2 --- Key Search --- p.49Chapter 5.3.3 --- Interface --- p.50Chapter 5.4 --- Implementation --- p.50Chapter 5.4.1 --- RC4 cell --- p.51Chapter 5.4.2 --- Floorplan --- p.53Chapter 5.5 --- Summary --- p.53Chapter 6 --- Blum Blum Shub Random Number Generator --- p.55Chapter 6.1 --- Introduction --- p.55Chapter 6.2 --- RRNG Algorithm . . --- p.56Chapter 6.3 --- PRNG Algorithm --- p.58Chapter 6.4 --- Architectural Overview --- p.59Chapter 6.5 --- Implementation --- p.59Chapter 6.5.1 --- Hardware RRNG --- p.60Chapter 6.5.2 --- BBS PRNG --- p.61Chapter 6.5.3 --- Interface --- p.66Chapter 6.6 --- Summary --- p.66Chapter 7 --- Experimental Results --- p.68Chapter 7.1 --- Design Platform --- p.68Chapter 7.2 --- IDEA Cipher --- p.69Chapter 7.2.1 --- Size of IDEA Cipher --- p.70Chapter 7.2.2 --- Performance of IDEA Cipher --- p.70Chapter 7.3 --- Variable Radix Systolic Array --- p.71Chapter 7.4 --- Parallel RC4 Engine --- p.75Chapter 7.5 --- BBS Random Number Generator --- p.76Chapter 7.5.1 --- Size --- p.76Chapter 7.5.2 --- Speed --- p.76Chapter 7.5.3 --- External Clock --- p.77Chapter 7.5.4 --- Random Performance --- p.78Chapter 7.6 --- Summary --- p.78Chapter 8 --- Conclusion --- p.81Chapter 8.1 --- Future Development --- p.83Bibliography --- p.8

Entropy in Image Analysis II

Image analysis is a fundamental task for any application where extracting information from images is required. The analysis requires highly sophisticated numerical and analytical methods, particularly for those applications in medicine, security, and other fields where the results of the processing consist of data of vital importance. This fact is evident from all the articles composing the Special Issue "Entropy in Image Analysis II", in which the authors used widely tested methods to verify their results. In the process of reading the present volume, the reader will appreciate the richness of their methods and applications, in particular for medical imaging and image security, and a remarkable cross-fertilization among the proposed research areas

Entropy in Image Analysis III

Image analysis can be applied to rich and assorted scenarios; therefore, the aim of this recent research field is not only to mimic the human vision system. Image analysis is the main methods that computers are using today, and there is body of knowledge that they will be able to manage in a totally unsupervised manner in future, thanks to their artificial intelligence. The articles published in the book clearly show such a future