Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].

Mestre em Sistemas e Computação

In this work will applied the technique of Differential Cryptanalysis, introduced in 1990 by Biham and Shamir, on Papílio s cryptosystem, developed by Karla Ramos, to test and most importantly, to prove its relevance to other block ciphers such as DES, Blowfish and FEAL-N (X). This technique is based on the analysis of differences between plaintext and theirs respective ciphertext, in search of patterns that will assist in the discovery of the subkeys and consequently in the discovery of master key. These differences are obtained by XOR operations. Through this analysis, in addition to obtaining patterns of Pap´ılio, it search to obtain also the main characteristics and behavior of Papilio throughout theirs 16 rounds, identifying and replacing when necessary factors that can be improved in accordance with pre-established definitions of the same, thus providing greater security in the use of his algoritm

An Approach Towards The Development Of An Efficient Symmetric Key Encryption Scheme

n the recent years protection of information in digital form is becoming more important. Image and video encryption has applications in various fields including Internet communications, multimedia systems, medical imaging, Tele-medicine and military communications. During storage as well as in transmission, the multimedia information is being exposed to unauthorized entities unless otherwise adequate security measures are built around the information system. There are many kinds of security threats during the transmission of vital classified information through insecure communication channels. Various encryption schemes are available today to deal with information security issues. Data encryption is widely used to protect sensitive data against the security threat in the form of “attack on confidentiality”. Secure transmission of information through insecure communication channels also requires encryption at the sending side and decryption at the receiving side. Encryption of large text message and image takes time before they can be transmitted, causing considerable delay in successive transmission of information in real-time. In order to minimize the latency, efficient encryption algorithms are needed. An encryption procedure with adequate security and high throughput is sought in multimedia encryption applications. Traditional symmetric key block ciphers like Data Encryption Standard (DES), Advanced Encryption Standard (AES) and Escrowed Encryption Standard (EES) are not efficient when the data size is large. With the availability of fast computing tools and communication networks at relatively lower costs today, these encryption standards appear to be not as fast as one would like. High throughput encryption and decryption are becoming increasingly important in the area of high-speed networking. Fast encryption algorithms are needed in these days for high-speed secure communication of multimedia data. It has been shown that public key algorithms are not a substitute for symmetric-key algorithms. Public key algorithms are slow, whereas symmetric key algorithms generally run much faster. Also, public key systems are vulnerable to chosen plaintext attack. In this research work, a fast symmetric key encryption scheme, entitled “Matrix Array Symmetric Key (MASK) encryption” based on matrix and array manipulations has been conceived and developed. Fast conversion has been achieved with the use of matrix table look-up substitution, array based transposition and circular shift operations that are performed in the algorithm. MASK encryption is a new concept in symmetric key cryptography. It employs matrix and array manipulation technique using secret information and data values. It is a block cipher operated on plain text message (or image) blocks of 128 bits using a secret key of size 128 bits producing cipher text message (or cipher image) blocks of the same size. This cipher has two advantages over traditional ciphers. First, the encryption and decryption procedures are much simpler, and consequently, much faster. Second, the key avalanche effect produced in the ciphertext output is better than that of AES.

Matrix based Key Generation to Enhance Key Avalanche in Advanced Encryption Standard

In symmetric block ciphers, substitution and diffusion operations are performed in multiple rounds using sub-keys generated from a key generation procedure called key schedule. The key schedule plays a very important role in deciding the security of block ciphers. In this paper we propose a complex key generation procedure, based on matrix manipulations, which could be introduced in symmetric ciphers. The proposed key generation procedure offers two advantages. First, the procedure is simple to implement and has complexity in determining the sub-keys through crypt analysis. Secondly, the procedure produces a strong avalanche effect making many bits in the output block of a cipher to undergo changes with one bit change in the secret key. As a case study, matrix based key generation procedure has been introduced in Advanced Encryption Standard (AES) by replacing the existing key schedule of AES. The key avalanche and differential key propagation produced in AES have been observed. The paper describes the matrix based key generation procedure and the enhanced key avalanche and differential key propagation produced in AES. It has been shown that, the key avalanche effect and differential key propagation characteristics of AES have improved by replacing the AES key schedule with the Matrix based key generation procedure

As integrais de Riemann, Riemann-Stieltjes e Lebesgue

Pós-graduação em Matemática Universitária - IGCE

Compreender o trabalho na Atenção Primária à Saúde para desenvolver ações em Saúde do Trabalhador: o caso de um município de médio porte

INTRODUCTION: Attention in Worker's Health (WH) integrality incites expansion of Primary Health Care (PHC) actions. So, it is necessary to understand the work carried out at PHC units and its possibilities to subside WH plans and procedures aiming at workers' health integral attention. OBJECTIVE: To present PHC workers' perception concerning WH actions performed in health care units of a mediumsized municipality in the state of São Paulo. METHODOLOGY: data collected through a 20 question-self-assessment questionnaire prepared by the researcher, using descriptive analysis of closed questions and content analysis of open questions. RESULTS: 45% of all workers answered the questionnaire. All health units in the municipality and all the professional categories part of the PHC teams were enclosed. The answers indicated that the PHC personnel, when providing assistance to users, take their jobs into consideration, and that some actions concerning worker's health are carried out at health care units. The respondents also pointed out that their difficulties to perform these actions are much more related to aspects of the system organization and management, than to the particularities of the worker's health area. CONCLUSION: The study indicates that health care worker's working condition is an important issue for the implementation of PHC worker's health actions

Vector Boolean Functions: Applications in Symmetric Cryptography

Esta tesis establece los fundamentos teóricos y diseña una colección abierta de clases C++ denominada VBF (Vector Boolean Functions) para analizar funciones booleanas vectoriales (funciones que asocian un vector booleano a otro vector booleano) desde una perspectiva criptográfica. Esta nueva implementación emplea la librería NTL de Victor Shoup, incorporando nuevos módulos que complementan a las funciones de NTL, adecuándolas para el análisis criptográfico. La clase fundamental que representa una función booleana vectorial se puede inicializar de manera muy flexible mediante diferentes estructuras de datas tales como la Tabla de verdad, la Representación de traza y la Forma algebraica normal entre otras. De esta manera VBF permite evaluar los criterios criptográficos más relevantes de los algoritmos de cifra en bloque y de stream, así como funciones hash: por ejemplo, proporciona la no-linealidad, la distancia lineal, el grado algebraico, las estructuras lineales, la distribución de frecuencias de los valores absolutos del espectro Walsh o del espectro de autocorrelación, entre otros criterios. Adicionalmente, VBF puede llevar a cabo operaciones entre funciones booleanas vectoriales tales como la comprobación de igualdad, la composición, la inversión, la suma, la suma directa, el bricklayering (aplicación paralela de funciones booleanas vectoriales como la empleada en el algoritmo de cifra Rijndael), y la adición de funciones coordenada. La tesis también muestra el empleo de la librería VBF en dos aplicaciones prácticas. Por un lado, se han analizado las características más relevantes de los sistemas de cifra en bloque. Por otro lado, combinando VBF con algoritmos de optimización, se han diseñado funciones booleanas cuyas propiedades criptográficas son las mejores conocidas hasta la fecha. ABSTRACT This thesis develops the theoretical foundations and designs an open collection of C++ classes, called VBF, designed for analyzing vector Boolean functions (functions that map a Boolean vector to another Boolean vector) from a cryptographic perspective. This new implementation uses the NTL library from Victor Shoup, adding new modules which complement the existing ones making VBF better suited for cryptography. The fundamental class representing a vector Boolean function can be initialized in a flexible way via several alternative types of data structures such as Truth Table, Trace Representation, Algebraic Normal Form (ANF) among others. This way, VBF allows the evaluation of the most relevant cryptographic criteria for block and stream ciphers as well as for hash functions: for instance, it provides the nonlinearity, the linearity distance, the algebraic degree, the linear structures, the frequency distribution of the absolute values of the Walsh Spectrum or the Autocorrelation Spectrum, among others. In addition, VBF can perform operations such as equality testing, composition, inversion, sum, direct sum, bricklayering (parallel application of vector Boolean functions as employed in Rijndael cipher), and adding coordinate functions of two vector Boolean functions. This thesis also illustrates the use of VBF in two practical applications. On the one hand, the most relevant properties of the existing block ciphers have been analysed. On the other hand, by combining VBF with optimization algorithms, new Boolean functions have been designed which have the best known cryptographic properties up-to-date.

Existence of complementary pairs of proportionally balanced designs

Proportionally balanced designs (pi BDs) were introduced by Gray and Matters in response to a need for the allocation of markers of the Queensland Core Skills Test to have a certain property. Subsequent papers extended the theoretical results relating to such designs and provided further instances and general constructions. This work focused on designs comprising blocks of precisely two sizes, and when each variety occurs with one of precisely two possible frequencies. Two designs based on the set V of varieties are complementary if, whenever B is a block of one, then its complement with regard to the set V is a block of the other. Here we present necessary conditions for the existence of complementary pairs of such pi BDs and provide lists of some restricted parameter sets satisfying these necessary conditions. The lists are arranged according to the number of blocks. We demonstrate that not all of these parameter sets give rise to designs. However we establish by construction of the sets of blocks that, for every feasible number of blocks less than or equal to 100, with the possible exception of 63, there exists at least one pair of complementary pi BDs. We also investigate the conditions under which the complementary design can be isomorphic to the original design, and again provide a list of feasible parameters for pairs of such designs with at most 400 blocks.

Product cipher negotiation with on-line evaluation for private communication over computer networks

A method is proposed to offer privacy in computer communications, using symmetric product block ciphers. The security protocol involved a cipher negotiation stage, in which two communicating parties select privately a cipher from a public cipher space. The cipher negotiation process includes an on-line cipher evaluation stage, in which the cryptographic strength of the proposed cipher is estimated. The cryptographic strength of the ciphers is measured by confusion and diffusion. A method is proposed to describe quantitatively these two properties. For the calculation of confusion and diffusion a number of parameters are defined, such as the confusion and diffusion matrices and the marginal diffusion. These parameters involve computationally intensive calculations that are performed off-line, before any communication takes place. Once they are calculated, they are used to obtain estimation equations, which are used for on-line, fast evaluation of the confusion and diffusion of the negotiated cipher. A technique proposed in this thesis describes how to calculate the parameters and how to use the results for fast estimation of confusion and diffusion for any cipher instance within the defined cipher space.

Plaintext Recovery in DES-like Cryptosystems Based on S-boxes with Embedded Parity Check

We describe an approach for recovering the plaintext in block ciphers having a design structure similar to the Data Encryption Standard but with improperly constructed S-boxes. The experiments with a backtracking search algorithm performing this kind of attack against modified DES/Triple-DES in ECB mode show that the unknown plaintext can be recovered with a small amount of uncertainty and this algorithm is highly efficient both in time and memory costs for plaintext sources with relatively low entropy. Our investigations demonstrate once again that modifications resulting to S-boxes which still satisfy some design criteria may lead to very weak ciphers. ACM Computing Classification System (1998): E.3, I.2.7, I.2.8.

A biographical and critical dictionary of painters and engravers : from the revival of the art under Cimabue, and the alledged discovery of engraving by Finiguerra, to the present time : with the ciphers, monograms, and marks, used by each engraver, and an ample list of their principal works, together with two indexes, alphabetical and chronological, to which is prefixed, an introduction, containing a brief account of the painters of antiquity /

Includes indexes.

WATER ACTIVITY OF AQUEOUS SOLUTIONS OF ETHYLENE OXIDE-PROPYLENE OXIDE BLOCK COPOLYMERS AND MALTODEXTRINS

The water activity of aqueous solutions of EO-PO block copolymers of six different molar masses and EO/PO ratios and of maltodextrins of three different molar masses was determined at 298.15 K. The results showed that these aqueous solutions present a negative deviation from Raoult`s law. The Flory-Huggins and UNIFAC excess Gibbs energy models were employed to model the experimental data. While a good agreement was obtained with the Flory-Huggins equation, discrepancies were observed when predicting the experimental behavior with the UNIFAC model. The water activities of ternary systems formed by a synthetic polymer, maltodextrin and water were also measured and used to test the predictive capability of both models.

Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

A study on the encryption algorithm for RFID tag (SEED : 8 Rounds × 64 bits block)

Although it is always weak between RFID Tag and Terminal in focus of the security, there are no security skills in RFID Tag. Recently there are a lot of studying in order to protect it, but because it has some physical limitation of RFID, that is it should be low electric power and high speed, it is impossible to protect with the skills. At present, the methods of RFID security are using a security server, a security policy and security. One of them the most famous skill is the security module, then they has an authentication skill and an encryption skill. In this paper, we designed and implemented after modification original SEED into 8 Round and 64 bits for Tag.