São estudados alguns aspectos das álgebras alternativas, como o bar-radical de uma álgebra bárica alternativa e as identidades de grau 4 e 5 nas álgebras de Cayley-Dickson. Neste estudo fazemos uso da decomposição de Peirce e de diversas propriedades importantes das álgebras alternativas. Concluímos mostrando que as únicas identidades de grau 4 são as triviais e as de grau 5 são conseqüência de outras duas identidades conhecidas / We studied some aspects of alternative algebras, in special the bar radical of an alternative baric algebra and identities of degree 4 and 5 of Cayley-Dickson algebras. We made significant use of the Peirce decomposition and several properties of the alternative algebras, in order to show that the only identities of degree four are the trivial ones, and the identities of degree five are consequences of other two known identities.

São estudados alguns aspectos das álgebras alternativas, como o bar-radical de uma álgebra bárica alternativa e as identidades de grau 4 e 5 nas álgebras de Cayley-Dickson. Neste estudo fazemos uso da decomposição de Peirce e de diversas propriedades importantes das álgebras alternativas. Concluímos mostrando que as únicas identidades de grau 4 são as triviais e as de grau 5 são conseqüência de outras duas identidades conhecidas / We studied some aspects of alternative algebras, in special the bar radical of an alternative baric algebra and identities of degree 4 and 5 of Cayley-Dickson algebras. We made significant use of the Peirce decomposition and several properties of the alternative algebras, in order to show that the only identities of degree four are the trivial ones, and the identities of degree five are consequences of other two known identities.

壹、引言 近年來，訊號傳送的途徑，已擺脫了傳統上著重管線傳送的優勢；有愈來愈多的訊號 彌漫在廣闊的空間裡，而這種無線式的傳送所需面臨的問題是：不具有排它性，任何 有接收器材的非原始接收者都可以截聽到訊息，由於因應而生的保密技術格外受矚目 ，密碼學（CRYPTOGRAPHY）便是滿足此需要的學問。本論文所探討的排列多項式（PE RMUTATION POLYNOMIAL）是密碼學中重要的工具之一。 貳、論文主體 所謂排列多項式，即是佈於代數體上的多項式，把此多項式當成函數而作用於代數體 （FIELD ）上，如果此函數具有一對一的性質，則是排列多項式。即 ｆ（ｘ）＝ａ。+ ａ1 ｘ1 + ....ａnｘn ≡ Ｆq〔Ｘ〕且 ｆ（ａ）╪ｆ（ｂ），ａ，ｂ≡Ｆｑ，ａ╪ｂ． 在論文中，介紹先進學者對排列多項式的認識。如：LAGRANGE'S INTERPOLATION是利 用函數值來描繪多項式，著名的學者CARLITZ ，利用特殊多項式來合成出排列多項式 ，論文中有更進一步的合成法提出，而HERMITE 跟DICKSON 學者則提出Ft函數其冪次 的變化情形，來判別排列多項式之是否，是最通俗的判別理論。 此外，由吾人所蒐集的資料中發現，在祗有兩項的多項式中，被發現到其它更簡捷快 速的判別方法，故二項式的多項式的探討是本論文的第一主題，對於 k j Ｘ＋ｂｘ ≡Ｆｑ〔Ｘ〕， 給予固定類型的ｑ，ｋ，ｊ情形下，祗須檢定ｂ是否具特 殊性質就可決定是否為排列多項式，這是一種方法。另有學者並不固定ｑ，ｋ，ｊ， 反而從ｑ，ｋ，ｊ數字下手，找尋出某種關連性，其結果使得係數ｂ，只有當ｂ＝０ ，時才有機會是排列多項式，乘下單項式的判別過程，就很容易了。另外還有一種方 法也是找尋ｑ，ｋ，ｊ間的關係，不過其結果在找出：多項式為非排列多項式，是比 較特別的地方。上述三方法，本論文網羅大部份有關論文，綜合各家之長，並適當給 予一同於原作者的新觀點證明方法。 至於本論文第二主題是著名的CARLITZ'S CONJECTURE此預測敘述：對於任何具有最高 冪次是偶數的多項式，必定存在一個自然數ｋ，使得給定的代數體，其元素個數只要 超過ｋ，則此多項式必定不是排列多項式。此預測當degree n=10,12,14, and 2m 時 已被證實為真。本論文僅就n=2m，做系統地探討及重新證明。 參、結語 本論文所論的兩主題，對於佈於代數體上的多項式是否為排列多項式，在判別的過程 上應有相當的助益才是。

The objective of this research is to determine if it is possible to reduce the number of organic solar cells required to power a load using a DC to DC converter thereby reducing the cost of the organic solar array system. An organic solar power system designer may choose an organic implementation of a DC to DC converter to go along with the organic solar cell array. Common DC to DC converters include the buck converter, boost converter, buck/boost converter, and Cuk converter, all of which are not good candidates for organic implementation due to their use of inductors. Organic inductors are relatively more lossy than organic capacitors. So, an inductor-less DC to DC converter, such as the Dickson charge pump, would be a better candidate for organic implementation. Solar cells connected in an array configuration usually do not perform up to their full potential due to current and voltage mismatches between solar cells. These mismatches can be related to each solar cell's circuit model parameters such as the photon current density, diode ideality factor, diode reverse saturation current density, parallel resistance, and series resistance. This research varies these circuit model parameters as dependent variables, and observes the loads and power levels that make the Dickson charge pump a feasible option. The results show that current mismatch does produce an opportunity to use a DC to DC converter to save the use of a few solar cells. However, the Dickson charge pump was found to be infeasible due to an input voltage requirement that could not be met using the tested organic solar cells.

S-boxes are key components of many symmetric cryptographic primitives. Among them, some block ciphers and hash functions are vulnerable to attacks based on differential cryptanalysis, a technique introduced by Biham and Shamir in the early 90’s. Resistance against attacks from this family depends on the so-called differential properties of the S-boxes used. When we consider S-boxes as functions over finite fields of characteristic 2, monomials turn out to be good candidates. In this Master’s Thesis, we study the differential properties of a particular family of monomials, namely those with exponent 2ͭᵗ-1 In particular, conjectures from Blondeau’s PhD Thesis are proved. More specifically, we derive the differential spectrum of monomials with exponent 2ͭᵗ-1 for several values of t using a method similar to the proof Blondeau et al. made of the spectrum of x -<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Crightarrow" /> x⁷. The first two chapters of this Thesis provide the mathematical and cryptographic background necessary while the third and fourth chapters contain the proofs of the spectra we extracted and some observations which, among other things, connect this problem with the study of particular Dickson polynomials.

No description available.

壹、引言 近年來，訊號傳送的途徑，已擺脫了傳統上著重管線傳送的優勢；有愈來愈多的訊號 彌漫在廣闊的空間裡，而這種無線式的傳送所需面臨的問題是：不具有排它性，任何 有接收器材的非原始接收者都可以截聽到訊息，由於因應而生的保密技術格外受矚目 ，密碼學（CRYPTOGRAPHY）便是滿足此需要的學問。本論文所探討的排列多項式（PE RMUTATION POLYNOMIAL）是密碼學中重要的工具之一。 貳、論文主體 所謂排列多項式，即是佈於代數體上的多項式，把此多項式當成函數而作用於代數體 （FIELD ）上，如果此函數具有一對一的性質，則是排列多項式。即 ｆ（ｘ）＝ａ。+ ａ1 ｘ1 + ....ａnｘn ≡ Ｆq〔Ｘ〕且 ｆ（ａ）╪ｆ（ｂ），ａ，ｂ≡Ｆｑ，ａ╪ｂ． 在論文中，介紹先進學者對排列多項式的認識。如：LAGRANGE'S INTERPOLATION是利 用函數值來描繪多項式，著名的學者CARLITZ ，利用特殊多項式來合成出排列多項式 ，論文中有更進一步的合成法提出，而HERMITE 跟DICKSON 學者則提出Ft函數其冪次 的變化情形，來判別排列多項式之是否，是最通俗的判別理論。 此外，由吾人所蒐集的資料中發現，在祗有兩項的多項式中，被發現到其它更簡捷快 速的判別方法，故二項式的多項式的探討是本論文的第一主題，對於 k j Ｘ＋ｂｘ ≡Ｆｑ〔Ｘ〕， 給予固定類型的ｑ，ｋ，ｊ情形下，祗須檢定ｂ是否具特 殊性質就可決定是否為排列多項式，這是一種方法。另有學者並不固定ｑ，ｋ，ｊ， 反而從ｑ，ｋ，ｊ數字下手，找尋出某種關連性，其結果使得係數ｂ，只有當ｂ＝０ ，時才有機會是排列多項式，乘下單項式的判別過程，就很容易了。另外還有一種方 法也是找尋ｑ，ｋ，ｊ間的關係，不過其結果在找出：多項式為非排列多項式，是比 較特別的地方。上述三方法，本論文網羅大部份有關論文，綜合各家之長，並適當給 予一同於原作者的新觀點證明方法。 至於本論文第二主題是著名的CARLITZ'S CONJECTURE此預測敘述：對於任何具有最高 冪次是偶數的多項式，必定存在一個自然數ｋ，使得給定的代數體，其元素個數只要 超過ｋ，則此多項式必定不是排列多項式。此預測當degree n=10,12,14, and 2m 時 已被證實為真。本論文僅就n=2m，做系統地探討及重新證明。 參、結語 本論文所論的兩主題，對於佈於代數體上的多項式是否為排列多項式，在判別的過程 上應有相當的助益才是。

For radio frequency energy transmission, the conversion efficiency of the receiver is decisive not only for reducing sending power, but also for enabling energy transmission over long and variable distances. In this contribution, we present a passive RF-DC converter for energy harvesting at ultra-low input power at 868 MHz. The novel converter consists of a reactive matching circuit and a combined voltage multiplier and rectifier. The stored energy in the input inductor and capacitance, during the negative wave, is conveyed to the output capacitance during the positive one. Although Dickson and Villard topologies have principally comparable efficiency for multi-stage voltage multipliers, the Dickson topology reaches a better efficiency within the novel ultra-low input power converter concept. At the output stage, a low-pass filter is introduced to reduce ripple at high frequencies in order to realize a stable DC signal. The proposed rectifier enables harvesting energy at even a low input power from −40 dBm for a resistive load of 50 kΩ. It realizes a significant improvement in comparison with state of the art solutions

It is well known that communication systems employing multiple transmit and multiple receive antennas provide high data rates along with increased reliability. Some of the design criteria of the space-time block codes (STBCs) for multiple input multiple output (MIMO)communication system are that these codes should attain large transmit diversity, high data-rate, low decoding-complexity, low decoding –delay and low peak-to-average power ratio (PAPR). STBCs based on real orthogonal designs (RODs) and complex orthogonal designs (CODs) achieve full transmit diversity and in addition, these codes are single-symbol maximum-likelihood (ML) decodable. It has been observed that the data-rate (in number of information symbols per channel use) of the square CODs falls exponentially with increase in number of antennas and it has led to the construction of rectangular CODs with high rate. We have constructed a class of maximal-rate CODs for n transmit antennas with rate if n is even and if n is odd. The novelty of the above construction is that they 2n+1 are constructed from square CODs. Though these codes have a high rate, this is achieved at the expense of large decoding delay especially when the number of antennas is 5or more. Moreover the rate also converges to half as the number of transmit antennas increases. We give a construction of rate-1/2 CODs with a substantial reduction in decoding delay when compared with the maximal- rate codes. Though there is a significant improvement in the rate of the codes mentioned above when compared with square CODs for the same number of antennas, the decoding delay of these codes is still considerably high. For certain applications, it is desirable to construct codes which are balanced with respect to both rate and decoding delay. To this end, we have constructed high rate and low decoding-delay RODs and CODs from Cayley-Dickson Algebra. Apart from the rate and decoding delay of orthogonal designs, peak-to-average power ratio (PAPR) of STBC is very important from implementation point of view. The standard constructions of square complex orthogonal designs contain a large number of zeros in the matrix result in gin high PAPR. We have given a construction for square complex orthogonal designs with lesser number of zero entries than the known constructions. When a + 1 is a power of 2, we get codes with no zero entries. Further more, we get complex orthogonal designs with no zero entry for any power of 2 antennas by introducing co- ordinate interleaved variables in the design matrix. These codes have significant advantage over the existing codes in term of PAPR. The only sacrifice that is made in the construction of these codes is that the signaling complexity (of these codes) is marginally greater than the existing codes (with zero entries) for some of the entries in the matrix consist of co-ordinate interleaved variables. Also a class of maximal-rate CODs (For mathematical equations pl see the pdf file)

This diploma thesis deals with the design of a partially integrated charge pump in 0.25 micron technology ACMOS. The work is divided into two main parts, theoretical and practical. The theoretical section describes in detail various topologies of higher voltage generation of a charge pump and selected methods of regulating the output voltage of charge pumps. The practical part deals with the the actual design of a charge pump together with the arguments for the choice of the TPVD topology and the type of the regulation. Three regulation methods of a charge pump were implemented, tested and are dealt with: Pulse Skip, Constant frequency and PWM. There are 3 sub chapters, each describing a different regulation method, defining all the key elements of the design of such a charge pump and the results of the simulations are discussed. Conclusion of the thesis summarizes the results of the design of charge pumps, comparing them on the basis of the chosen type of output voltage regulation.