Perancangan Perangkat Lunak dengan Metode RSA dengan Pembangkit Bilangan Prima Secara Opsional

Pengguna dalam memilih algoritma Kriptografi akan juga sangat memperhatikan faktor kecepatan selain kekuatannya. Kompleksitas RSA barkaitan dengan bilangan prima menghasilkan karakteristik  kecepatan RSA berbading terbalik dengan kekuatannya. Proses pembangkitan bilangan prima menentukan kekuatan RSA. Jika bilangan yang dibangkitkan berupa prima asli maka menghasilakan penyandian yang kuat.  Sedangkan jika  yang dibangkitkan berupa bilangan prima yang lemah (pseudo prima) maka menghasilkan penyandian yang lemah pula. Secara konsep upaya pengamanan data harus sesuai dengan nilai (ekonomis dan strategis) data yang akan diamankan. Data yang bernilai murah cukup diamankan dengan kekuatan yang tidak terlalu besar sedangkan data yang bernilai mahal harus diamankan dengan kekuatan besar Oleh karena itu untuk mengatasi persoalan lambatnya RSA maka dilakukan pemilihan metode pembangkit prima yang sesuai dengan tingkat keamanan yang dibutuhkan pengguna.Peneitian  ini bertujuan untuk melakukan perancangan perangkat lunak yang mengimplementasikan RSA dengan metode pembangkit bilangan prima yang dapat dipilih oleh pengguna. Metode yang digunakan dalam penelitian ini adalah Sieve of Eratosthenes, Sieve of Sundaram dan Sieve of Atkin. Perancangan awal telah dihasilkan dalam penelitian ini berupa diagram use-case, skenario dan kelas analisis. Untuk pengembangan perangkat lunak secara utuh tperlu dilanjutkan ke perancangan detail dan implementsi pada bahasa program tertentu

Parallelization of JStar Programs on a Distributed Computer

In the past, the performance of sequential programs grew exponentially as the performance of CPUs increased with Moore’s Law. Since 2005 however, performance improvements have come in the form of more parallel CPU cores. Writing parallel programs using existing programming languages can be difficult and error-prone. JStar is a new programming language that allows programs to be written in a naturally parallel way. The JStar project aims to produce compilers that can produce executables for a variety of architectures (such as many-core, GPUs and distributed computers). This thesis proposes a process for compiling these programs into distributed executables, and investigates various trade-offs and techniques for implementing JStar programs on a distributed computer. In this process, first a parallel design is created, then this design is expressed by a separate set of distribute statements that are combined with the original program to create a distributed program. The expressiveness and effectiveness of this approach is investigated for two case study JStar programs: (1) a prime number counting program (2) a version of Conway’s Game of Life. Various designs were hand-translated into a distributed Java programs and benchmarks were run to assess the performance of different designs. For each of these case studies, parallel designs were found that achieved high levels of speedup

Grained integers and applications to cryptography

To meet the requirements of the modern communication society, cryptographic techniques are of central importance. In modern cryptography, we try to build cryptographic primitives, whose security can be reduced to solving a particular number theoretic problem for which no fast algorithmic method is known by now. Thus, any advance in the understanding of the nature of such problems indirectly gives insight in the analysis of some of the most practical cryptographic techniques. In this work we analyze exactly this aspect much more deeply: How can we use some of the purely theoretical results in number theory to answer very practical questions on the security of widely used cryptographic algorithms and how can we use such results in concrete implementations? While trying to answer these kinds of security-related questions, we always think two-fold: From a cryptographic, security-ensuring perspective and from a cryptanalytic one. After we outlined -- with a special focus on the historical development of these results -- the necessary analytic and algorithmic foundations of number theory, we first delve into the question how point addition on certain elliptic curves can be done efficiently. The resulting formulas have their application in the cryptanalysis of crypto systems that are insecure if factoring integers can be done efficiently. The rest of the thesis is devoted to the study of integers, all of whose prime factors are neither too small nor too large. We show with the help of two applications how one can use the properties of such kinds of integers to answer very practical questions in the design and the analysis of cryptographic primitives: The optimization of a hardware-realization of the cofactorization step of the General Number Field Sieve and the analysis of different standardized key-generation algorithms

Implementation and Evaluation of Algorithmic Skeletons: Parallelisation of Computer Algebra Algorithms

This thesis presents design and implementation approaches for the parallel algorithms of computer algebra. We use algorithmic skeletons and also further approaches, like data parallel arithmetic and actors. We have implemented skeletons for divide and conquer algorithms and some special parallel loops, that we call ‘repeated computation with a possibility of premature termination’. We introduce in this thesis a rational data parallel arithmetic. We focus on parallel symbolic computation algorithms, for these algorithms our arithmetic provides a generic parallelisation approach. The implementation is carried out in Eden, a parallel functional programming language based on Haskell. This choice enables us to encode both the skeletons and the programs in the same language. Moreover, it allows us to refrain from using two different languages—one for the implementation and one for the interface—for our implementation of computer algebra algorithms. Further, this thesis presents methods for evaluation and estimation of parallel execution times. We partition the parallel execution time into two components. One of them accounts for the quality of the parallelisation, we call it the ‘parallel penalty’. The other is the sequential execution time. For the estimation, we predict both components separately, using statistical methods. This enables very confident estimations, although using drastically less measurement points than other methods. We have applied both our evaluation and estimation approaches to the parallel programs presented in this thesis. We haven also used existing estimation methods. We developed divide and conquer skeletons for the implementation of fast parallel multiplication. We have implemented the Karatsuba algorithm, Strassen’s matrix multiplication algorithm and the fast Fourier transform. The latter was used to implement polynomial convolution that leads to a further fast multiplication algorithm. Specially for our implementation of Strassen algorithm we have designed and implemented a divide and conquer skeleton basing on actors. We have implemented the parallel fast Fourier transform, and not only did we use new divide and conquer skeletons, but also developed a map-and-transpose skeleton. It enables good parallelisation of the Fourier transform. The parallelisation of Karatsuba multiplication shows a very good performance. We have analysed the parallel penalty of our programs and compared it to the serial fraction—an approach, known from literature. We also performed execution time estimations of our divide and conquer programs. This thesis presents a parallel map+reduce skeleton scheme. It allows us to combine the usual parallel map skeletons, like parMap, farm, workpool, with a premature termination property. We use this to implement the so-called ‘parallel repeated computation’, a special form of a speculative parallel loop. We have implemented two probabilistic primality tests: the Rabin–Miller test and the Jacobi sum test. We parallelised both with our approach. We analysed the task distribution and stated the fitting configurations of the Jacobi sum test. We have shown formally that the Jacobi sum test can be implemented in parallel. Subsequently, we parallelised it, analysed the load balancing issues, and produced an optimisation. The latter enabled a good implementation, as verified using the parallel penalty. We have also estimated the performance of the tests for further input sizes and numbers of processing elements. Parallelisation of the Jacobi sum test and our generic parallelisation scheme for the repeated computation is our original contribution. The data parallel arithmetic was defined not only for integers, which is already known, but also for rationals. We handled the common factors of the numerator or denominator of the fraction with the modulus in a novel manner. This is required to obtain a true multiple-residue arithmetic, a novel result of our research. Using these mathematical advances, we have parallelised the determinant computation using the Gauß elimination. As always, we have performed task distribution analysis and estimation of the parallel execution time of our implementation. A similar computation in Maple emphasised the potential of our approach. Data parallel arithmetic enables parallelisation of entire classes of computer algebra algorithms. Summarising, this thesis presents and thoroughly evaluates new and existing design decisions for high-level parallelisations of computer algebra algorithms

Scheduling Tasks on Intermittently-Powered Real-Time Systems

Batteryless systems go through sporadic power on and off phases due to intermittently available energy; thus, they are called intermittent systems. Unfortunately, this intermittence in power supply hinders the timely execution of tasks and limits such devices’ potential in certain application domains, e.g., healthcare, live-stock tracking. Unlike prior work on time-aware intermittent systems that focuses on timekeeping [1, 2, 3] and discarding expired data [4], this dissertation concentrates on finishing task execution on time. I leverage the data processing and control layer of batteryless systems by developing frameworks that (1) integrate energy harvesting and real-time systems, (2) rethink machine learning algorithms for an energy-aware imprecise task scheduling framework, (3) develop scheduling algorithms that, along with deciding what to compute, answers when to compute and when to harvest, and (4) utilize distributed systems that collaboratively emulate a persistently powered system. Scheduling Framework for Intermittently Powered Computing Systems. Batteryless systems rely on sporadically available harvestable energy. For example, kinetic-powered motion detector sensors on the impalas can only harvest energy when the impalas are moving, which cannot be ascertained in advance. This uncertainty poses a unique real-time scheduling problem where existing real-time algorithms fail due to the interruption in execution time. This dissertation proposes a unified scheduling framework that includes both harvesting and computing. Imprecise Deep Neural Network Inference in Deadline-Aware Intermittent Systems. This dissertation proposes Zygarde- an energy-aware and outcome-aware soft-real-time imprecise deep neural network (DNN) task scheduling framework for intermittent systems. Zygarde leverages the semantic diversity of input data and layer-dependent expressiveness of deep features and infers only the necessary DNN layers based on available time and energy. Zygarde proposes a novel technique to determine the imprecise boundary at the runtime by exploiting the clustering classifiers and specialized offline training of the DNNs to minimize the loss of accuracy due to partial execution. It also proposes a single metric, η to represent a system’s predictability that measures how close a harvesterâs harvesting pattern is to a constant energy source. Besides, Zygarde consists of a scheduling algorithm that takes available time, available energy, impreciseness, and the classifier's performance into account. Scheduling Mutually Exclusive Computing and Harvesting Tasks in Deadline-Aware Intermittent Systems. The lack of sufficient ambient energy to directly power the intermittent systems introduces mutually exclusive computing and charging cycles of intermittently powered systems. This introduces a challenging real-time scheduling problem where the existing real-time algorithms fail due to the lack of interruption in execution time. To address this, this dissertation proposes Celebi, which considers the dynamics of the available energy and schedules when to harvest and when to compute in batteryless systems. Using data-driven simulation and real-world experiments, this dissertation shows that Celebi significantly increases the number of tasks that complete execution before their deadline when power was only available intermittently. Persistent System Emulation with Distributed Intermittent System. Intermittently-powered sensing and computing systems go through sporadic power-on and off periods due to the uncertain availability of energy sources. Despite the recent efforts to advance time-sensitive intermittent systems, such systems fail to capture important target events when the energy is absent for a prolonged time. This event miss limits the potential usage of intermittent systems in fault- intolerant and safety-critical applications. To address this problem, this dissertation proposes Falinks, a framework that allows a swarm of distributed intermittently powered nodes to collaboratively imitate the sensing and computing capabilities of a persistently powered system. This framework provides power-on and off schedules for the swamp of intermittent nodes which has no communication capability with each other.Doctor of Philosoph

Mathematical surfaces models between art and reality

In this paper, I want to document the history of the mathematical surfaces models used for the didactics of pure and applied “High Mathematics” and as art pieces. These models were built between the second half of nineteenth century and the 1930s. I want here also to underline several important links that put in correspondence conception and construction of models with scholars, cultural institutes, specific views of research and didactical studies in mathematical sciences and with the world of the figurative arts furthermore. At the same time the singular beauty of form and colour which the models possessed, aroused the admiration of those entirely ignorant of their mathematical attraction

Die Herausforderungen nichtlinearer Parameter und Variablen in automatischer Schleifenparallelisierung

With the rise of manycore processors, parallelism is becoming a mainstream necessity. Unfortunately, parallel programming is inherently more difficult than sequential programming; therefore, techniques for automatic parallelisation will become indispensable. We aim at extending the well-known polyhedron model, which promises this automation, beyond some of its current restrictions. Up to now, loop bounds and array subscripts in the modelled codes must be expressions linear in both the variables and the parameters. We lift this restriction and allow certain polynomial expressions instead of linear ones. With our extensions, we are able to handle more programs in all phases of the parallelisation process (dependence analysis, transformation of the program model, code generation). We extend Banerjee's classical dependence analysis to handle one non-linear parameter p, i.e., we are able to determine precisely the solutions of the system of conflict equalities for input programs with non-linear array accesses like A[p*i] in dependence of the residue class of p. We make contributions to three transformations desirable in automatic parallelisation. First, we show that using a generalised Simplex algorithm, which we have developed, schedules with non-linear parameters like theta(i)=floor(i/n) can be computed. In addition, such schedules can be expressed easily as a quantifier elimination problem but this approach turns out to be computationally less efficient with the available implementation. As a second transformation, we study parametric tiling which is used to adapt a parallelised program to the number of available processors at run time. Third, we present a localisation technique to exploit scratchpad memories on architectures on which data caching has to be handled by software. We transform a given code such that it keeps values which are reused in successive iterations of a sequential loop in the scratchpad. An access to a value written in an earlier iteration is served from the scratchpad to accelerate the access. In general, this transformation introduces non-linear loop bounds in the transformed model. Finally, we present an algorithm for generating code for arbitrary semi-algebraic iteration sets, i.e., for iteration sets described by polynomial inequalities in the variables and parameters. This is a vast generalisation of existing polyhedral code generation techniques. Although our algorithm is less efficient than polyhedral code generators, this paves the way for a code generator that can handle arbitrary parametric tilings and other transformations which introduce non-linear parameters (like non-linear schedules and the localisation we present) or even non-linear variables

Structure and Interpretation of Computer Programs

Structure and Interpretation of Computer Programs has had a dramatic impact on computer science curricula over the past decade. This long-awaited revision contains changes throughout the text. There are new implementations of most of the major programming systems in the book, including the interpreters and compilers, and the authors have incorporated many small changes that reflect their experience teaching the course at MIT since the first edition was published. A new theme has been introduced that emphasizes the central role played by different approaches to dealing with time in computational models: objects with state, concurrent programming, functional programming and lazy evaluation, and nondeterministic programming. There are new example sections on higher-order procedures in graphics and on applications of stream processing in numerical programming, and many new exercises. In addition, all the programs have been reworked to run in any Scheme implementation that adheres to the IEEE standard

End-to-End Encrypted Group Messaging with Insider Security

Our society has become heavily dependent on electronic communication, and preserving the integrity of this communication has never been more important. Cryptography is a tool that can help to protect the security and privacy of these communications. Secure messaging protocols like OTR and Signal typically employ end-to-end encryption technology to mitigate some of the most egregious adversarial attacks, such as mass surveillance. However, the secure messaging protocols deployed today suffer from two major omissions: they do not natively support group conversations with three or more participants, and they do not fully defend against participants that behave maliciously. Secure messaging tools typically implement group conversations by establishing pairwise instances of a two-party secure messaging protocol, which limits their scalability and makes them vulnerable to insider attacks by malicious members of the group. Insiders can often perform attacks such as rendering the group permanently unusable, causing the state of the group to diverge for the other participants, or covertly remaining in the group after appearing to leave. It is increasingly important to prevent these insider attacks as group conversations become larger, because there are more potentially malicious participants. This dissertation introduces several new protocols that can be used to build modern communication tools with strong security and privacy properties, including resistance to insider attacks. Firstly, the dissertation addresses a weakness in current two-party secure messaging tools: malicious participants can leak portions of a conversation alongside cryptographic proof of authorship, undermining confidentiality. The dissertation introduces two new authenticated key exchange protocols, DAKEZ and XZDH, with deniability properties that can prevent this type of attack when integrated into a secure messaging protocol. DAKEZ provides strong deniability in interactive settings such as instant messaging, while XZDH provides deniability for non-interactive settings such as mobile messaging. These protocols are accompanied by composable security proofs. Secondly, the dissertation introduces Safehouse, a new protocol that can be used to implement secure group messaging tools for a wide range of applications. Safehouse solves the difficult cryptographic problems at the core of secure group messaging protocol design: it securely establishes and manages a shared encryption key for the group and ephemeral signing keys for the participants. These keys can be used to build chat rooms, team communication servers, video conferencing tools, and more. Safehouse enables a server to detect and reject protocol deviations, while still providing end-to-end encryption. This allows an honest server to completely prevent insider attacks launched by malicious participants. A malicious server can still perform a denial-of-service attack that renders the group unavailable or "forks" the group into subgroups that can never communicate again, but other attacks are prevented, even if the server colludes with a malicious participant. In particular, an adversary controlling the server and one or more participants cannot cause honest participants' group states to diverge (even in subtle ways) without also permanently preventing them from communicating, nor can the adversary arrange to covertly remain in the group after all of the malicious participants under its control are removed from the group. Safehouse supports non-interactive communication, dynamic group membership, mass membership changes, an invitation system, and secure property storage, while offering a variety of configurable security properties including forward secrecy, post-compromise security, long-term identity authentication, strong deniability, and anonymity preservation. The dissertation includes a complete proof-of-concept implementation of Safehouse and a sample application with a graphical client. Two sub-protocols of independent interest are also introduced: a new cryptographic primitive that can encrypt multiple private keys to several sets of recipients in a publicly verifiable and repeatable manner, and a round-efficient interactive group key exchange protocol that can instantiate multiple shared key pairs with a configurable knowledge relationship