On the Comparative Study of Some Mathematical Tools for Specific Sequences Design

In modern communication system, cryptography and automatic test patterns, some specific sequences with strictly defined properties are required to meet the application demands. [1,2,3,4…] These requirements are: Good pseudorandom (PN) properties (large period length, uniform distrbution…). Low periodic correlation property. Low aperiodic correlation property. Large linear complexity. Large cardinality (number of sequences in the set). Unfortunately, there is not any set of sequence satisfying all these requirements, despite the fact that a lot of efforts have been given for design such sequences. For this purpose, different mathematical tools have been widely used such as: matrix, d-transform and trace function representations. However, to the best of our knowledge, there has been no any comparative study on these mathematicals tools carried out so far! In this contribution, we try to fill some parts of this gap by considering some typical applications of these tools. The paper is constructed as below: In the introduction, the basic concepts and definitions of matrix, d-transform and trace are given (briefly). In section II, some typical applications (for demonstration) will be shown. In this regard, we will give some discussions and suggestions for choosing the appropriate mathematical tools for each application. Especially, in section III, we will show the relationship (interchanging or equivalencies) between them. Keywords: specific sequences, mathematical tool, matrix, d-transform and trace

Electromagnetic Side-Channel Resilience against Lightweight Cryptography

Side-channel attacks are an unpredictable risk factor in cryptography. Therefore, observations of leakages through physical parameters, i.e., power and electromagnetic (EM) radiation, etc., of digital devices are essential to minimise vulnerabilities associated with cryptographic functions. Compared to costs in the past, performing side-channel attacks using inexpensive test equipment is becoming a reality. Internet-of-Things (IoT) devices are resource-constrained, and lightweight cryptography is a novel approach in progress towards IoT security. Thus, it would provide sufficient data and privacy protection in such a constrained ecosystem. Therefore, cryptanalysis of physical leakages regarding these emerging ciphers is crucial. EM side-channel attacks seem to cause a significant impact on digital forensics nowadays. Within existing literature, power analysis seems to have considerable attention in research whereas other phenomena, such as EM, should continue to be appropriately evaluated in playing a role in forensic analysis.The emphasis of this thesis is on lightweight cryptanalysis. The preliminary investigations showed no Correlation EManalysis (CEMA) of PRESENT lightweight algorithm. The PRESENT is a block cipher that promises to be adequate for IoT devices, and is expected to be used commercially in the future. In an effort to fill in this research gap, this work examines the capabilities of a correlation EM side-channel attack against the PRESENT. For that, Substitution box (S-box) of the PRESENT was targeted for its 1st round with the use of a minimum number of EM waveforms compared to other work in literature, which was 256. The attack indicates the possibility of retrieving 8 bytes of the secret key out of 10 bytes. The experimental process started from a Simple EMA (SEMA) and gradually enhanced up to a CEMA. The thesis presents the methodology of the attack modelling and the observations followed by a critical analysis. Also, a technical review of the IoT technology and a comprehensive literature review on lightweight cryptology are included

Cryptanalysis, Reverse-Engineering and Design of Symmetric Cryptographic Algorithms

In this thesis, I present the research I did with my co-authors on several aspects of symmetric cryptography from May 2013 to December 2016, that is, when I was a PhD student at the university of Luxembourg under the supervision of Alex Biryukov. My research has spanned three different areas of symmetric cryptography. In Part I of this thesis, I present my work on lightweight cryptography. This field of study investigates the cryptographic algorithms that are suitable for very constrained devices with little computing power such as RFID tags and small embedded processors such as those used in sensor networks. Many such algorithms have been proposed recently, as evidenced by the survey I co-authored on this topic. I present this survey along with attacks against three of those algorithms, namely GLUON, PRINCE and TWINE. I also introduce a new lightweight block cipher called SPARX which was designed using a new method to justify its security: the Long Trail Strategy. Part II is devoted to S-Box reverse-engineering, a field of study investigating the methods recovering the hidden structure or the design criteria used to build an S-Box. I co-invented several such methods: a statistical analysis of the differential and linear properties which was applied successfully to the S-Box of the NSA block cipher Skipjack, a structural attack against Feistel networks called the yoyo game and the TU-decomposition. This last technique allowed us to decompose the S-Box of the last Russian standard block cipher and hash function as well as the only known solution to the APN problem, a long-standing open question in mathematics. Finally, Part III presents a unifying view of several fields of symmetric cryptography by interpreting them as purposefully hard. Indeed, several cryptographic algorithms are designed so as to maximize the code size, RAM consumption or time taken by their implementations. By providing a unique framework describing all such design goals, we could design modes of operations for building any symmetric primitive with any form of hardness by combining secure cryptographic building blocks with simple functions with the desired form of hardness called plugs. Alex Biryukov and I also showed that it is possible to build plugs with an asymmetric hardness whereby the knowledge of a secret key allows the privileged user to bypass the hardness of the primitive