A cohomological approach to the classification of pp-groups

In this thesis we apply methods from homological algebra to the study of finite $p$-groups. Let $G$ be a finite $p$-group and let $\mathbb{F}_p$ be the field of $p$ elements. We consider the cohomology groups $\operatorname{H}^1(G,\mathbb{F}_p)$ and $\operatorname{H}^2(G,\mathbb{F}_p)$ and the Massey product structure on these cohomology groups, which we use to deduce properties about $G$. We tie the classical theory of Massey products in with a general method from deformation theory for constructing hulls of functors and see how far the strictly defined Massey products can take us in this setting. We show how these Massey products relate to extensions of modules and to relations, giving us cohomological presentations of $p$-groups. These presentations will be minimal pro-$p$ presentations and will often be different from the presentations we are used to. This enables us to shed some new light on the classification of $p$-groups, in particular we give a `tree construction' illustrating how we can `produce' $p$-groups using cohomological methods. We investigate groups of exponent $p$ and some of the families of groups appearing in the tree. We also investigate the limits of these methods. As an explicit example illustrating the theory we have introduced, we calculate Massey products using the Yoneda cocomplex and give 0-deficiency presentations for split metacyclic $p$-groups using strictly defined Massey products. We also apply these methods to the modular isomorphism problem, i.e. the problem whether (the isomorphism class of) $G$ is determined by \F_pG. We give a new class $\mathcal{C}$ of finite $p$-groups which can be distinguished using $\mathbb{F}_pG$

Asymmetric image encryption scheme based on Massey Omura scheme

Asymmetric image encryption schemes have shown high resistance against modern cryptanalysis. Massey Omura scheme is one of the popular asymmetric key cryptosystems based on the hard mathematical problem which is discrete logarithm problem. This system is more secure and efficient since there is no exchange of keys during the protocols of encryption and decryption. Thus, this work tried to use this fact to propose a secure asymmetric image encryption scheme. In this scheme the sender and receiver agree on public parameters, then the scheme begin deal with image using Massey Omura scheme to encrypt it by the sender and then decrypted it by the receiver. The proposed scheme tested using peak signal to noise ratio, and unified average changing intensity to prove that it is fast and has high security

Linear feedback shift registers and the minimal realization problem

[EN] The Berlekamp-Massey algorithm solves the problem of finding the shortest linear feedback shift register which generates a given finite sequence of scalars. This problem is reinterpreted from the point of view of the realization theory and several extensions to sequences of matrices are analyzed. We give a generalization of the result on which the Berlekamp-Massey algorithm is based in terms of the partial Brunovsky indices of a sequence of matrices and propose an algorithm to obtain them for sequences of vectors. The results we obtain hold for arbitrary fields.The first author is partially supported by grants MINECO MTM2017-83624-P, MTM2017-90682-REDT, and UPV/EHU GIU16/42. The second author is partially supported by grants MINECO MTM2017-83624-P and MTM2017-90682-REDT.Baragana, I.; Roca Martinez, A. (2019). Linear feedback shift registers and the minimal realization problem. Linear Algebra and its Applications. 576:200-227. https://doi.org/10.1016/j.laa.2018.06.009S20022757

Public Fora, Neutral Governments, and the Prism of Property

The validity of speech restrictions on government property effectively depends upon the property\u27s status as a public forum or not. Professor Massey asserts that this preoccupation with the forum status of public property occludes understanding of the real factors that guide the Court\u27s resolution of the validity of such speech restrictions. In its public forum cases the Court is committed to two propositions: (1) speech on government property can interfere with legitimate non-speech uses of the property, and (2) the government\u27s obligation is to remain neutral in public discourse, rather than to promote as much discourse as possible. Building on those premises, Professor Massey argues that the real issue in public forum cases is whether the speech or the restriction induces deviations from government neutrality, not the forum status of the property. To address the real issue, Professor Massey suggests that we compare the harm and utility of speech on public property and restrictions upon that speech. Both harm and utility is measured by the extent to which the speech or the restriction increases governmental departure from neutrality. Professor Massey then reassesses the principal public forum cases in light of the harm/utility calculus in an effort to demonstrate that his proposed method adds clarity to our understanding of the public forum problem

The development of an improved business game for use in Massey University marketing courses : a thesis presented in partial fulfillment of the requirements for the degree of Master of Agricultural Business and Administration in Marketing at Massey University

The thesis is a response to a problem situation in which a business game, having been used in undergraduate courses for several years, was thought to be inadequate by course and game administrators. The problem is first defined and objectives for the study are set. This is followed by a comprehensive overview of business gaming and a more specific review of the processes and problems of business game design. A description of the game in use, MARKSIM, is given. The MARKSIM experience at Massey University is evaluated from the game administrators' and game players' points of view, the latter by a survey of 41 second and third year marketing students. The specifications of a more satisfactory game are derived from this evaluation and alternative means of acquiring such a game are investigated. The solution chosen as most appropriate is to modify the game already in use and this is carried out. Improvements to the game include reparameterization of the game to reflect the New Zealand business environment, adoption of a two-product product mix, inclusion of optional qualitative administrator inputs reflecting advertising efficiency and annual report quality, superimposition of a share market on the model business community, increased market research capabilities, and general improvement of the game's robustness against administrator and player errors. Evaluation of the resultant game in terms of the problem situation is not possible within the time horizon of the thesis. Program listings are appended

On the primitivity of Lai-Massey schemes

In symmetric cryptography, the round functions used as building blocks for iterated block ciphers are often obtained as the composition of different layers providing confusion and diffusion. The study of the conditions on such layers which make the group generated by the round functions of a block cipher a primitive group has been addressed in the past years, both in the case of Substitution Permutation Networks and Feistel Networks, giving to block cipher designers the receipt to avoid the imprimitivity attack. In this paper a similar study is proposed on the subject of the Lai-Massey scheme, a framework which combines both Substitution Permutation Network and Feistel Network features. Its resistance to the imprimitivity attack is obtained as a consequence of a more general result in which the problem of proving the primitivity of the Lai-Massey scheme is reduced to the simpler one of proving the primitivity of the group generated by the round functions of a strictly related Substitution Permutation Network