Cryptography: Math and Codes
Cryptography: Math and Codes is a CTY Online course open to students in grades 4-6, who have satisfied the prerequisite of a qualifying math score on the SCAT and have completed grade 3 math. The course lasts about 3 months and its course code is CMC.
Contents
Course Description
From the CTY Online catalog:
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 Assignments are based on a text that is purchased separately by the student.
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
