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This thesis follows up the results of article A. Drápal a I. M. Wanless, On the number of quadratic orthomorphisms that produce maximally nonassociative quasigroups. This paper dealt with the density of maximally non-associative quasigroups of a certain cons- truction. However, certain cases had to be neglected in the calculations due to restrictive conditions. The examination of these cases is the subject of this work. It turned out that the asymptotic behavior in the general case as in the article differs from the beha- vior in cases examined in our work. In addition to the calculations themselves, the work contains a theoretical introduction with an explanation of the constructions used in the previous article, as well as our own theory necessary for our calculations. In addition, we experimentally verified our results. 1

This thesis deals with properties of permutations and three-line latin rectan- gles. In the first part it offers solutions to several combinatorial problems and derrives formula for enumeration of three-line latin rectangles and its simplifica- tion based on articles by J. Riordan, but unlike Riordan's articles, without use of generating functions. In the second part it shows algebraic properties of permu- tation conjugation. Furthermore it provides an algorithm that constructs set of permutations commuting with a given permutation and enumerates orbits of the set of three-line latin rectangles when conjugating by the group of permutations Sn for small n.

In this work an attack upon Wieschebrink's version of Niederreiter cryptosystem using GRS codes by Couvreur et. al. from 2014 is described. Relevant notions of error-correcting code theory are presented, definitions of McEliece scheme, Niederreiter scheme and their respective Wieschebrink's modifications are shown. A description of the attack using distinguisher as described by Couvreur et. al. Based on componentwise code products and shortened codes properties follows, as does Sidelnikov-Shestakov attack on Niederreiter scheme with relevant group theory notions. Implementation details are also outlined. The attack is then summarized and its complexity is mentioned. The attack duration measured by the C++ implementation is presented in the last chapter. The program implementing the cryptosystem as well as the attack is located in the appendix with the program documentation. Powered by TCPDF (www.tcpdf.org)

Steganography is a technique which hides secret information. In this work, we will hide a secret information in the packets which are produced during a Skype call. Skype is one of the best known and the most widely used VoIP applications. We will propose, describe and implement a steganography method by which we will send the secret message during the Skype call. For embedding the message into packets and extracting them, we will use steganographic method called matrix encoding. To avoid packet loss, we will increase the robustness of this method by error-correcting and self-synchronising codes. As error-correcting codes, we will use the binary Hamming (7, 4) -codes and for the self-synchronising, we will use T-codes. 1

This bachelor thesis deals with the theory of continued fractions which is design of a stream cipher in article On the use of continued fractions for stream ciphers based on. Since results about probability for a positive integer number to be a partial quotient of a generalised continued fraction which are necessary for proving the cipher secure, has not been proved yet, there are summarized previous results which could lead to proving them. In particular, basic properties of classical and generalised continued fractions and proof of Kuzmin theorem are presented here. Distribution of probability for a positive integer number to be a partial quotient of a classical continued fraction follows from Kuzmin theorem. The design of the stream cipher from the article is briefly introduced at the end of the thesis. Powered by TCPDF (www.tcpdf.org)

In this thesis, we study some properties of MDS codes and we mainly focus on the MDS codes conjecture. In the first chapter we define MDS codes, show some examples and basic properties of MDS codes, for example a link between MDS codes and Latin squares or rectangles. Afterwards we state the MDS codes conjecture and prove it in several cases. In the third chapter we can observe the relationship between MDS codes and narcs in projective geometries. Finally we present those known cases, for which the MDS conjecture holds.

Modern steganography is a relatively new discipline with many applications in information security. Contrary to the cryptography which is trying to make a message unreadable to third party using cryptographic algorithms, the aim of steganography is to hide a communication between parties. Applications of error-correcting codes and covering functions markedly increases abilities and security of steganographic algorithms. This thesis is attended to steganography using error-correcting codes which has the best results nowadays regarding embedding efficiency. New constructions will help us to work with non-linear codes and providing new steganographic algorithms. We will see that these algorithms have a better ability to hide communication, resp. a message in a digital medium. Further improvements can be made using applications of general q-ary codes. Many new questions are coming out with that which need to be answered. Several comparisons are showing that the area of steganography is in a beginning and we will be participants of such a progress as cryptography experienced in the last two decades.