Differential cryptanalysis and linear cryptanalysis are the first significant methods used to attack on block ciphers. These concepts compose the keystones for most of the attacks in recent years. Also, while designing a cipher, these attacks should be taken into consideration and the cipher should be created as secure against them. Although differential cryptanalysis and linear cryptanalysis are still important, they started to be inecient due to the improvements in the technology. So, these attacks are extended. For instance, higher order differential cryptanalysis, truncated differential cryptanalysis, generalized linear cryptanalysis, partitioning linear cryptanalysis, linear cryptanalysis using multiple linear approximations are introduced as the extended versions of these attacks. There exists significant applications of these extended attacks. Algebraic attack is a method of cryptanalysis that consists of obtaining a representation of the cipher as a system of equations and then, solving this system. Up to today, just a few attacks that are practically possible to mount are presented. However, due to the fact that algebraic cryptanalysis requires only a handful of known plaintexts to perform, it is a promising and significant attack. This thesis is a survey covering all the methods of attacks described above. Illustrations and summaries of some important papers including these cryptanalysis techniques are given.

The crux of elliptic curve cryptography, a popular mechanism for securing data, is an asymmetric problem. The elliptic curve discrete logarithm problem, as it is called, is hoped to be generally hard in one direction but not the other, and it is this asymmetry that makes it secure. This paper describes the mathematics (and some of the computer science) necessary to understand and compute an attack on the elliptic curve discrete logarithm problem that works in a special case. The algorithm, proposed by Nigel Smart, renders the elliptic curve discrete logarithm problem easy in both directions for elliptic curves of so-called "trace one." The implication is that these curves can never be used securely for cryptographic purposes. In addition, it calls for further investigation into whether or not the problem is hard in general.

In this work we study cryptanalysis one of the most current stream ciphers A5/1. The cipher is used to provide mobile communication privacy in the GSM cellular telephone standard. An essential element of the cipher A5/1 is LFSR( Linear feedback shift register) which is used in stream ciphers because it produces a sequence of bits with high periodicity, has good statistical properties and is easily analyzed using various algebraic methods. At work, we describe and implement three known-plaintext attacks on the cipher. The first two attacks are of the type Guess and Determine and the last one is correlation attack. The focus of the work is cryptanalysis by Golić, which assumes only 64 bits of plaintext. The character of implementation allows to split the work and use parallel-computing, making it possible to use the program in practice. At the end of the work we devote to correlation attack, that is considerably faster, but it assumes knowledge of the relatively large amount of plaintext.

Quantum computers and quantum computing is a reality of the near feature. Companies such as Google and IBM have already declared they have built a quantum computer and tend to increase their size and capacity moving forward. Quantum computers have the ability to be exponentially more powerful than classical computers today. With this power modeling behavior of atoms or chemical reactions in unusual conditions, improving weather forecasts and traffic conditions become possible. Also, their ability to exponentially speed up some computations makes the security of todays data and items a major concern and interest. In the area of cryptography, some encryption schemes (such as RSA) are already deemed broken by the onset of quantum computing. Some encryption algorithms have already been created to be quantum secure and still more are being created each day. While these algorithms in use today are considered quantum-safe not much is known of what a quantum attack would look like on these algorithms. Specifically, this paper discusses how many quantum bits, quantum gates and even the depth of these gates that would be needed for such an attack. The research below was completed to shed light on these areas and offer some concrete numbers of such an attack. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

The traditional model of cryptography examines the security of cryptographic primitives as mathematical functions. This approach does not account for the physical side effects of using these primitives in the real world. A more realistic model employs the concept of a <I>side channel</I>. A side channel is a source of information that is inherent to a physical implementation of a primitive. Research done in the last half of the 1990s has shown that the information transmitted by side channels, such as execution time, computational faults and power consumption, can be detrimental to the security of ciphers like DES and RSA. This thesis surveys the techniques of side channel cryptanalysis presented in [Kocher1996], [Boneh1997], and [Kocher1998] and shows how side channel information can be used to break implementations of DES and RSA. Some specific techniques covered include the timing attack, differential fault analysis, simple power analysis and differential power analysis. Possible defenses against each of these side channel attacks are also discussed.

The traditional model of cryptography examines the security of cryptographic primitives as mathematical functions. This approach does not account for the physical side effects of using these primitives in the real world. A more realistic model employs the concept of a <I>side channel</I>. A side channel is a source of information that is inherent to a physical implementation of a primitive. Research done in the last half of the 1990s has shown that the information transmitted by side channels, such as execution time, computational faults and power consumption, can be detrimental to the security of ciphers like DES and RSA. This thesis surveys the techniques of side channel cryptanalysis presented in [Kocher1996], [Boneh1997], and [Kocher1998] and shows how side channel information can be used to break implementations of DES and RSA. Some specific techniques covered include the timing attack, differential fault analysis, simple power analysis and differential power analysis. Possible defenses against each of these side channel attacks are also discussed.

The RSA cryptosystem, named after its inventors, Rivest, Shamir and Adleman, is the most widely known and widely used public-key cryptosystem in the world today. Compared to other public-key cryptosystems, such as elliptic curve cryptography, RSA requires longer keylengths and is computationally more expensive. In order to address these shortcomings, many variants of RSA have been proposed over the years. While the security of RSA has been well studied since it was proposed in 1977, many of these variants have not. In this thesis, we investigate the security of five of these variants of RSA. In particular, we provide detailed analyses of the best known algebraic attacks (including some new attacks) on instances of RSA with certain special private exponents, multiple instances of RSA sharing a common small private exponent, Multi-prime RSA, Common Prime RSA and Dual RSA.

This report discusses some of the uses of algorithms within number theory. Topics examined include the applications of algorithms in the study of cryptology, the Euclidean Algorithm, prime generating functions, and the connections between algorithmic number theory and high school algebra. / text

La sécurité des chiffrements par bloc évolue constamment au fur et à mesure que de nouvelles techniques de cryptanalyse sont découvertes. Lors de la conception de nouveaux chiffrements par bloc, il est donc nécessaire de considérer ces nouvelles techniques dans l'analyse de sécurité. Dans cette thèse, nous montrons comment construire certaines opérations internes des chiffrements par bloc pour améliorer la résistance à certaines attaques. Nous commençons par donner une méthode pour trouver les permutations paires-impaires optimales selon un certain critère pour les Réseaux de Feistel Généralisés. Grâce à une nouvelle caractérisation et à un algorithme efficace, nous sommes notamment capables de résoudre un problème ouvert depuis 10 ans. Nous donnons ensuite de nouvelles techniques de cryptanalyse pour améliorer la division property, qui nous permet également de donner un nouveau critère optimal pour la conception de boîtes-S. Nous continuons avec de nouvelles observations pour un cadencement de clé alternatif pour AES. Ceci nous permet de donner un nouveau cadencement de clé, à la fois plus efficace et augmentant la sécurité face à certaines attaques par rapport à l’original. Pour finir, nous présentons un algorithme général très effiace permettant d’attaquer la majorité des propositions pour la cryptographie en boîte blanche, ainsi qu’une attaque dédiée sur un schéma non attaqué jusque là, donnant lieu à une attaque qui n’a besoin que de quelques secondes pour retrouver la clé. / Along with new cryptanalysis techniques, the security of block ciphers is always evolving. When designing new block ciphers, we thus need to consider these new techniques during the security analysis. In this thesis, we show how to build some core operations for block ciphers to improve the security against some attacks. We first start by describing a method to find optimal (according to some criterion) even-odd permutations for a Generalized Feistel Network. Using a new characterization and an efficient algorithm, we are able to solve a 10-years old problem. We then give new cryptanalysis techniques to improve the division property, along with a new proven optimal criterion for designing S-boxes. We continue with new observations for the design of an alternative key-schedule for AES. We thus give a new key-schedule, which is both more efficient and more secure against some attacks compared to the original one. Finally, we describe a very efficient generic algorithm to break most proposals in white-box cryptography, as well as a dedicated attack on a previously not analyzed scheme, leading to a key-recovery attack in a few seconds.

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