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Cryptography: Math and Codes

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Eligibility: CTY-level or Advanced CTY-level math score required

Prerequisites: Successful completion of Grade 4 Mathematics or equivalent

Course Format: Individually Paced

Course Length: Typically 3 months

Course Code: CMC

Course Description

Description

Cryptography: Math and Codes introduces students to the exciting practice of making and breaking secret codes. This popular course is designed for for mathematical enrichment for students in grades 4-6.

Students begin with simple Caesar Ciphers, learning to encrypt and decrypt messages as well as the history behind the cipher. They will move through history and more advanced mathematical concepts to learn substitution ciphers, Vigenère ciphers, and multiplicative and affine ciphers. Students will need to put all their newly acquired knowledge to the test by finishing with public key cryptography and the modern day RSA cryptosystem. This course intersects the disciplines of mathematics, computer science, and electrical engineering. Applications of cryptography include ATM cards, computer passwords, and electronic commerce.

Throughout the course, students will have the opportunity to encrypt and decrypt messages, invent their own ciphers, discuss relevant historical events and literature, and learn some mathematical concepts that are often not seen until college!

Mathematical Topics covered Include:

  • positive and negative numbers
  • decimals and percents
  • data analysis and probability
  • prime numbers and factorization
  • modular arithmetic
  • inverses
  • exponentiation

For a detailed list of topics, click the List of Topics tab.

Assignments are based on a text that is purchased separately by the student.

Caesar Cipher

Materials Needed

There is a textbook purchase required for this course:

The Cryptoclub: Using Mathematics to Make and Break Secret Codes. Janet Beissinger and Vera Pless (AK Peters, 2006)

Cryptoclub textbook cover

List of Topics

Introduction to Cryptography

  • Caesar Ciphers
  • ROT13
  • Steganography
  • Sending Messages with Numbers
  • Breaking Caesar Ciphers
  • Navajo Code Talkers

Substitution Ciphers

  • Keyword Ciphers
  • Cryptography in Fiction
  • Letter Frequencies
  • Breaking Substitution Ciphers
  • Nomenclators

Vigenère Ciphers

  • Combining Caesar Ciphers
  • Transposition Ciphers
  • Cracking Vigenère Ciphers Using Key Length
  • Factorization
  • Solving Problems Using Number Theory
  • Cracking Vigenère Ciphers Using Common Factors
  • Long Keywords

Modular Arithmetic

  • Introduction to Modular Arithmetic
  • The Zimmerman Telegram
  • Applications of Modular Arithmetic
  • Check Digits

Multiplicative and Affine Ciphers

  • Multiplicative Ciphers
  • Password Security
  • Using Inverses to Decrypt
  • The Enigma Machine
  • Affine Ciphers
  • Atbash and Pigpen Ciphers

Math for Modern Cryptography

  • Finding Prime Numbers
  • Properties of Exponents
  • Raising to Powers in Modular Arithmetic
  • Numeration Systems

Public Key Cryptography

  • The RSA Cryptosystem
  • Cryptographic Hash Functions
  • Revisiting Inverses in Modular Arithmetic
  • Sending RSA Messages

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Demo

Demo

In addition to the textbook, there are interactive websites and videos in the course.

Caesar Cipher demo

In a Caesar Cipher, the alphabet is shifted a certain number of places and each letter of a message is replaced by the corresponding shifted letter. With this tool, you can shift the alphabet using the cipher wheel then encrypt your own message!

Solving Problems Using Number Theory demo

Navajo War Code demo

Sample Quiz

Sample Cryptography quiz

 

Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Adobe Connect Add-in or Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile appStudents who are unable to attend live sessions will need a computer with the Adobe Connect Add-in or Adobe Flash plugin installed to watch recorded meetings. The Adobe Connect Add-in, Adobe Flash plugin, and Adobe Connect Mobile app are available for free download. Students who do not have the Flash plug-in installed or enabled on their browsers will be prompted to download and install the Adobe Connect add-in when accessing the virtual classroom.