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Cryptographic Protocols
This is another activity that achieves something that doesn't seem possible - people who don't trust each other and can't see each other are able to agree on the outcome of a random coin flip.
This is an absorbing activity for an individual student or a whole classroom.
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The Royal Institution UK and Microsoft Research together have produced activities in encryption, cryptography, and zero knowledge protocols for the classroom at the locations below:
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Logic Circuit Builder applet from Johns Hopkins University lets you create your logic circuits and compute them to view the resulting input/output truth tables. You can view the truth tables for the common gate elements here
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An online course in Digital Circuitry was developed for ThinkQuest by Montgomery Blair High School Magnet Program for Science, Mathematics, and Computer Science is at An Online DIGitAL Circuitry Course .
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Robin Forry from the University of Cincinnati has an activity in desinging Integrated Circuits called Computer Chip Design where in the first activity students create a layout for a special purpose computer that uses mathematical functions to compute a target value given two inputs. There is also a second activity where students create a layout of components of a processor that minimizes area on the chip. This activity was developed for high school students.
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Michael Wolf from the University of Cincinnati has an activity in Input, Output and Data Communications called LMR Communication where students learn about land mobile radios through experimenting with walkie-talkies for hands on learning of general radio functions. Then the students will learn about conventional and trunked queues. This activity was developed for high school students.
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Do I.T. has logic gates tryout applets at Computer Logic
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Hobart and William Smith Colleges has the xLogicCircuits Lab that explores logic circuits created out of AND, OR and NOT gates. The relationship between circuits and Boolean algebra is also covered.
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Claude Shannon's Experiment to Calculate the Entropy of English is aimed at determining the entropy of an English letter (the amount of information in bits that we obtain on the average when we learn one letter of English).
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Illuminations has an application that explains Cryptography at Codes . Cryptography is science that uses mathematics to encrypt and decrypt data.
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Illuminations has an activity Arithme-Tic-Toc where students will be introduced to modular arithmetic by first examining a five-hour analog clock and its mathematical properties. Then students will investigate patterns and relationships that exist in 12-hour addition and multiplication clock tables.
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University of California, San Diego Maths Department has applets that demonstrate concepts in Cryptography in the module Introduction To Cryptography .
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Centre for Innovation in Mathematics Teaching has the following teaching packages developed to teach Codes and Ciphers in their Maths Curriculum:
- Substitution Ciphers: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Braille:Teacher Guide, Student Guide, OHP Slides, Lesson Plans. Another Exercise that might be of interest is Find the Braille Codes
- EAN Bar Codes:Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- ISBN Numbers: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Binary Codes: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Genetic Fingerprinting: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Postcodes: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- ITF Symbols: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Code 3 of 9: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Public Key Cryptography: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Transposition: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- One-Time Pads: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Semaphore: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Morse Code: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Vehicle Registration Marks: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Modern Encryption: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Huffman Codes: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Arithmetic Coding: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
- Lorenz Cipher Machine: Teacher Guide, Student Guide, OHP Slides, Lesson Plans. See also the Simplified Lorenz Cipher Toolkit
- Enigma Cipher: Teacher Guide, Student Guide, OHP Slides, Lesson Plans
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University of Cambridge Caret has the Enigma Game which is an interactive code breaking game for ages 11-14 and 15-18 incorporating 4 levels of difficulty. Download the Enigma Activity PDF for more documentation.
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Herong Yang has a free Cryptography Tutorials book which is a collection of notes and sample codes written by the author while he was learning cryptography technologies himself. It can be used as a tutorial guide for beginners.
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Dr. Lisa N. Michaud has the following resources of interest:
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Shodor Interactivate has the following resources in Ciphers and Codes that includes activities and explanations for learners and instructors with discussions:
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Jim Loy has the following guides, notes and puzzles that can be used as ideas for classroom activities in Cryptography, Codes and Ciphers:
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Simon Singh offers a page full of growing resources for teaching codes and code-breaking. These resources are organised to be offered on "Spy Days" where pupils can learn about these topics using lessons and activities that span over a day.
Spy Day Ideas and Lessons (developed for Year 9 pupils in the UK)
Cipher Challenge (developed for Years 5-8 pupils in the UK)
Code Challenge (developed for gifted children)
Teacher Packs (developed for Years 5,6, and 7 in the UK) / Key Stage 2/3
- Pig Pen Cipher
- Caesar Wheel
- The Caesar Cipher - Worksheets
- Frequency Analysis Worksheets
- Frequency Analysis Teachers’ Notes
- Scytale template
- The Code Book on CD-ROM
- Further Resources
Senior Resources
- Frequency Analysis Investigation
- Code Book CD-ROM
- Further Resources
- Mini Cipher Challenge 1
- Mini Cipher Challenge 2
- Mini Cipher Challenge - Teachers Notes
See the entire set of resources with additional documentation at Teaching Resources .
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The Enigma Project has a good demonstration section on the Enigma Machine. Watch the Video: James Grime Demonstrates the Enigma Machine . To discover more about the history of code breaking download the Code Book CD-ROM by Simon Singh and Nick Mee, and take the 5 challenges on the page.
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SCOUTS, South Africa has a website dedicated to learning secret codes and how to use them at Codes for Cubs and Scouts . This site gives an gentle introduction to most codes with exercises to try out.
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PBS' NOVA Online has the following resources available in codes and ciphers with worked out examples:
- Crack the Ciphers : offers three World War II-style ciphers of different levels of difficulty for you to try to break
- Send a Coded Message : offers an online version of an Enigma-like machine to encode your own message, then e-mail that message to a friend with instructions on how to decode it using a secret key.
- A Simple Cipher: lets you learn some of the tricks codebreakers use to solve ciphers, and use your new talents to make sense of what looks like a bunch of gibberish.
- Are Web Transactions Safe?: looks at all the ways encryption affects you, with a special emphasis on the Internet.
- Mind of a Codebreaker: led by Alan Turing, inventor of the computer, the codebreakers of Bletchley Park were a brilliant, quirky bunch who broke the Engima in large part by learning to think like the German codemakers themselves.
- How the Enigma Works: The Enigma looks roughly like a typewriter, but it is infinitely more complex, with fully 17,576 ring settings for each of 60 possible wheel orders—and that is just to set it up for use.
Decoding Nazi Secrets: a television broadcast from November 9, 1999 offers some materials for teacher use which based on the program. Please note that the video is not required for using these activities:
- Classroom Activity: includes materials, lesson plans and answers
- Teaching Ideas from Other Teachers
- Complete Transcript of the television broadcast: can be used for research and further reading
- Send a Coded Message: an interactive online activity for students
Melissa Salpietra has the following interactive online activities:
- Cryptography 101: an interactive activity that demonstrates different ways to make messages secret including transposition and substitution ciphers
- Send a Secret Message: an interactive activity that lets you write a note, encode it, and send it to a friend for decoding.
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Stephen C Phillips has the following fun activities and resources on Morse Code:
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SECRET CODE BREAKER is a comprehensive site covering a series of cryptography publications for young readers that provide detailed instructions explaining how to "crack" secret codes and ciphers for beginning cryptanalysts. Included are computer programs for code breaking and a series of coded secret messages actually sent by secret agents, spies and military commanders beginning with the Revolutionary War to the present including messages from the CIA "mole" Aldrich Ames to the KGB.
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Frode Weierud has a collection of cipher machine simulators that can be downloaded for understanding how these machines work. For the complete list of simulators with sample screens and documentation please visit Enigma Variations: An Extended Family of Machines . These resources could be used for classroom tasks and teaching ideas at a senior school level.
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Dirk Rijmenants has an entire website Cipher Machines and Cryptology with loads of resources in Cryptography. A great activity challenge of interest is the following challenge which could be used as teaching tools:
- Enigma Challenge: The Enigma cipher challenge gives you the chance to show your code breaking skills. Anyone, interested in the Enigma machine, can join the challenge.
- Cryptobox Challenge: The Crypto Box Challenge is a contest to decipher three scrambled pieces of text.
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University of Southampton School of Mathematics has the National Cipher Challenge that offers the following teacher resources and materials:
- Teachers Notes and Lesson Plans(Slow Download)
- National Cipher Challenge - Main Site: choose "The Challenges" under the Main Menu for the latest challenges available. Also all "Previous Challenges" are available from the past years on the right side of the Main Menu
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GK-12 at Harvard University has some useful resources and worksheets in Encryption.
Description: Introduces students to some basic ciphers and the concept of encryption. Can be extended with a programming exercise in which one or both are implemented. Can also be extended with a discussion of public-key encryption works to provide the encryption we use online today. Note that the examples and problems given are best if they are customized to be phrases that are meaningful to the students in the class.
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Center for Discrete Mathematics & Theoretical Computer Science at Rutgers University has the following relevant resources created by various high school teachers:
- Matrices In Encryption And Decryption Of Codes
- Using the TI-83 to Encode a Message. See Wikipedia: TI-83.
- Using the TI-83 to Understand RSA. See Wikipedia: TI-83.
- Discrete Dots and the TI-83. See Wikipedia: TI-83.
- Cryptography on the TI-83. See Wikipedia: TI-83.
- Secret Sharing with Linear Equations
- Cryptography and Geometry, Beyond the Triangular Grille
- A Programming Challenge in Cryptography (by Eric Collazo)
- Codes and Inverse Operations
- Basic Crypto Systems I
- Basic Crypto Systems II
- Secret Messages and Matrices
- Cryptography Implementation
- The Rotating Grille
- Does the falling tree make a sound if no one if there to hear it? (or communication via encryption)
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Purdue University's GK-12 has a lesson plan for teaching Caeser Ciphers: An Introduction to Cryptography
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CSIRO's SCIENCE BY EMAIL has the following activities:
- Fair Coin Flip that explains encryption using square roots
- Cipher Wheel to create this simple device for creating secret messages
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The Thomas Beale Cipher is a 10-minute award-winning film that tells the true legend of history's most challenging cipher. Professor White, cryptographer extraordinaire, is on the trail of the notoriously uncrackable Thomas Beale cipher—a century-old riddle hiding the location of a fortune in gold that has tormented its pursuers since inception. But White is not alone—shadowy forces are tight on his tail. The film contains 16 hidden messages that hold clues to the characters' secrets. Eight are fairly easy and require only a close eye. Six are moderately difficult using various encryption methods. Two are extremely difficult and will require a genius mind to decrypt.
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Wolfram Demonstrations Project has the following demonstration activities. Note: You will need to install the Wolfram CDF Player in order to use these activities. You can either download each demonstration or use your browser to run it.
- Solve the Cryptoquote: Try your hand at decoding some famous quotes encoded using a substitution cipher. The person to whom the quote is attributed is encoded after the quote. Each cipher is a derangement of the letters of the alphabet, so that no letter stands for itself. If you need a hint to get started, the "show hint" button will randomly select a letter in the coded message and decode it for you.
- Solve the Cryptoquote Automatically: A cryptoquote is a puzzle, commonly found in newspapers, in which a substitution cipher is used to encrypt a famous quote. Here a brute force approach is taken to automatically decipher the encrypted text for 33 different puzzles listed in order of difficulty. The encrypted puzzle is dynamically updated as the solution progresses. Experiment with different solving strategies to enhance or degrade performance.
- Decoding the Arecibo Message: In 1974 a message was beamed from the Arecibo radio telescope towards a cluster of stars 25,000 light years distant in the constellation of Hercules. It consisted of 1679 binary digits transmitted in sequence. To read the message, the binary digits must be formed into a low resolution image on a two dimensional grid. But what sized grid should be used? Use the slider control to vary the number of columns in the grid and "decode" the Arecibo message.
- Learn the Radio Code: This Demonstration is one way to learn the International Civil Aviation Organization (ICAO) radio code. It lists several words and displays the conversion to the radio code. It can also speak the converted answer.
- Substitution Cipher Encoder: Substitution ciphers are one of the simplest forms of encryption, where replacement rules are provided that map each letter of the alphabet onto a different letter.This tool will generate randomly chosen keys that map the 26 letters of the English alphabet onto themselves. It also generates snippets of sample text from a range of English sources.
- Vernam Cipher: This Demonstration generates a random bit key for both sender and receiver of the Vernam cipher and provides a simple way to encryptand decrypt messages in various Unicode-supported languages.
- Hackers Language: Criminal hackers usually leave messages when breaking into a website or any system. The messages are written in a kind of code. It is not meant to be cryptography; the idea is just to show that it was left by a hacker. The language replaces some characters, for example: t to 7, B to 8, l to 1, i to !, s to z, and so on, but there is no strong rule. There are also legal hackers who program free software and open source projects such as Linux Kernel, KDE and Gnome user interfaces, Apache web server, and many others.
- RSA Encryption and Decryption: The RSA algorithm for public-key encryption was originated by Ron Rivest, Adi Shamir, and Leonard Adleman at MIT in 1977. Several similar methods had been proposed by earlier workers. The algorithm is based on the fact that it is far more difficult to factor a product of two primes than it is to multiply the two primes. Even the most powerful modern supercomputers would require more time than the age of the universe to factor a 400-digit number.
- Hill Cipher Encryption and Decryption: In a Hill cipher encryption, the plaintext message is broken up into blocks of length according to the matrix chosen. Each block of plaintext letters is then converted into a vector of numbers and is dotted with the matrix. The results are then converted back to letters and the ciphertext message is produced. For decryption of the ciphertext message, the inverse of the encryption matrix must be found. Once found, the decryption matrix is then dotted with each -block of ciphertext, producing the plaintext message.
- An Unforgettable Substitution Code: The characters in the two keywords give the beginning of the encryption alphabet completed by the remaining characters.
- Additive Cipher: The mono-alphabetic substitution cipher provides the simplest form of cryptography, where the cipher alphabet is simply a rearrangement of the plaintext alphabet. In an additive cipher, the cipher alphabet is a shift of the plaintext alphabet.
- Visual Encryption Pad: Only one position of the random mask will reveal clear text hidden in the cypher pad. The security of the code depends on a safe way to pass or keep the random mask. Application of the trivial rules {0->1, 1->0, 2->1} to the sum of clear text and random mask generates the cypher pad.
- Redundancy in Written Language: Languages have different levels of redundancy. Move the slider to remove increasing numbers of letters. Some languages remain readable even after removing a significant portion of the letters, while others become unreadable much sooner.
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Count On has a complete section dedicated to Codebreaking with lots of online activities students can try in the following Ciphers and techniques:
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Math Night has a module Secret Codes:
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Mike Koss has the following resources:
- Paper Enigma Machine, where students can create a paper version of the Enigma machine and make it work as per the instructions on the sheet
- Enigma Machine Simulator (Web Page) : encode and decode Enigma messages directly from the web.
- Pocket Engima Machine (Android mobile phones), a highly realistic simulation using images and sounds from an authentic Enigma machine ($2 in the Android Market).
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BEYOND DISCOVERY has a great section on The Code War
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National Security Agency (NSA) Cryptokids has a section meant for young children on Codes and Ciphers:
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Jacob Mathai has a concise page on History of Computer Cryptography and Secrecy Systems
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DIMACS, Rutgers University has the following sections for teaching Cryptography & Network Security at high school level:
- Keeping Secrets: a great section discussing some topics which could be addressed in some high school courses
- Teacher breaks code on summer vacation: article about Connie Cunningham, a math teacher at Rocky Grove High School, learned the mathematics behind cryptography at a summer forum at Rutgers State University.
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White Haven Maths has an extensive section on Codes and Ciphers which features detailed explanations and tools for learning how each cipher works
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Frank Speiss has a very well designed Enigma Machine Simulator using Flash with the Help File on how to use the simulator
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GCHQ Challenge (Cheltenham Science Festival) has some of their code breaking challenges available for students to try out from various past years with solution pages for each:
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Simon Singh has The Black Chamber , where you can learn about codes and codebreaking, encrypt your own messages, crack those of your enemies, and play with interactive enciphering programmes. The Black Chamber provides a brief history of cryptography from Ancient Rome to today's Information Age, and it is also a mini-tutorial in codes and codebreaking. If you want to know more, then a not-for-profit CD-ROM containing all the material in this website and lots more is available. It contains more sophisticated material (e.g., an Enigma emulator), advanced tools (RSA encryption), items that would not work over the Internet (animations of quantum cryptography), and notes for teachers. Listed below are the contents:
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Abdullah Seddiq (MIT Blossoms) has The Magic Picture: Steganography in Bitmap Files , a video with teacher guides and other resources. This video aims to connect many topics in computer science to reach the writing of an application that can do something useful in actual life. The student will get to know the concept of ciphering and hiding (Steganography in bitmap files), will have a glance at the American Standard Code for Information Interchange table "ASCII", will understand the structure of bitmap (BMP), and learn how color is stored.
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Monticello has the following resources on the Wheel Cipher:
- Read about the Wheel Cipher
- Try out the Wheel Cipher
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Virtual Science Fair has a science fair project See the Unseen, Hear the Unheard - Exploring the Limits of Steganography