Collision Resistance from Multi-Collision Resistance for all Constant Parameters

A $t$-multi-collision-resistant hash function ($t$-MCRH) is a family of shrinking functions for which it is computationally hard to find $t$ distinct inputs mapping to the same output for a function sampled from this family. Several works have shown that $t$-MCRHs are sufficient for many of the applications of collision-resistant hash functions (CRHs), which correspond to the special case of $t = 2$. An important question is hence whether $t$-MCRHs for $t > 2$ are fundamentally weaker objects than CRHs. As a first step towards resolving this question, Rothblum and Vasudevan (CRYPTO \u2722) recently gave non-black-box constructions of infinitely-often secure CRHs from $t$-MCRHs for $t \in \{3,4\}$ assuming the MCRH is sufficiently shrinking. Earlier on, Komargodski and Yogev (CRYPTO \u2718) also showed that $t$-MCRHs for any constant $t$ imply the weaker notion of a distributional CRH. In this paper, we remove the limitations of prior works, and completely resolve the question of the power of $t$-MCRHs for constant $t$ in the infinitely-often regime, showing that the existence of such a function family always implies the existence of an infinitely-often secure CRH. As in the works mentioned above, our construction is non-blackbox and non-constructive. We further give a new domain extension result for MCRHs that enables us to show that the underlying MCRH need only have arbitrarily small linear shrinkage (mapping $(1 + \epsilon)n$ bits to $n$ bits for any fixed $\epsilon > 0$) to imply the existence of CRHs

Finding twin smooth integers by solving Pell equations

Any pair of consecutive B-smooth integers for a given smoothness bound B corresponds to a solution (x, y) of the equation x^2 - 2Dy^2 = 1 for a certain square-free, B-smooth integer D and a B-smooth integer y. This paper describes algorithms to find such twin B-smooth integers that lie in a given interval by using the structure of solutions of the above Pell equation. The problem of finding such twin smooth integers is motivated by the quest for suitable parameters to efficiently instantiate recent isogeny-based cryptosystems. While the Pell equation structure of twin B-smooth integers has previously been used to describe and compute the full set of such pairs for very small values of B, increasing B to allow for cryptographically sized solutions makes this approach utterly infeasible. We start by revisiting the Pell solution structure of the set of twin smooth integers. Instead of using it to enumerate all twin smooth pairs, we focus on identifying only those that lie in a given interval. This restriction allows us to describe algorithms that navigate the vast set of Pell solutions in a more targeted way. Experiments run with these algorithms have provided examples of twin B-smooth pairs that are larger and have smaller smoothness bound B than previously reported pairs. Unfortunately, those examples do not yet provide better parameters for cryptography, but we hope that our methods can be generalized or used as subroutines in future work to achieve that goal

Foto-obrazy architektury: Fotografia jako medium referujące i projektujące architekturę

Praca recenzowana / peer-reviewed paperNiniejszy zbiór prac teoretycznych, fotoesejów i kronika studenckich konkursów fotograficznych organizowanych od 2008 roku na Wydziale Architektury i Sztuk Pięknych Krakowskiej Akademii im. Andrzeja Frycza Modrzewskiego, ma być zapisem refleksji związanych ze specyficzną, jak dotąd mało zbadaną a wszechobecną częścią teorii architektury, jaką jest fotografia. Jej szczególna odmiana ściśle związana ze sztuką budowania jest określana mianem fotografii architektonicznej, jednakże niniejsza monografia nie została tą definicją ograniczona.This book contains a selection of theoretical works and photo essays as well as a chronicle of photo competitions organised in the Faculty of Architecture and Fine Arts at Andrzej Frycz Modrzewski Krakow University since 2008, which is meant as the record of thoughts related to the specific, omnipresent though little examined so far, realm of the theory of architecture, i.e. photography. Its specific variant closely related to the building practice is called architectural photography. This monograph, however, is not restricted by means of the said definition and attempts at a slightly broader description of the phenomenon, reaching beyond its boundaries.Monografia powstała w ramach projektu badawczego nr WAiSP/DS/4/201

Genomic Diversity in Two Related Plant Species with and without Sex Chromosomes - Silene latifolia and S. vulgaris

Genome size evolution is a complex process influenced by polyploidization, satellite DNA accumulation, and expansion of retroelements. How this process could be affected by different reproductive strategies is still poorly understood.We analyzed differences in the number and distribution of major repetitive DNA elements in two closely related species, Silene latifolia and S. vulgaris. Both species are diploid and possess the same chromosome number (2n = 24), but differ in their genome size and mode of reproduction. The dioecious S. latifolia (1C = 2.70 pg DNA) possesses sex chromosomes and its genome is 2.5× larger than that of the gynodioecious S. vulgaris (1C = 1.13 pg DNA), which does not possess sex chromosomes. We discovered that the genome of S. latifolia is larger mainly due to the expansion of Ogre retrotransposons. Surprisingly, the centromeric STAR-C and TR1 tandem repeats were found to be more abundant in S. vulgaris, the species with the smaller genome. We further examined the distribution of major repetitive sequences in related species in the Caryophyllaceae family. The results of FISH (fluorescence in situ hybridization) on mitotic chromosomes with the Retand element indicate that large rearrangements occurred during the evolution of the Caryophyllaceae family.Our data demonstrate that the evolution of genome size in the genus Silene is accompanied by the expansion of different repetitive elements with specific patterns in the dioecious species possessing the sex chromosomes

Evaluation of a Center of Excellence Specialized in Financial Securities in a Concrete International Company

The aim of this paper is to describe the activities of a companys center of excellence specialized in handling financial securities, analyze its performance measurement system and potentially propose improvements. The theoretical part focuses first on centers of excellence, performance measurement and credit policy and management. Next, there is an introduction to financial securities and RACI charts. In the practical part, there is a description of the company and its center of excellence and most importantly an analysis of the given performance measurement system, a questionnaire among the companys employees and a proposal of new measures

Use of Business Intelligence Tools in Activity Based Budgeting (Based on a Specific Company)

Tato diplomová práce je zaměřena na vývoj databázového systému pro správu alokačního modelu na bázi activity based technik a tvorbu návazného reportingu ve vybraném nástroji business intelligence. Hlavním cílem práce je představit a posoudit využitelnost nástrojů business intelligence v modelech založených na přiřazování nákladů aktivitám, a to na příkladu reálného projektu v konkrétní společnosti. Teoretická část práce se zabývá oblastmi business intelligence a manažerského účetnictví se zaměřením na kalkulace a activity based techniky. V praktické části je zpracován projekt vyvinutí databázového systému a návazného reportingu v nástroji business intelligence. V závěru je zhodnocena využitelnost daného řešení.This thesis focuses on development of a database system used for managing an allocation model based on activity based techniques and creation of related reports in a selected business intelligence tool. The main goal of the thesis is to present and evaluate usability of business intelligence tools in models based on activity based costing. This is illustrated on a real project in a specific company. The theoretical part of the thesis deals with business intelligence and managerial accounting with a focus on costing systems and activity based techniques. The practical part of the thesis then focuses on development of a database system and related reports in a business intelligence tool. At the end of the thesis, there is an overall evaluation of the solution