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Components of CryptographyChapter 3© Copyright 2012-2013.docx

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The document provides an overview of cryptography components, including various types of cryptosystems such as symmetric and asymmetric cryptography, steganography, and message integrity controls. It discusses techniques for hiding information, such as null ciphers and digital watermarking, and includes examples of substitution and transposition ciphers. Additionally, it covers the characteristics and applications of stream and block ciphers.

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Components of Cryptography Chapter 3 © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Categories of Cryptosystems © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Organization of Cryptosystems Two-Way Cryptography Symmetric Asymmetric Steganography
Message Integrity Controls Stream Block Factoring the Product of Large Primes Discreet Logarithms
Steganography Art of hiding information Plaintext hidden/disguised Prevents a third party from knowing that a secret message exists Traditionally accomplished in a number of ways: Physical techniques Null ciphers © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Null Cipher Example Cipher text: News Eight Weather: Tonight increasing snow. Unexpected precipitation smothers eastern towns. Be extremely cautious and use snowtires especially heading east. The highway is not knowingly slippery. Highway evacuation is suspected. Police report emergency situations in downtown ending near Tuesday. Taking the first letter in each word successively yields the real message: "Newt is upset because he thinks he is President." © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under
Any Circumstances Image-based Steganography RGB* values altered to contain a message File sizes are identical Different hash values E1089197693F6C4C26E0033F8C8AF00C 57694B77DCB55C543C6C0BA8E1FF2D17 © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Digital Watermarking Digital watermarks are visible or invisible markings embedded within a digital file to indicate copyright or other handling instructions, or to embed a fingerprint to detect unauthorized copying and distribution of images © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only.
Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Substitution and Transposition © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Cryptography Substitution Simple Polyalphabetic Transposition Scytale
Running Key Codes Substitution Ciphers Four-square Playfair Caesar Cipher: Shift (rotate) alphabet (move letters three spaces) A B C D E F ... BAD
D E F G H I ... EDG Scramble alphabet: Substitute one letter for another A B C D E F ... BAD Q E Y R T M ... EQR © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Polyalphabetic Ciphers – Vigenère Cipher This is a simple substitution cipher that uses multiple alphabets rather than just one Encrypt the plaintext ‘FEEDBACK’ using a key of 3241 © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Running Key Ciphers Use the value of plaintext letters and a value of key based on a shared book
Value of Message ‘THIS message …’ + Value of Key ‘on periodic …’ = Value of Ciphertext © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances One-time Pads (OTPs) The keys are the same size (length) as the plaintext message, and the keys must be randomly generated for this scheme to be truly effective It is the requirement for randomness that makes OTPs particularly challenging to generate, since the best that we can typically achieve when generating such pads using computer processors are pseudo-random values © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances
© Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Codes A group of navy ships is operating under conditions of radio silence to avoid detection by the enemy Maneuvering signals and comments are communicated by flag signals A separate flag is used for each letter To send a paragraph of information would be a real workout for the signalmen, so codes are used to minimize the effort and time involved; for instance, the letters BZ are the signal that the addressee performed well or did a good job © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Transposition Ciphers Columnar – rearranging the message in a table Plaintext “This is an example of transposition” Ciphertext “tsaonihamfstinptpiselrooixeasn” Key: grid shape and reading direction Example: the Spartan Scytale © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only.
Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances 1 MATH 115 6381 (2182) Mid Term Exam Name___________________________________ By signing my name above, I certify that I have completed this assignment individually, working independently and not consulting anyone except the instructor. Instructions for Mid-Term Exam: The Mid-Term Exam consists of 12 problems for a total of 100 points. It is based on the material
covered in the first 3 weeks of the course, but with considerable focus on the Week 4 material: Chapter 6 (Sections 6.2 through 6.5) of the “College Algebra, 3 rd Corrected Edition” text and Chapter 10 (Section 10.1) of the “College Trigonometry, Stitz and Zeager” text. It is open book and open notes. It is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone. YOU MAY USE YOUR GRAPHING CALCULATOR (TI-83/84 or EQUIVALENT, nothing more sophisticated) TO ASSIST IN GRAPHING OR ANY NUMERICAL CALCULATIONS). You must show your work. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document containing your work. Scanned work is acceptable also. When you have completed the exam, upload your solutions file to the Mid-Term Exam assignment
in the Assignment folder. DUE DATE is NLT 11:59pm EDT, Sunday, September 16. If you have any questions, please contact me by e-mail. 2 1. (8 points). Find all real solutions to the following equation: √� − � + √� − � = 4
Answer: x = ______________________ 2. (8 points). Consider the following functions: f(x) = 3 – x 2 ; g(x) = √� + � (a). Compute the composition function (f ◦ g)(x). Answer: (f ◦ g)(x) = ___________________________ (b). Compute (f ◦ g)(2).
Answer: (f ◦ g)(2) = ________________ 3 3. (8 points). (a) Rewrite the following exponential expression as a logarithmic expression. ( � � ) −� = � Answer: ___________________________________ (b). Rewrite the following logarithmic expression as an exponential expression:
���� ( � �� ) = −� Answer: ___________________________________ 4. (8 points). Use the properties of logarithms to condense the expression below as a single logarithm. � � ����(�) − �����(�) − ����(�)
Answer: ___________________________________ 4 5. (8 points). A can of soda at 83 o F is placed in a refrigerator that maintains a constant temperature of 35 o F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by the equation below: T(t) = 35 + 48 e – 0.058 t Find the temperature of the soda 25 minutes after it is placed in the refrigerator. (Round to the nearest degree.)
Answer: ___________________________________ 6. (8 points). Solve the following exponential equation for x: ���−� = �� Answer: x = ____________________
5 7. (10 points). Solve the following logarithmic equation for x (Hint: Use properties of logarithms to condense the expression on the left-hand side of the given equation FIRST. Also, check all solutions in the original equation): ����(�� + �) + ����(� + �) = � Answer: x = ________________________
8. (10 points). Solve the rational equation shown below for x. (Check all solutions in the original equation). �� + �� � + � = � + � Answer: x = _______________________________
6 9. (14 points). For the quadratic function shown below, answer the following 7 questions: f(x) = -2(x + 1) 2 + 4 (a). Determine the coordinates of the x-intercepts (if any). Answer: Coordinates of x-intercepts: ______________________________ (b). Determine the coordinates of the y-intercept. Answer: Coordinates of y-intercept: ______________________________
(c). Determine the domain of f(x). Answer: Domain of f(x) (in interval notation): ______________________ (d). Determine the range of f(x). Answer: Range of f(x) (in interval notation): ______________________ (e). Determine the coordinates of the vertex. Answer: Coordinates of the vertex: __________________________
7 (f). Identify the coordinates of any relative minimum or maximum. Answer: Relative MINIMUM or MAXIMUM (CIRCLE WHICH IT IS): Coordinates: _____________ (g). Sketch a graph of f(x) on the coordinate axes below.
8 10. (6 points). Suppose we are given the function f(x) = √�. (a). Find a formula for a function g(x) whose graph is obtained from the above f(x) by shifting f(x) right 2 units, followed by a shift 3 units down.
Answer: g(x) = ________________________ (b). Find a formula for a function h(x) whose graph is obtained from the above f(x) by shifting f(x) 1 unit up, followed by a reflection across the x-axis. Answer: h(x) = _____________________ 11. (6 points). (a). Convert the angle given in degrees to radians. Express your answer in terms of π. 54 o
Answer: 54 o = ____________________ radians (b). Convert the angle given in radians to degrees. � � � Answer: � � � radians = ____________________ degrees 9 12. (6 points).
(a). Find a positive angle (measured in degrees) less than 360 o that is co-terminal with the given angle. 548 o Answer: ____________________ degrees (b). Find a positive angle (measured in radians) less than 2π that is co-terminal with the given angle. �� � � Answer: ____________________ radians
Algorithms and Ciphers Chapter 4 © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Module Agenda Stream Ciphers Block Ciphers Modes of Symmetric Block Ciphers Symmetric Algorithms Asymmetric Algorithms Hybrid Systems © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Categories of Cryptosystems © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved.
For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Organization of Cryptosystems Two-Way Cryptography Symmetric Asymmetric Steganography Message Integrity Controls Stream Block Factoring the Product of Large Primes Discrete Logarithms
Symmetric Key Algorithms Same key used for both the encryption and decryption operations Document to Be Encrypted Encryption Algorithm (i.e., AES) Encrypted Document Decrypted Document Encryption Algorithm
Encrypted Document Key © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances 4 Stream Ciphers A keystream (sequence of bits used as a key) is generated and combined with the plaintext using an Exclusive-OR (XOR) operation: Statistically unpredictable and unbiased Not linearly related to the key Operates on individual bits or bytes Functionally complex Long periods with no repeats © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved.
For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Stream Ciphers: Advantages and Disadvantages Advantages: Emulates a one-time pad No size difference between plaintext and ciphertext Very suitable for hardware implementation and serial communications Disadvantages: Can be difficult to implement correctly Generally weaker than a block-mode cipher Difficult to generate a truly random unbiased keystream © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Stream Cipher Uses Wireless: WEP, WPA Audio/video streaming GSM © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved.
For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Examples of Stream-based Algorithms RC-4: Ron Rivest of RSA Security (1987) One of the most widely used stream ciphers today TLS (Transport Layer Security), WEP (Wired Equivalent Privacy), WPA (Wi-Fi Protected Access), TKIP (Temporal Key Integrity Protocol), Microsoft XBox, Oracle SQL, Microsoft PPTP, Microsoft Office, and Adobe Acrobat. SEAL: Software-optimized Encryption Algorithm A5/1, A5/2, A5/3: These are stream ciphers used in GSM (Global Systems for Mobile Communications) systems. © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Block Cipher Blocks of plaintext are encrypted into ciphertext blocks Multiple modes of operation Variable key size, block size, rounds dark
On a ptuf NeQj Data Block 2 Data Block 1 Cryptosystem Cipher Block 2 Cipher Block 1 Ciphertext Key IV © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Block Cipher Uses Data transport AES (Advanced Encryption Standard): Created by NIST in 2001 Triple DES (Data Encryption Standard)
Data storage AES in counter mode © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Advanced Encryption Standard (AES) Based on Rijndael algorithm: Developed by Daemen and Rijmen in 1998 © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Rijndael Block Options AES Block Options
128,192,256 Key Options 128, 192, 256 Rounds 10, 12, 14 128, 192, 256 Rounds 10, 12, 14 Key Options 128
Examples of Block Mode Algorithms AES (Rijndael) IDEA RC2 RC5 RC6 Blowfish Twofish CAST SAFER Data Encryption Standard (DES) 3DES Serpent Mars Skipjack © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Microsoft Online Clipart 12
Components of CryptographyChapter 3© Copyright 2012-2013.docx

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Components of CryptographyChapter 3© Copyright 2012-2013.docx

  • 1. Components of Cryptography Chapter 3 © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Categories of Cryptosystems © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Organization of Cryptosystems Two-Way Cryptography Symmetric Asymmetric Steganography
  • 2. Message Integrity Controls Stream Block Factoring the Product of Large Primes Discreet Logarithms
  • 3. Steganography Art of hiding information Plaintext hidden/disguised Prevents a third party from knowing that a secret message exists Traditionally accomplished in a number of ways: Physical techniques Null ciphers © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Null Cipher Example Cipher text: News Eight Weather: Tonight increasing snow. Unexpected precipitation smothers eastern towns. Be extremely cautious and use snowtires especially heading east. The highway is not knowingly slippery. Highway evacuation is suspected. Police report emergency situations in downtown ending near Tuesday. Taking the first letter in each word successively yields the real message: "Newt is upset because he thinks he is President." © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under
  • 4. Any Circumstances Image-based Steganography RGB* values altered to contain a message File sizes are identical Different hash values E1089197693F6C4C26E0033F8C8AF00C 57694B77DCB55C543C6C0BA8E1FF2D17 © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Digital Watermarking Digital watermarks are visible or invisible markings embedded within a digital file to indicate copyright or other handling instructions, or to embed a fingerprint to detect unauthorized copying and distribution of images © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only.
  • 5. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Substitution and Transposition © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Cryptography Substitution Simple Polyalphabetic Transposition Scytale
  • 6. Running Key Codes Substitution Ciphers Four-square Playfair Caesar Cipher: Shift (rotate) alphabet (move letters three spaces) A B C D E F ... BAD
  • 7. D E F G H I ... EDG Scramble alphabet: Substitute one letter for another A B C D E F ... BAD Q E Y R T M ... EQR © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Polyalphabetic Ciphers – Vigenère Cipher This is a simple substitution cipher that uses multiple alphabets rather than just one Encrypt the plaintext ‘FEEDBACK’ using a key of 3241 © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Running Key Ciphers Use the value of plaintext letters and a value of key based on a shared book
  • 8. Value of Message ‘THIS message …’ + Value of Key ‘on periodic …’ = Value of Ciphertext © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances One-time Pads (OTPs) The keys are the same size (length) as the plaintext message, and the keys must be randomly generated for this scheme to be truly effective It is the requirement for randomness that makes OTPs particularly challenging to generate, since the best that we can typically achieve when generating such pads using computer processors are pseudo-random values © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances
  • 9. © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Codes A group of navy ships is operating under conditions of radio silence to avoid detection by the enemy Maneuvering signals and comments are communicated by flag signals A separate flag is used for each letter To send a paragraph of information would be a real workout for the signalmen, so codes are used to minimize the effort and time involved; for instance, the letters BZ are the signal that the addressee performed well or did a good job © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Transposition Ciphers Columnar – rearranging the message in a table Plaintext “This is an example of transposition” Ciphertext “tsaonihamfstinptpiselrooixeasn” Key: grid shape and reading direction Example: the Spartan Scytale © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only.
  • 10. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances 1 MATH 115 6381 (2182) Mid Term Exam Name___________________________________ By signing my name above, I certify that I have completed this assignment individually, working independently and not consulting anyone except the instructor. Instructions for Mid-Term Exam: The Mid-Term Exam consists of 12 problems for a total of 100 points. It is based on the material
  • 11. covered in the first 3 weeks of the course, but with considerable focus on the Week 4 material: Chapter 6 (Sections 6.2 through 6.5) of the “College Algebra, 3 rd Corrected Edition” text and Chapter 10 (Section 10.1) of the “College Trigonometry, Stitz and Zeager” text. It is open book and open notes. It is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone. YOU MAY USE YOUR GRAPHING CALCULATOR (TI-83/84 or EQUIVALENT, nothing more sophisticated) TO ASSIST IN GRAPHING OR ANY NUMERICAL CALCULATIONS). You must show your work. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document containing your work. Scanned work is acceptable also. When you have completed the exam, upload your solutions file to the Mid-Term Exam assignment
  • 12. in the Assignment folder. DUE DATE is NLT 11:59pm EDT, Sunday, September 16. If you have any questions, please contact me by e-mail. 2 1. (8 points). Find all real solutions to the following equation: √� − � + √� − � = 4
  • 13. Answer: x = ______________________ 2. (8 points). Consider the following functions: f(x) = 3 – x 2 ; g(x) = √� + � (a). Compute the composition function (f ◦ g)(x). Answer: (f ◦ g)(x) = ___________________________ (b). Compute (f ◦ g)(2).
  • 14. Answer: (f ◦ g)(2) = ________________ 3 3. (8 points). (a) Rewrite the following exponential expression as a logarithmic expression. ( � � ) −� = � Answer: ___________________________________ (b). Rewrite the following logarithmic expression as an exponential expression:
  • 15. ���� ( � �� ) = −� Answer: ___________________________________ 4. (8 points). Use the properties of logarithms to condense the expression below as a single logarithm. � � ����(�) − �����(�) − ����(�)
  • 16. Answer: ___________________________________ 4 5. (8 points). A can of soda at 83 o F is placed in a refrigerator that maintains a constant temperature of 35 o F. The temperature T of the soda t minutes after it is placed in the refrigerator is given by the equation below: T(t) = 35 + 48 e – 0.058 t Find the temperature of the soda 25 minutes after it is placed in the refrigerator. (Round to the nearest degree.)
  • 17. Answer: ___________________________________ 6. (8 points). Solve the following exponential equation for x: ���−� = �� Answer: x = ____________________
  • 18. 5 7. (10 points). Solve the following logarithmic equation for x (Hint: Use properties of logarithms to condense the expression on the left-hand side of the given equation FIRST. Also, check all solutions in the original equation): ����(�� + �) + ����(� + �) = � Answer: x = ________________________
  • 19. 8. (10 points). Solve the rational equation shown below for x. (Check all solutions in the original equation). �� + �� � + � = � + � Answer: x = _______________________________
  • 20. 6 9. (14 points). For the quadratic function shown below, answer the following 7 questions: f(x) = -2(x + 1) 2 + 4 (a). Determine the coordinates of the x-intercepts (if any). Answer: Coordinates of x-intercepts: ______________________________ (b). Determine the coordinates of the y-intercept. Answer: Coordinates of y-intercept: ______________________________
  • 21. (c). Determine the domain of f(x). Answer: Domain of f(x) (in interval notation): ______________________ (d). Determine the range of f(x). Answer: Range of f(x) (in interval notation): ______________________ (e). Determine the coordinates of the vertex. Answer: Coordinates of the vertex: __________________________
  • 22. 7 (f). Identify the coordinates of any relative minimum or maximum. Answer: Relative MINIMUM or MAXIMUM (CIRCLE WHICH IT IS): Coordinates: _____________ (g). Sketch a graph of f(x) on the coordinate axes below.
  • 23. 8 10. (6 points). Suppose we are given the function f(x) = √�. (a). Find a formula for a function g(x) whose graph is obtained from the above f(x) by shifting f(x) right 2 units, followed by a shift 3 units down.
  • 24. Answer: g(x) = ________________________ (b). Find a formula for a function h(x) whose graph is obtained from the above f(x) by shifting f(x) 1 unit up, followed by a reflection across the x-axis. Answer: h(x) = _____________________ 11. (6 points). (a). Convert the angle given in degrees to radians. Express your answer in terms of π. 54 o
  • 25. Answer: 54 o = ____________________ radians (b). Convert the angle given in radians to degrees. � � � Answer: � � � radians = ____________________ degrees 9 12. (6 points).
  • 26. (a). Find a positive angle (measured in degrees) less than 360 o that is co-terminal with the given angle. 548 o Answer: ____________________ degrees (b). Find a positive angle (measured in radians) less than 2π that is co-terminal with the given angle. �� � � Answer: ____________________ radians
  • 27. Algorithms and Ciphers Chapter 4 © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Module Agenda Stream Ciphers Block Ciphers Modes of Symmetric Block Ciphers Symmetric Algorithms Asymmetric Algorithms Hybrid Systems © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Categories of Cryptosystems © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved.
  • 28. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Organization of Cryptosystems Two-Way Cryptography Symmetric Asymmetric Steganography Message Integrity Controls Stream Block Factoring the Product of Large Primes Discrete Logarithms
  • 29. Symmetric Key Algorithms Same key used for both the encryption and decryption operations Document to Be Encrypted Encryption Algorithm (i.e., AES) Encrypted Document Decrypted Document Encryption Algorithm
  • 30. Encrypted Document Key © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances 4 Stream Ciphers A keystream (sequence of bits used as a key) is generated and combined with the plaintext using an Exclusive-OR (XOR) operation: Statistically unpredictable and unbiased Not linearly related to the key Operates on individual bits or bytes Functionally complex Long periods with no repeats © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved.
  • 31. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Stream Ciphers: Advantages and Disadvantages Advantages: Emulates a one-time pad No size difference between plaintext and ciphertext Very suitable for hardware implementation and serial communications Disadvantages: Can be difficult to implement correctly Generally weaker than a block-mode cipher Difficult to generate a truly random unbiased keystream © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Stream Cipher Uses Wireless: WEP, WPA Audio/video streaming GSM © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved.
  • 32. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Examples of Stream-based Algorithms RC-4: Ron Rivest of RSA Security (1987) One of the most widely used stream ciphers today TLS (Transport Layer Security), WEP (Wired Equivalent Privacy), WPA (Wi-Fi Protected Access), TKIP (Temporal Key Integrity Protocol), Microsoft XBox, Oracle SQL, Microsoft PPTP, Microsoft Office, and Adobe Acrobat. SEAL: Software-optimized Encryption Algorithm A5/1, A5/2, A5/3: These are stream ciphers used in GSM (Global Systems for Mobile Communications) systems. © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Block Cipher Blocks of plaintext are encrypted into ciphertext blocks Multiple modes of operation Variable key size, block size, rounds dark
  • 33. On a ptuf NeQj Data Block 2 Data Block 1 Cryptosystem Cipher Block 2 Cipher Block 1 Ciphertext Key IV © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Block Cipher Uses Data transport AES (Advanced Encryption Standard): Created by NIST in 2001 Triple DES (Data Encryption Standard)
  • 34. Data storage AES in counter mode © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Advanced Encryption Standard (AES) Based on Rijndael algorithm: Developed by Daemen and Rijmen in 1998 © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Rijndael Block Options AES Block Options
  • 35. 128,192,256 Key Options 128, 192, 256 Rounds 10, 12, 14 128, 192, 256 Rounds 10, 12, 14 Key Options 128
  • 36. Examples of Block Mode Algorithms AES (Rijndael) IDEA RC2 RC5 RC6 Blowfish Twofish CAST SAFER Data Encryption Standard (DES) 3DES Serpent Mars Skipjack © Copyright 2012 – 2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances © Copyright 2012-2013 (ISC)², Inc. All Rights Reserved. For Personal Use of (ISC)2 Seminar Attendee Only. Contents May Not Be Copied or Otherwise Distributed Under Any Circumstances Microsoft Online Clipart 12