The document discusses the RSA encryption algorithm which is based on modular arithmetic and uses a "trap door" property related to prime factorization. It describes how RSA works including: generating public and private keys from two primes, encrypting messages using modular exponentiation, and decrypting ciphertext using the private key and Euler's theorem. The security of RSA relies on the fact that factoring large numbers is computationally infeasible, while setting up the system is relatively fast.
We allow Eve to modify DH parameters as well as public keys of Alice and Bob. This allows Eve to derive the secret key and break the DH crypto system. We demonstrate that the DH key exchange algorithm should not be used without digital signatures.
Signyourd digital signature certificate providerKishankant Yadav
a digital code (generated and authenticated by public key encryption) which is attached to an electronically transmitted document to verify its contents and the sender's identity.
This definition explains how digital signatures work and what they are used for. Learn about the mathematical underpinnings of digital signature technology
A digital signature is basically a way to ensure that an electronic document (e-mail, spreadsheet, text file, etc.) is authentic. Authentic means that you know who created the document and you know that it has not been altered in any way since that person created it.
https://signyourdoc.com/
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
We allow Eve to modify DH parameters as well as public keys of Alice and Bob. This allows Eve to derive the secret key and break the DH crypto system. We demonstrate that the DH key exchange algorithm should not be used without digital signatures.
Signyourd digital signature certificate providerKishankant Yadav
a digital code (generated and authenticated by public key encryption) which is attached to an electronically transmitted document to verify its contents and the sender's identity.
This definition explains how digital signatures work and what they are used for. Learn about the mathematical underpinnings of digital signature technology
A digital signature is basically a way to ensure that an electronic document (e-mail, spreadsheet, text file, etc.) is authentic. Authentic means that you know who created the document and you know that it has not been altered in any way since that person created it.
https://signyourdoc.com/
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Computer graphics lab report with code in cppAlamgir Hossain
This is the lab report for computer graphics in cpp language. Basically this course is only for the computer science and engineering students.
Problem list:
1.Program for the generation of Bresenham Line Drawing.
2. Program for the generation of Digital Differential Analyzer (DDA) Line Drawing.
3. Program for the generation of Midpoint Circle Drawing.
4. Program for the generation of Midpoint Ellipse Drawing.
5. Program for the generation of Translating an object.
6. Program for the generation of Rotating an Object.
7. Program for the generation of scaling an object.
All programs are coaded in cpp language .
The following slides explains about elliptic curves, their interpretation over Gallois finite fields, algorithms that reduces arithmetic computational requirements and primarly applications of the ECC.
This Presentation Elliptical Curve Cryptography give a brief explain about this topic, it will use to enrich your knowledge on this topic. Use this ppt for your reference purpose and if you have any queries you'll ask questions.
In this paper, we present a complete digital signature message stream, just the way the RSA digital
signature scheme does it. We will focus on the operations with large numbers due to the fact that operating
with large numbers is the essence of RSA that cannot be understood by the usual illustrative examples with
small numbers[1].
Elliptic Curve Cryptography and Zero Knowledge ProofArunanand Ta
Elliptic Curve Cryptography and Zero Knowledge Proof
Presentation by Nimish Joseph, at College of Engineering Cherthala, Kerala, India, during Faculty Development Program, on 06-Nov-2013
These questions are prepared by Classical Programming Experts and are asked during job interviews.The Solution to the given programs are prepared by Programming Experts and are often asked in job interviews. Knowing solution to these problems will help you clear your concepts.
Computer graphics lab report with code in cppAlamgir Hossain
This is the lab report for computer graphics in cpp language. Basically this course is only for the computer science and engineering students.
Problem list:
1.Program for the generation of Bresenham Line Drawing.
2. Program for the generation of Digital Differential Analyzer (DDA) Line Drawing.
3. Program for the generation of Midpoint Circle Drawing.
4. Program for the generation of Midpoint Ellipse Drawing.
5. Program for the generation of Translating an object.
6. Program for the generation of Rotating an Object.
7. Program for the generation of scaling an object.
All programs are coaded in cpp language .
The following slides explains about elliptic curves, their interpretation over Gallois finite fields, algorithms that reduces arithmetic computational requirements and primarly applications of the ECC.
This Presentation Elliptical Curve Cryptography give a brief explain about this topic, it will use to enrich your knowledge on this topic. Use this ppt for your reference purpose and if you have any queries you'll ask questions.
In this paper, we present a complete digital signature message stream, just the way the RSA digital
signature scheme does it. We will focus on the operations with large numbers due to the fact that operating
with large numbers is the essence of RSA that cannot be understood by the usual illustrative examples with
small numbers[1].
Elliptic Curve Cryptography and Zero Knowledge ProofArunanand Ta
Elliptic Curve Cryptography and Zero Knowledge Proof
Presentation by Nimish Joseph, at College of Engineering Cherthala, Kerala, India, during Faculty Development Program, on 06-Nov-2013
These questions are prepared by Classical Programming Experts and are asked during job interviews.The Solution to the given programs are prepared by Programming Experts and are often asked in job interviews. Knowing solution to these problems will help you clear your concepts.
Discrete Logarithmic Problem- Basis of Elliptic Curve CryptosystemsNIT Sikkim
ECC was developed in 1985 independently by Neal Koblitz and Victor Miller. Both men saw the application of the elliptic curve discrete log problem (ECDLP) as a replacement for the conventional discrete log problem (DLP) which is used in DSA, and the integer factorization problem found in RSA. For both problems, sub-exponential solutions have been generated; the
same which cannot be said for ECDLP . In addition to offering increased security for a smaller key size, operations of adding and doubling can be optimized successfully on a mobile
platform . ECC offers a viable replacement to the most common public-key cryptography algorithms on mobile devices.
This file contains the contents about dynamic programming, greedy approach, graph algorithm, spanning tree concepts, backtracking and branch and bound approach.
Linear Discriminant Analysis (LDA) Under f-Divergence MeasuresAnmol Dwivedi
For more details, please have a look at:
1. https://www.mdpi.com/1099-4300/24/2/188
2. https://ieeexplore.ieee.org/document/9518004
Abstract:
In statistical inference, the information-theoretic performance limits can often be expressed in terms of a notion of divergence between the underlying statistical models (e.g., in binary hypothesis testing, the total error probability is equal to the total variation between the models). As the data dimension grows, computing the statistics involved in decision-making and the attendant performance limits (divergence measures) face complexity and stability challenges. Dimensionality reduction addresses these challenges at the expense of compromising the performance (divergence reduces due to the data processing inequality for divergence). This paper considers linear dimensionality reduction such that the divergence between the models is \emph{maximally} preserved. Specifically, the paper focuses on the Gaussian models and characterizes an optimal projection of the data onto a lower-dimensional subspace with respect to four $f$-divergence measures (Kullback-Leibler, $\chi^2$, Hellinger, and total variation). There are two key observations. First, projections are not necessarily along the dominant modes of the covariance matrix of the data, and even in some situations, they can be along the least dominant modes. Secondly, under specific regimes, the optimal design of subspace projection is identical under all the $f$-divergence measures considered, rendering a degree of universality to the design independent of the inference problem of interest.
While many software engineers don't work directly with prime numbers on a daily basis, they play a crucial role in keeping your web applications secure in the form of Hypertext Transfer Protocol Secure (HTTPS).
In this talk, you will learn the inner workings of how HTTPS uses prime numbers to keep your data private as it travels over the internet. We will cover topics such as symmetric and asymmetric encryption, and why prime numbers are just so damn hard to crack. By the end, you will understand how to encrypt and decrypt data yourself with Rails and the Ruby standard library.
So come join me as we demystify HTTPS using code, color theory, and only a pinch of math
FellowBuddy.com is an innovative platform that brings students together to share notes, exam papers, study guides, project reports and presentation for upcoming exams.
We connect Students who have an understanding of course material with Students who need help.
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Elgamal Digital Signature Scheme.
The ElGamal signature scheme is a digital signature scheme which is based on the difficulty of computing discrete logarithms.
The Interplay Between Art and Math: Lessons from a STEM-based Art and Math co...Joshua Holden
This presentation describes the team-teaching of a course in mathematics and art. The goal of the class is to show students the interplay between art and math with a focus on having them make physical objects. Most math and art classes we have heard of focus primarily on introducing liberal arts students to mathematics. In a STEM context, we want to instead build on the mathematical knowledge that our students already have. We intend for students to use their existing mathematical (and perhaps artistic) knowledge to reinforce new artistic (and perhaps mathematical) experiences. Ideally, the knowledge and experience gained will increase their appreciation for both the beauty of mathematics and the importance of art.
Between the Two Cultures: Teaching Math and Art to Engineers (and Scientists ...Joshua Holden
C.P. Snow famously categorized modern intellectual life as being split between the culture of the sciences and the culture of the humanities, and said that solving the world's problems requires bringing these two cultures together. Math and art classes inherently try to do that. However, most math and art classes we have heard of focus primarily on introducing liberal arts students to mathematics. In the Spring Quarter of 2019 Soully Abas and I team-taught a different sort of course in mathematics and art at the Rose-Hulman Institute of Technology. Rose-Hulman is a private, undergraduate-focused institution, all of whose students major in engineering (predominantly), science, or mathematics. We wanted to build on the mathematical knowledge that our STEM students already have with a focus on having them make physical art objects. Soully is an art professor specializing in oil painting and printmaking. Josh is a math professor interested in the mathematics of fiber arts such as embroidery, knitting, crochet, and weaving. Our goal was for students to use their existing mathematical (and perhaps artistic) knowledge to reinforce new artistic (and perhaps mathematical) experiences. Ideally, the knowledge and experience gained will increase their appreciation for both the beauty of mathematics and the importance of art and help them prepare for productive lives solving the world's problems.
Teaching the Group Theory of Permutation CiphersJoshua Holden
One of the first topics often taught in an abstract algebra class is permutations, since they provide good examples of non-commutative finite groups which the students can manipulate and visualize. This visualization is often done through symmetry groups. For students who are less geometrically inclined, however, the use of permutation ciphers provides another good way of motivating permutations. They can easily be used to illustrate composition, non-commutativity, inverses, and the order of group elements, which are fundamental topics in group theory. We will give examples of how this can be done and suggest other courses besides abstract algebra in which this could also prove useful.
Granny’s Not So Square, After All: Hyperbolic Tilings with Truly Hyperbolic C...Joshua Holden
Until now, most methods for making a hyperbolic plane from crochet or similar fabrics have fallen into one of two categories. In one type, the work starts from a point or line and expands in a sequence of increasingly long rows, creating a constant negative curvature. In the other, polygonal tiles are created out of a more or less Euclidean fabric and then attached in such a way that the final product approximates a hyperbolic plane on the large scale with an average negative curvature. On the small scale, however, the curvature of the fabric will be closer to zero near the center of the tiles and more negative near the vertices and edges, depending on the amount of stretch in the fabric. The goal of this project is to show how crochet can be used to create polygonal tiles which themselves have constant negative curvature and can therefore be joined into a large region of a hyperbolic plane without significant stretching. Formulas from hyperbolic trigonometry are used to show how, in theory, any regular tiling of the hyperbolic plane can be produced in this way.
Stitching Graphs and Painting Mazes: Problems in Generalizations of Eulerian ...Joshua Holden
An Eulerian walk traverses each edge of a graph exactly once. What happens
if you want to traverse each edge of a graph exactly twice? If you want to
cover the graph with "double-running stitch", then you need to
traverse each edge twice but also put conditions on how many edges you
traverse in-between. Then you could add conditions on whether you traverse
the edges once in each direction or twice in the same direction. Which
graphs can you still traverse? Classical algorithms for solving mazes give
us some answers to these questions, but others are still open.
Braids, Cables, and Cells II: Representing Art and Craft with Mathematics and...Joshua Holden
The mathematical study of braids combines aspects of topology and group theory to study mathematical representations of one-dimensional strands in three-dimensional space. These strands are also sometimes viewed as representing the movement through a time dimension of points in two-dimensional space. On the other hand, the study of cellular automata usually involves a one- or two-dimensional grid of cells which evolve through a time dimension according to specified rules. This time dimension is often represented as an extra spacial dimension. The ideas of representing both strands in space and cellular automata have also been explored in many artistic media, including drawing, sculpture, knitting, crochet, and weaving.
Previous work as been shown that rules for cellular automata can be written in order to produce depictions of braids. This talk will extend the previous system into a more flexible one which more realistically captures the behavior of strands in certain media, such as knitting. Some theorems about what can and cannot be represented with these cellular automata will be presented.
A Good Hash Function is Hard to Find, and Vice VersaJoshua Holden
Secure hash functions are the unsung heroes of modern cryptography.
Introductory courses in cryptography often leave them out --- since
they don't have a secret key, it is difficult to use hash functions by
themselves for cryptography. In addition, most theoretical
discussions of cryptographic systems can get by without mentioning
them. However, for secure practical implementations of public-key
ciphers, digital signatures, and many other systems they are
indispensable. In this talk I will discuss the requirements for a
secure hash function and relate my attempts to come up with a "toy"
system which both reasonably secure and also suitable for students to
work with by hand in a classroom setting.
Braids, Cables, and Cells: An intersection of Mathematics, Computer Science, ...Joshua Holden
The mathematical study of braids combines aspects of topology and group theory to study mathematical representations of one-dimensional strands in three-dimensional space. These strands are also sometimes viewed as representing the movement through a time dimension of points in two-dimensional space. On the other hand, the study of cellular automata usually involves a one- or two-dimensional grid of cells which evolve through a time dimension according to specified rules. This time dimension is often represented as an extra spacial dimension. Therefore, it seems reasonable to ask whether rules for cellular automata can be written in order to produce depictions of braids. The ideas of representing both strands in space and cellular automata have also been explored in many artistic media, including knitting and crochet, where braids are called “cables”. We will view some examples of braids and their mathematical representations in these media.
Integrating the Use of Maple with the Collaborative Use of Wireless Tablet PCs. Workshop on the Impact of Pen-Based Technology on Education (poster session), Purdue University, October 16, 2008.
Braids, Cables, and Cells I: An Interesting Intersection of Mathematics, Comp...Joshua Holden
The mathematical study of braids combines aspects of topology and group theory to study mathematical representations of one-dimensional strands in three-dimensional space. These strands are also sometimes viewed as representing the movement through a time dimension of points in two-dimensional space. On the other hand, the study of cellular automata usually involves a one- or two-dimensional grid of cells which evolve through a time dimension according to specified rules. This time dimension is often represented as an extra spacial dimension.
Therefore, it seems reasonable to ask whether rules for cellular automata can be written in order to produce depictions of braids. The ideas of representing both strands in space and cellular automata have also been explored in many artistic media, including drawing, sculpture, knitting, crochet, and macramé, and we will touch on some of these.
Many people don't realize that what we now call "algorithm design" actually dates back to the ancient Greeks! Of course, if you think about it, there's always the "Euclidean Algorithm". A more dubious example might be Theseus's use of a ball of string to solve the "Labyrinth Problem". (Google "Theseus, Labyrinth, string".) Solutions to this problem got a lot less dubious after graph theory was invited, since a graph turns out to be a good way of representing a maze mathematically. We will examine the classical solutions to this problem, and then throw in a twist --- a Twisted Painting Machine that puts restrictions on which paths we can take to explore the maze. Applications to sewing may also appear, depending on the presence of audience interest and string.
Blackwork embroidery and algorithms for maze traversalsJoshua Holden
Blackwork embroidery is a needlework technique often associated with Elizabethan England. The patterns used in blackwork generally are traversed in a way that can be described by classical algorithms in graph theory, such as those used in “The Labyrinth Problem”. We investigate which of these maze-traversing algorithms can also be used to traverse blackwork patterns.
Cryptography and Computer Security for Undergraduates (Panel, SIGCSE 2004)
I have two goals in teaching cryptography to computer science students: to use cryptography as a cool way of introducing important areas of mathematics and computer science theory and to educate students in something that may be necessary for them to know in the future. For the past two years I have co-taught a course in cryptography at the Rose-Hulman Institute of Technology with David Mutchler, a colleague from the Computer Science department. The course is cross-listed in both the Computer Science and Mathematics departments, but most of the students are CS majors. The published prerequisites are one quarter of discrete mathematics and two quarters of computer science.
Understanding the Magic: Teaching Cryptography with Just the Right Amount of ...Joshua Holden
Cryptography is a field which has recently attracted a great deal of attention from both students and teachers of mathematics and of computer science. Students of computer science see cryptography as something which is not only "cool" but may be necessary for them to know in their future careers. Many of them do not realize, however, just how much mathematics they need to know in order to understand the algorithms which lie at the heart of modern cryptography.
The Pohlig-Hellman Exponentiation Cipher as a Bridge Between Classical and Mo...Joshua Holden
The Pohlig-Hellman exponentiation cipher is a symmetric-key cipher that uses some of the same mathematical operations as the better-known RSA and Diffie-Hellman public-key cryptosystems. First published in 1978, the Pohlig-Hellman cipher was never of practical importance due to its slow speed compared to ciphers such as DES and AES. The theoretical importance of the Pohlig-Hellman cipher comes from the fact that it relies on the Discrete Logarithm Problem for its resistance against known plain text attacks, as does RSA and several other modern cryptosystems. For this reason, the Pohlig-Hellman systemcan play a very important role pedagogically, since it also shares many features in common with classical ciphers such as shift ciphers and Hill ciphers. Thus, it allows the instructor to introduce the important concepts of the discrete logarithm and known plain text attacks separately from the more conceptually difficult idea of public-key cryptography.
Welocme to ViralQR, your best QR code generator.ViralQR
Welcome to ViralQR, your best QR code generator available on the market!
At ViralQR, we design static and dynamic QR codes. Our mission is to make business operations easier and customer engagement more powerful through the use of QR technology. Be it a small-scale business or a huge enterprise, our easy-to-use platform provides multiple choices that can be tailored according to your company's branding and marketing strategies.
Our Vision
We are here to make the process of creating QR codes easy and smooth, thus enhancing customer interaction and making business more fluid. We very strongly believe in the ability of QR codes to change the world for businesses in their interaction with customers and are set on making that technology accessible and usable far and wide.
Our Achievements
Ever since its inception, we have successfully served many clients by offering QR codes in their marketing, service delivery, and collection of feedback across various industries. Our platform has been recognized for its ease of use and amazing features, which helped a business to make QR codes.
Our Services
At ViralQR, here is a comprehensive suite of services that caters to your very needs:
Static QR Codes: Create free static QR codes. These QR codes are able to store significant information such as URLs, vCards, plain text, emails and SMS, Wi-Fi credentials, and Bitcoin addresses.
Dynamic QR codes: These also have all the advanced features but are subscription-based. They can directly link to PDF files, images, micro-landing pages, social accounts, review forms, business pages, and applications. In addition, they can be branded with CTAs, frames, patterns, colors, and logos to enhance your branding.
Pricing and Packages
Additionally, there is a 14-day free offer to ViralQR, which is an exceptional opportunity for new users to take a feel of this platform. One can easily subscribe from there and experience the full dynamic of using QR codes. The subscription plans are not only meant for business; they are priced very flexibly so that literally every business could afford to benefit from our service.
Why choose us?
ViralQR will provide services for marketing, advertising, catering, retail, and the like. The QR codes can be posted on fliers, packaging, merchandise, and banners, as well as to substitute for cash and cards in a restaurant or coffee shop. With QR codes integrated into your business, improve customer engagement and streamline operations.
Comprehensive Analytics
Subscribers of ViralQR receive detailed analytics and tracking tools in light of having a view of the core values of QR code performance. Our analytics dashboard shows aggregate views and unique views, as well as detailed information about each impression, including time, device, browser, and estimated location by city and country.
So, thank you for choosing ViralQR; we have an offer of nothing but the best in terms of QR code services to meet business diversity!
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Le nuove frontiere dell'AI nell'RPA con UiPath Autopilot™UiPathCommunity
In questo evento online gratuito, organizzato dalla Community Italiana di UiPath, potrai esplorare le nuove funzionalità di Autopilot, il tool che integra l'Intelligenza Artificiale nei processi di sviluppo e utilizzo delle Automazioni.
📕 Vedremo insieme alcuni esempi dell'utilizzo di Autopilot in diversi tool della Suite UiPath:
Autopilot per Studio Web
Autopilot per Studio
Autopilot per Apps
Clipboard AI
GenAI applicata alla Document Understanding
👨🏫👨💻 Speakers:
Stefano Negro, UiPath MVPx3, RPA Tech Lead @ BSP Consultant
Flavio Martinelli, UiPath MVP 2023, Technical Account Manager @UiPath
Andrei Tasca, RPA Solutions Team Lead @NTT Data
Essentials of Automations: Optimizing FME Workflows with ParametersSafe Software
Are you looking to streamline your workflows and boost your projects’ efficiency? Do you find yourself searching for ways to add flexibility and control over your FME workflows? If so, you’re in the right place.
Join us for an insightful dive into the world of FME parameters, a critical element in optimizing workflow efficiency. This webinar marks the beginning of our three-part “Essentials of Automation” series. This first webinar is designed to equip you with the knowledge and skills to utilize parameters effectively: enhancing the flexibility, maintainability, and user control of your FME projects.
Here’s what you’ll gain:
- Essentials of FME Parameters: Understand the pivotal role of parameters, including Reader/Writer, Transformer, User, and FME Flow categories. Discover how they are the key to unlocking automation and optimization within your workflows.
- Practical Applications in FME Form: Delve into key user parameter types including choice, connections, and file URLs. Allow users to control how a workflow runs, making your workflows more reusable. Learn to import values and deliver the best user experience for your workflows while enhancing accuracy.
- Optimization Strategies in FME Flow: Explore the creation and strategic deployment of parameters in FME Flow, including the use of deployment and geometry parameters, to maximize workflow efficiency.
- Pro Tips for Success: Gain insights on parameterizing connections and leveraging new features like Conditional Visibility for clarity and simplicity.
We’ll wrap up with a glimpse into future webinars, followed by a Q&A session to address your specific questions surrounding this topic.
Don’t miss this opportunity to elevate your FME expertise and drive your projects to new heights of efficiency.
SAP Sapphire 2024 - ASUG301 building better apps with SAP Fiori.pdfPeter Spielvogel
Building better applications for business users with SAP Fiori.
• What is SAP Fiori and why it matters to you
• How a better user experience drives measurable business benefits
• How to get started with SAP Fiori today
• How SAP Fiori elements accelerates application development
• How SAP Build Code includes SAP Fiori tools and other generative artificial intelligence capabilities
• How SAP Fiori paves the way for using AI in SAP apps
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
1. Modular arithmetic and trap door ciphers
Joshua Holden
Rose-Hulman Institute of Technology
http://www.rose-hulman.edu/~holden
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 1 / 41
2. RSA Setup
Ronald Rivest, Adi Shamir, Leonard Adleman, 1977.
Pick two primes p and q.
Compute n = pq.
Pick encryption exponent e such that e and (p − 1)(q − 1) don’t
have any common prime factors.
Make n and e public. Keep p and q private.
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 2 / 41
3. RSA Setup: Example
p = 53
q = 71
n = pq = 3763
(p − 1)(q − 1) = 23 · 5 · 7 · 13
e = 27 = 33
e and (p − 1)(q − 1) don’t have any common prime factors
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 3 / 41
4. RSA Setup: PGP public key block
From holden@math.duke.edu Thu Feb 8 14:07:19 2001
Date: Thu, 8 Feb 2001 14:07:18 -0500
X-Authentication-Warning: hamburg.math.duke.edu: holden set sender to holden@hamburg.math.duke.edu
From: Joshua Holden To: holden@math.duke.edu
Subject: message with PGP block
Here is my PGP block: now you can send me messages!
-----BEGIN PGP PUBLIC KEY BLOCK-----
Version: 2.6.2
Comment: Processed by Mailcrypt 3.5.5, an Emacs/PGP interface
mQCNAznRHaMAAAEEAPix/FD/jF/ixMvd9aIjhZ/K6o2kv/TaGAVkeIG5VZ48jzIa
NTqX1EKDw6aABUiQApqavOaQuiLbi/Ez9HXX9LfcTdcp8u94BKGgmEy6Jv1za08I
2YVL1kUJso6lauryr3Sc8wiQTwx3imohM4ai/1dVuq4Qp2WCBSRdyaafdchdAAUR
tC9Kb3NodWEgSG9sZGVuICgxMDI0IGJpdCkgPGhvbGRlbkBtYXRoLmR1a2UuZWR1
Pg==
=VgE9
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Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 4 / 41
5. Modular Arithmetic
Karl Friedrich Gauss, 1801.
Modular Arithmetic = “Wrap-around” computations
Example: Start at 12 o’clock. 5 hours plus 8 hours equals 1 o’clock.
5 + 8 ≡ 1 (mod 12)
Example: Start at 12 o’clock. 11 hours times 5 equals 7 o’clock.
11 · 5 ≡ 7 (mod 12)
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 5 / 41
6. RSA Encryption
Anyone can encrypt, because n and e are public.
To encrypt, convert your message into a set of plaintext numbers
P, each less than n.
For each P, compute C ≡ P e (mod n).
The numbers C are your ciphertext.
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 6 / 41
7. RSA Encryption: Example
Send the message “cats and dogs”:
ca ts an dd og sx
0200 1918 0013 0303 1406 1823
200e ≡ 12 (mod n)
1918e ≡ 1918 (mod n)
13e ≡ 1550 (mod n)
303e ≡ 3483 (mod n)
1406e ≡ 2042 (mod n)
1823e ≡ 2735 (mod n)
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 7 / 41
8. RSA Encryption: PGP message
From holden@math.duke.edu Thu Feb 8 14:09:25 2001
Date: Thu, 8 Feb 2001 14:09:24 -0500
X-Authentication-Warning: hamburg.math.duke.edu: holden set sender to holden@hamburg.math.duke.edu
From: Joshua Holden To: holden@math.duke.edu
Subject: This message is encrypted
-----BEGIN PGP MESSAGE-----
Version: 2.6.2
Comment: Processed by Mailcrypt 3.5.5, an Emacs/PGP interface
hIwDJF3Jpp91yF0BBAC6gnKTMhGWg9hUELd7WfJgUn7OqObCNmvm9V8ff+tyq0re
nSQqCYw784CAkm5gaUtJ0AW4go2pDyI2hm5ocoVfMeBOJpKeckSchncV9zHSH2zx
jBM8W0NYPAaa7AHFisz19rqxkkt1aQ4W49i7LUxq6rXheoSPMMcHbHyBa/mQEaYA
AABEmtEXwkUSMOh+x4dSM/6ZUswVZznmei9TOw+md8OM+LiOSakw91GT431tJPAN
c44q+q2Yq8ehykaz0sV4fXscPy2H9A0=
=v1z0
-----END PGP MESSAGE-----
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 8 / 41
9. Trap Door
Leonhard Euler, 1736.
Let φ(n) be the number of positive integers less than or equal to n
which don’t have any common factors with n.
Example: If n = 15, then the positive integers less than or equal to n
which don’t have any common factors with n are 1, 2, 4, 7, 8, 11, 13,
14. So φ(15) = 8.
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 9 / 41
10. Trap Door: RSA
In the RSA system n = pq, so φ(n) is the number of positive integers
less than or equal to n which don’t have p or q as a factor.
How many positive integers less than or equal to n do have p as a
factor? p, 2p, 3p, . . . , n = qp so there are q of them.
Similarly, there are p positive integers less than or equal to n with
q as a factor.
Only one positive integer less than or equal to n has both p and q
as factors, namely n = pq. So we should only count this once.
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 10 / 41
11. Trap Door: Formula
Therefore,
φ(n) = n − p − q + 1 = pq − p − q + 1 = (p − 1)(q − 1).
This is private! You can’t calculate it without knowing p and q.
Why is this useful?
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 11 / 41
12. Euler’s Theorem
Euler’s Theorem: If x is an integer which has no common prime factors
with n, then
x φ(n) ≡ 1 (mod n).
Why is Euler’s Theorem true?
Two versions of the answer: Number Theory and Group Theory
Number Theory idea: We consider the positive integers less than or
equal to n which don’t have any common factors with n, and multiply
each of them by x modulo n. Compare them to the same integers
without multiplying by x.
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 12 / 41
13. Euler’s Theorem: Example (I)
For n = 15, consider
x, 2x, 4x, 7x, 8x, 11x, 13x, 14x (mod 15),
and compare them to 1, 2, 4, 7, 8, 11, 13, 14.
If we multiply all of the first set we get
x 8 · 1 · 2 · 4 · 7 · 8 · 11 · 13 · 14 (mod 15)
and if we multiply all of the second set we get
1 · 2 · 4 · 7 · 8 · 11 · 13 · 14 (mod 15).
What if we do all of this for x = 11?
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 13 / 41
15. Euler’s Theorem: Example (III)
The first set is the same as the second set, only in a different
order!
In fact, this always happens.
So
x 8 · 1 · 2 · 4 · 7 · 8 · 11 · 13 · 14 ≡ 1 · 2 · 4 · 7 · 8 · 11 · 13 · 14 (mod 15)
or
x8 ≡ 1 (mod 15).
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 15 / 41
16. Cayley diagram
Arthur Cayley, 1878.
89:;
?>=< o ¢¾ 89:;
?>=<
_?? ? O
??
??¢½ ¢½
??
??
?
89:;
?= o 89:;
?=
½½
¢¾ O
Group Theory idea: We make
¢¾ ¢¾ ¢¾ ¢¾ a Cayley diagram for the num-
bers less than n.
89:;
?= ¢¾ / ?=
89:;
?½ ½¿ _?
??
??
??
¢½ ¢½ ????
89:;
?=
½ / ?=
89:;
¾
¢¾
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 16 / 41
17. Cayley diagram: Example (II)
Say x = 11. Follow the arrows from 1 to 11. This is one x14 arrow
and two x2 arrows. If you do this 7 more times, you will be
following a total of eight x14 arrows and sixteen x2 arrows, and
you should end up at 11 to the eighth. However, eight x14 arrows
and sixteen x2 arrows clearly ends you up back where you started!
(Note that it doesn’t matter in what order you follow the arrows....)
So how do we use Euler’s Theorem as a trap door?
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 17 / 41
18. RSA: One More Piece
We need one more piece of (private) information.
Euclid, about 300 B.C.E.
Theorem If a and b don’t have any common prime factors, then there
are integers c and d such that
ac + bd = 1.
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 18 / 41
19. Euclidean Algorithm
Since we picked e such that e and (p − 1)(q − 1) don’t have any
common prime factors, then there are integers c and d such that
(p − 1)(q − 1)c + ed = 1
or
φ(n)c + ed = 1.
Euclid also tells us how to find c and d, using the Euclidean
Algorithm.
Once we have found the decryption exponent d, which is private,
we can decrypt.
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 19 / 41
20. RSA Decryption
For each C, compute C d (mod n).
What will this give you?
We know C ≡ P e (mod n), although we don’t yet know what P is.
So
C d ≡ (P e )d ≡ P ed ≡ P 1−φ(n)c ≡ P(P φ(n) )−c (mod n).
But P φ(n) ≡ 1 (mod n) by Euler’s Theorem!
So C d ≡ P (mod n) and we get our original plaintext back.
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 20 / 41
21. RSA Decryption: Example (I)
p = 53
q = 71
(p − 1)(q − 1) = 3640
e = 27
The Euclidean Algorithm tells us
16(p − 1)(q − 1) − 2157e = 1.
d = −2157
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 21 / 41
22. RSA Decryption: Example (II)
12d ≡ 200 (mod n)
1918d ≡ 1918 (mod n)
1550d ≡ 13 (mod n)
3483d ≡ 303 (mod n)
2042d ≡ 1406 (mod n)
2735d ≡ 1823 (mod n)
0200 1918 0013 0303 1406 1823
ca ts an dd og sx
“cats and dogs”
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 22 / 41
23. Breaking RSA: Factoring
So why do we think RSA is secure?
As far as we know, the only way to break RSA is to find p and q by
factoring n. The fastest known factoring algorithm takes
something about like
1/3 (log(log n))2/3
e(log n)
time units to factor n. (The size of the time unit depends on things
like how fast the computer is!)
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 23 / 41
24. Breaking RSA: Fast computers
For the fastest single computer in 2006, it would probably take about 1
billion years to factor a number with 300 decimal digits. However, with
networked computers, a large company might be able to improve this
by a factor of as much as 1 million.
(More technically, it is estimated that factoring a number with 300
decimal digits would take about 1011 MIPS-years. 1 MIPS-year is a
million-instructions-per-second processor running for one year. A
1-GHz Pentium is about a 250-MIPS machine.)
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 24 / 41
25. Breaking RSA: Factoring vs. Setup
On the other hand, finding p and q and multiplying them together is
very fast. Finding a number p which is (probably) prime takes about
100(log p)4 time units. This looks large, but it isn’t really; for a 300-digit
number this should only take a few minutes. (Multiplying p and q
together is even faster.)
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 25 / 41
26. Breaking RSA: A Graph
exp(ln(n)^(1/3)*ln(ln(n))^(2/3))
100*ln(n)^4
At some size of n it will always
be easier to make the cipher
than to break it!
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 26 / 41
27. RSA Digital Signatures
As a bonus, RSA gives us a way to digitally “sign” messages, thereby
proving who wrote them. This uses the same public n and e and
private d as before.
For each plaintext P, compute S ≡ P d (mod n).
The numbers S are your signed message.
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 27 / 41
28. RSA Digital Signatures: Example
Sign the message “cats and dogs”:
ca ts an dd og sx
0200 1918 0013 0303 1406 1823
200d ≡ 648 (mod n)
1918d ≡ 1918 (mod n)
13d ≡ 914 (mod n)
303d ≡ 1946 (mod n)
1406d ≡ 664 (mod n)
1823d ≡ 2735 (mod n)
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 28 / 41
29. RSA Digital Signatures: PGP message
From holden@math.duke.edu Thu Feb 8 14:10:42 2001
Date: Thu, 8 Feb 2001 14:10:41 -0500
X-Authentication-Warning: hamburg.math.duke.edu: holden set sender to holden@hamburg.math.duke.edu
From: Joshua Holden To: holden@math.duke.edu
Subject: This message is signed but not encrypted
-----BEGIN PGP SIGNED MESSAGE-----
I’m signing this message so that you know it’s me!
-----BEGIN PGP SIGNATURE-----
Version: 2.6.2
Comment: Processed by Mailcrypt 3.5.5, an Emacs/PGP interface
iQCVAwUBOoLvKyRdyaafdchdAQELuQP+PBR2lY8rEPrgA4GzWQS/MbE4UDECkgBk
v+6Q/gAwrHzMwemXcZxKU1FGFClvfHxxyjoy8hJgYeLYiGvD+q11gtNGZtTdLzqh
xL/Bdw75fseFxal/32ZS45jMA3gA2220m70hkJg4EzyvlhDUdUI1SIQHn/V26H0g
I25VOm/Ib8s=
=CRW2
-----END PGP SIGNATURE-----
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 29 / 41
30. Verifying the Signature
Since only you know the decryption exponent d, only you can sign a
message. Anyone you send it to can prove it was you by computing S e
(mod n) (since n and e are public) and getting back P de (mod n),
which we know is congruent to P.
If this matches the P which you sent separately, then the message
was correctly signed, so it must have come from someone who
knows d.
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 30 / 41
31. Verifying the Signature: Example
648e ≡ 200 (mod n)
1918e ≡ 1918 (mod n)
914e ≡ 13 (mod n)
1946e ≡ 303 (mod n)
664e ≡ 1406 (mod n)
2735e ≡ 1823 (mod n)
0200 1918 0013 0303 1406 1823
ca ts an dd og sx
“cats and dogs”
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 31 / 41
32. Encrypting and Signing
One can even sign an encrypted message this way. Suppose Alice
wants to send Bob an encrypted message.
She first encrypts with Bob’s public nB and eB .
Secondly, she signs the message with her nA and private dA .
Since her dA is different from Bob’s dB , they don’t cancel out.
Then Bob can “unsign” the message with Alice’s public nA and eA .
Finally, Bob decrypts the message with his nB and private dB !
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 32 / 41
33. Encrypting and Signing: Example (I)
Alice:
Private: pA = 53, qA = 71
Public: nA = pA qA = 3763
Public: eA = 27
Private: dA = −2157 (same as before)
Bob:
Private: pB = 41, qB = 67
Public: nB = pB qB = 2747
Private: (pB − 1)(qB − 1) = 24 · 3 · 5 · 11
Public: eB = 49 = 72
Private: The Euclidean Algorithm tells Bob
8(pB − 1)(qB − 1) − 431eB = 1.
Private: db − −431
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 33 / 41
34. Encrypting and Signing: Example (II)
Alice encrypts the message with Bob’s public information:
ca ts an dd og sx
0200 1918 0013 0303 1406 1823
200eB ≡ 2411 (mod nB )
1918eB ≡ 1836 (mod nB )
13eB ≡ 1401 (mod nB )
303eB ≡ 2314 (mod nB )
1406eB ≡ 2143 (mod nB )
1823eB ≡ 1154 (mod nB )
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 34 / 41
35. Encrypting and Signing: Example (III)
Alice signs the message with her private information and send the
result to Bob:
2411dA ≡ 2041 (mod nA )
1836dA ≡ 814 (mod nA )
1401dA ≡ 1249 (mod nA )
2314dA ≡ 1396 (mod nA )
2143dA ≡ 772 (mod nA )
1154dA ≡ 3139 (mod nA )
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 35 / 41
36. Encrypting and Signing: Example (IV)
Bob “unsigns” the message using Alice’s public information:
2041eA ≡ 2411 (mod nA )
814eA ≡ 1836 (mod nA )
1249eA ≡ 1401 (mod nA )
1396eA ≡ 2314 (mod nA )
772eA ≡ 2143 (mod nA )
3139eA ≡ 1154 (mod nA )
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 36 / 41
37. Encrypting and Signing: Example (V)
and then decrypts it using his private information:
2411dB ≡ 200 (mod nB )
1836dB ≡ 1918 (mod nB )
1401dB ≡ 13 (mod nB )
2314dB ≡ 303 (mod nB )
2143dB ≡ 1406 (mod nB )
1154dB ≡ 1823 (mod nB )
0200 1918 0013 0303 1406 1823
ca ts an dd og sx
“cats and dogs”
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 37 / 41
38. Attacks on RSA
Finding out someone’s private d is about as hard as factoring n. But
sometimes we can find out a particular message without breaking the
general code. Usually this is because e is too small — small e makes
the encrypting faster, but can weaken security.
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 38 / 41
39. Small Message Attack (I)
p = 53, q = 71
n = pq = 3763
e=3
“abaracadabara”
ab ar ac ad ab ar ax
0001 0017 0002 0003 0002 0017 0023
1e ≡ 1 (mod n)
17e ≡ 1150 (mod n)
2e ≡ 8 (mod n)
3e ≡ 27 (mod n)
2e ≡ 8 (mod n)
17e ≡ 1150 (mod n)
23e ≡ 878 (mod n)
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 39 / 41
40. Small Message Attack (II)
But:
√
3
1=1
√
3
1150 = 10.4769
√
3
8=2
√
3
27 = 3
√
3
8=2
√
3
1150 = 10.4769
√
3
878 = 9.5756
0001 ???? 0002 0003 0002 ???? ????
ab ?? ac ad ab ?? ??
An eavesdropper can recover most of the message!
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 40 / 41
41. HNAT SOFK LSIR EINT GZXN!
Joshua Holden (RHIT) Modular arithmetic and trap door ciphers 41 / 41