Modular Arithmetic: Addition and Subtraction
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The document discusses modular arithmetic and provides examples of addition, subtraction, and finding remainders when dividing numbers by various moduli (9, 4, 6). It shows that when dividing numbers by the modulus, the remainders repeat in a cyclic pattern from 0 back to the modulus - 1. For example, when dividing by 9, the remainders are 0, 1, 2, 3, 4, 5, 6, 7, 8 before repeating at 0 again.
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Reference:
Nivera, G. C. (2013), Grade 7 Mathematics: Pattern and Practicalities. Don Bosco Press Inc. Makati City, Philippines.
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3) A coefficient is the number multiplied by a variable, like 6 is the coefficient of m in the expression "6m + 5".
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For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
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Reference:
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multiplication_facts_flash_cards.ppt
This document provides a multiplication flash card worksheet with problems ranging from 2x2 to 10x10. It includes the multiplication problem and answer for students to practice their multiplication facts.
Similar to Modular Arithmetic: Addition and Subtraction (20)
Solutions manual for business math 10th edition by cleaves
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Cyberwar
The document discusses various topics related to cyberwar including Mastodon, Lockheed-Martin's kill chain model, and Mitre's ATT&CK framework. It notes that China, Russia, Iran, and North Korea pose major cyber threats according to the FBI and CISA. China is described as the broadest cyber espionage threat. Russia conducts destructive malware and ransomware operations. Iran's growing cyber expertise makes it a threat. North Korea's program poses an espionage, cybercrime, and attack threat and continues cryptocurrency heists.
3: DNS vulnerabilities
- DNS vulnerabilities can arise from configuration errors, architecture mistakes, vulnerable software implementations, protocol weaknesses, and failure to use security extensions.
- Common mistakes include single points of failure, exposure of internal information, leakage of internal queries, unnecessary recursiveness, failure to restrict access, and unprotected zone transfers.
- Software vulnerabilities have included buffer overflows and flaws in randomization of source ports, transaction IDs, and domain name ordering that enable cache poisoning and man-in-the-middle attacks.
8. Software Development Security
This chapter discusses software development security. It covers topics like programming concepts, compilers and interpreters, procedural vs object-oriented languages, application development methods like waterfall vs agile models, databases, object-oriented design, assessing software vulnerabilities, and artificial intelligence techniques. The key aspects are securing the entire software development lifecycle from initial planning through operation and disposal, using secure coding practices, testing for vulnerabilities, and continually improving processes.
4 Mapping the Application
For a Securing Web Applications class at college.
More info: https://samsclass.info/129S/129S_S23.shtml
3. Attacking iOS Applications (Part 2)
This document discusses attacking iOS applications by exploiting vulnerabilities in the iOS runtime, interprocess communication, and through injection attacks. Specifically, it covers instrumenting the iOS runtime using method swizzling, attacking applications using interprocess communication techniques like application extensions, and exploiting entry points like UIWebViews, client-side data stores, and file handling routines to perform injection attacks on iOS apps.
12 Elliptic Curves
This document provides an overview of elliptic curve cryptography including what an elliptic curve is, the elliptic curve discrete logarithm problem (ECDLP), Diffie-Hellman key agreement and digital signatures using elliptic curves. It discusses NIST standard curves like P-256 and Curve25519 as well as choosing appropriate curves and potential issues like attacks if randomness is not properly implemented or an invalid curve is used.
11. Diffie-Hellman
The document discusses the Diffie-Hellman key exchange protocol. It describes how Diffie-Hellman works by having two parties agree on a shared secret over an insecure channel without transmitting the secret itself. It also covers potential issues like using proper cryptographic techniques to derive keys from the shared secret and using safe prime numbers to prevent attacks.
2a Analyzing iOS Apps Part 1
This document provides an overview of analyzing iOS apps, including jailbreaking mobile devices. It discusses iOS security features like code signing and sandboxing. It explains how to set up a test environment for analyzing apps by jailbreaking a device and using Unix tools. Key files like property lists and databases that can be explored are also outlined.
9 Writing Secure Android Applications
This document discusses various techniques for writing secure Android apps, including minimizing unnecessary permissions and exposure, securing data storage and communication, and making apps difficult to reverse engineer. It provides examples of implementing essential security mechanisms like permission protection and securing activities, content providers, and web views. It also covers more advanced techniques such as protection level downgrades, obfuscation, and tamper detection.
12 Investigating Windows Systems (Part 2 of 3)
The document discusses investigating Windows systems by analyzing the Windows Registry. It describes the purpose and structure of the Registry, including the main hive files and user-specific hives. It provides an overview of important Registry keys that can contain forensic artifacts, such as system configuration keys, network information keys, user and security information keys, and auto-run keys that can indicate malware persistence. Specific Registry keys and values are highlighted that are most useful for analyzing evidence on a compromised system, including ShellBags, UserAssist, MRU lists, and Internet Explorer TypedURLs and TypedPaths. Tools for Registry analysis like RegRipper, AutoRuns, and Nirsoft utilities are also mentioned.
10 RSA
This document provides an overview of the RSA cryptosystem. It begins with the mathematical foundations of RSA, including the group ZN* and Euler's totient function. It then covers the RSA trapdoor permutation using modular exponentiation and key generation. The document discusses encrypting and signing with RSA, as well as implementations using libraries and algorithms like square-and-multiply. It concludes with topics like side-channel attacks, optimizations for speed, and ways implementations can fail like the Bellcore attack on RSA-CRT.
12 Investigating Windows Systems (Part 1 of 3
This document provides an overview of analyzing the Windows file system, NTFS metadata, and logs to investigate security incidents and recover deleted files. It discusses the Master File Table (MFT) structure, timestamps, alternate data streams, prefetch files, event logs, and scheduled tasks. The MFT stores file metadata including attributes, timestamps, and data runs. File deletion only marks the MFT entry inactive, allowing recovery of deleted file contents and metadata. Event and security logs can reveal lateral movement and suspicious processes. Prefetch files indicate program execution history. Scheduled tasks configure automated programs through .job files logged by Task Scheduler.
9. Hard Problems
This document discusses computational hardness and complexity classes related to cryptography. It covers the computational complexity of problems like factoring large numbers and the discrete logarithm problem. These problems are assumed to be hard, even for quantum computers, and form the basis for cryptographic techniques. The document also discusses how cryptography could be broken if faster algorithms were found for these problems or if the key sizes used were too small.
8 Android Implementation Issues (Part 1)
This document discusses exploiting vulnerabilities in Android devices. It covers identifying pre-installed apps that could provide access, techniques for remotely or locally exploiting devices, and the different privilege levels an attacker may obtain including non-system app access, installed package access, ADB shell access, system user access, and root user access. Specific exploitation techniques mentioned include exploiting update mechanisms, remote code loading, webviews, listening services, and messaging apps. Tools discussed include Drozer, Ettercap, and Burp.
11 Analysis Methodology
This document provides an overview of the incident response analysis methodology process. It discusses defining objectives, understanding the situation and available resources, identifying leadership, avoiding impossible tasks like proving a negative, asking why to define scope, knowing where data is stored, accessing raw data, selecting analysis methods like searching for malware or using tools like VirusTotal, manual review, filtering data, statistical analysis using tools like Sawmill, string searching, analyzing unallocated space, and file carving. It stresses periodically evaluating results to ensure progress and only making definitive statements if supported by evidence.
8. Authenticated Encryption
This document discusses authenticated encryption, which both encrypts messages and authenticates them with a tag. It covers several authenticated encryption schemes:
1. Authenticated Encryption with Associated Data (AEAD) which encrypts a plaintext and authenticates additional associated data with a tag.
2. AES-GCM, the standard authenticated cipher, which uses AES in Galois/Counter Mode. It has two layers - encryption then authentication.
3. OCB, faster than GCM but limited by licensing. It blends encryption and authentication into one layer.
4. SIV, considered the safest as it is secure even if nonces are reused, but it is not streamable.
7. Attacking Android Applications (Part 2)
This document summarizes part 2 of a course on attacking Android applications. It discusses how application components like activities and services can be exploited if not properly protected. Specific vulnerabilities in the Sieve password manager application are demonstrated, including insecure content providers, SQL injection, and an insecure file-backed content provider. The document also covers how services and broadcast receivers can be abused if not protected correctly.
7. Attacking Android Applications (Part 1)
This document discusses attacking Android applications through their components. It covers exploiting vulnerabilities in an app's security model, intercepting communications, and compromising application containers or internet servers that apps rely on. Specific attacks examined include bypassing the lock screen, tapjacking, accessing private app data through recently used screenshots, and changing a PIN without knowing the old one using fragment injection. The document provides examples of how to interact with an app's activities, services, content providers and permissions through intents and other techniques.
5. Stream Ciphers
The document discusses stream ciphers and how they can be implemented in either hardware or software. It describes how stream ciphers work by generating a pseudorandom bitstream from a key and nonce that is XOR'd with the plaintext. Hardware-oriented stream ciphers were initially more efficient to implement than block ciphers using dedicated circuits like LFSRs. However, LFSR-based designs are insecure and modern software-oriented stream ciphers like Salsa20 are more efficient on CPUs. The document cautions that stream ciphers can be broken if the key and nonce are reused or if there are flaws in the implementation.
6 Scope & 7 Live Data Collection
Live data collection on Windows systems can be done using prebuilt kits like Mandiant Redline or Velociraptor, by creating your own scripted toolkit using built-in and free tools to collect processes, network connections, system logs and other volatile data, while following best practices like testing your methods first and being cautious of malware on investigated systems.
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A Strategic Approach: GenAI in Education
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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Modular Arithmetic: Addition and Subtraction
- 1. Modular Arithmetic Addition and Subtraction
- 2. Modulus 9 0 mod 9 = 0 1 mod 9 = 1 2 mod 9 = 2 3 mod 9 = 3 4 mod 9 = 4 5 mod 9 = 5 6 mod 9 = 6 7 mod 9 = 7 8 mod 9 = 8 0 1 2 3 5 6 8 7 4 9 mod 9 = 0 10 mod 9 = 1 11 mod 9 = 2 12 mod 9 = 3 13 mod 9 = 4 14 mod 9 = 5 15 mod 9 = 6 16 mod 9 = 7 17 mod 9 = 8
- 3. Modulus 9 18 mod 9 = 0 19 mod 9 = 1 20 mod 9 = 2 21 mod 9 = 3 22 mod 9 = 4 23 mod 9 = 5 24 mod 9 = 6 25 mod 9 = 7 26 mod 9 = 8 27 mod 9 = 0 28 mod 9 = 1 29 mod 9 = 2 30 mod 9 = 3 31 mod 9 = 4 32 mod 9 = 5 33 mod 9 = 6 34 mod 9 = 7 35 mod 9 = 8 0 1 2 3 5 6 8 7 4
- 4. Modulus 9 -9 mod 9 = 0 -8 mod 9 = 1 -7 mod 9 = 2 -6 mod 9 = 3 -5 mod 9 = 4 -4 mod 9 = 5 -3 mod 9 = 6 -2 mod 9 = 7 -1 mod 9 = 8 0 1 2 3 5 6 8 7 4
- 5. Modulus 9 (0 + 1) mod 9 = 1 (1 + 5) mod 9 = 6 (8 + 3) mod 9 = 11 mod 9 = 2 (15 + 13) mod 9 = 28 mod 9 = 1 = 15 mod 9 + 13 mod 9 = (6 + 4) mod 9 = 10 mod 9 = 1 0 1 2 3 5 6 8 7 4
- 6. Modulus 9 (7 - 2) mod 9 = 5 (16 - 5) mod 9 = 11 mod 9 = 2 = 16 mod 9 - 5 mod 9 = (7 - 5) mod 9 = 2 0 1 2 3 5 6 8 7 4
- 7. Modulus 4 0 mod 4 = 0 1 mod 4 = 1 2 mod 4 = 2 3 mod 4 = 3 4 mod 4 = 0 5 mod 4 = 1 12 mod 4 = 0 13 mod 4 = 1 0 1 2 3
- 8. Modulus 6 0 mod 6 = 0 1 mod 6 = 1 2 mod 6 = 2 3 mod 6 = 3 4 mod 6 = 4 5 mod 6 = 5 6 mod 6 = 0 7 mod 6 = 1 8 mod 6 = 2 0 1 2 3 5 4