Cryptology: Math and Codes
- Grades 5-7
Make and break secret codes in this exciting introductory cryptology course. You’ll begin with simple Caesar ciphers, learning to encrypt and decrypt messages as well as the history behind the cipher. We’ll then move through more advanced mathematical concepts to learn substitution ciphers, Vigenère ciphers, and multiplicative and affine ciphers. All of your newly acquired knowledge will be put to the test by finishing with public key cryptography and the modern-day RSA cryptosystem.
This course combines mathematics, computer science, and electrical engineering, and it’s an excellent choice for those wishing to enhance their grasp of modern cryptology concepts such as ATM cards, computer passwords, and e-commerce. Prepare to be challenged, though—many of the concepts covered in this course are often not seen until college.
Your assigned CTY instructor will be available for learning support and one-on-one review sessions for graded assessments.
Recommended length of enrollment: 3 months
Group Session Meeting Times (optional): Mondays - 8 p.m. ET
Time Commitment: 5-8 hours per week (1-hour optional meeting, 5-7 hours of independent work).
What we'll do
We’ll work through lessons and assignments covering all seven units of the textbook. Each unit includes lessons with videos, graded homework for each chapter, a unit exam, and a part of a simulated scavenger hunt. There are discussion forums throughout the course.
What we'll learn
- How to create and break Caesar ciphers
- How to use letter frequencies to break substitution ciphers
- How to use multiple methods to crack Vigenère ciphers
- How to perform calculations in modular (clock) arithmetic
- How to work with multiplicative and affine ciphers
- How to send messages with the RSA cryptosystem
By the end of the course, you will be able to:
- Encrypt and decrypt messages with a variety of codes
- Invent your own ciphers
- Discuss relevant historical events and literature
- Apply number theory concepts to cryptology
How we’ll measure learning
Multiple-choice and short answer questions on chapter homework assignments and major exams are graded instantly by the Moodle platform. Students are also graded on their participation in the forum discussions. The course is aligned to applicable Common Core State Standards.
Students enroll in a course by selecting an open class below. Students progress at their own pace following course guidelines, with guidance from instructors who strive to meet individual needs. While the course provides students with independence and flexibility, students must manage their time to complete the course before the end date.
Note: You need an active CTY Account to complete registration through MyCTY.
Testing and Prerequisites
|Required Level||CTY-Level||Not required|
Students must achieve qualifying scores on an advanced assessment to be eligible for CTY programs. If you don’t have qualifying scores, you have several different testing options. We’ll help you find the right option for your situation.Sign up for Testing Learn More
Course PrerequisitesCryptology: Math and Codes requires:
Successful completion of Grade 4 Mathematics or equivalent
Cost and Financial Aid
- Nonrefundable Application Fee - $15 (Waived for financial aid applicants)
- Nonrefundable International Fee - $20 (outside US only)
We have concluded our financial aid application review process for Academic Year 2023-2024 Online Programs (Courses with start dates July 1, 2023-June 30, 2024). Our application for Academic Year 2024-2025 Online Programs is expected to open in January. We encourage those who may need assistance in the future to apply for aid as early as possible.
Please acquire all course materials by the course start date, unless noted as perishable. Items marked as “perishable” should not be acquired until the student needs them in the course. If you have questions about these materials or difficulty locating them, please contact [email protected].
Book Title: The Cryptoclub: Using Mathematics to Make and Break Secret Codes
Authors: Janet Beissinger and Vera Pless
This course requires a computer with high-speed Internet access and an up-to-date web browser such as Chrome or Firefox. You must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.
This course uses a virtual classroom for instructor-student communication. The classroom works on standard computers with the Zoom desktop client, and on tablets or handhelds that support the Zoom Mobile app. Recorded meetings can only be viewed on a computer with the Zoom desktop client installed. The Zoom desktop client and Zoom Mobile App are both free to download.
About Mathematics at CTY
Our online Mathematics courses—spanning elementary through college-level curricula—cover a wide range of topics, from algebra and geometry to chess, cryptology, and AP Calculus and are guided by expert instructors. You’ll join group sessions with classmates to ensure you stay on track with challenging course content. Whether you’re looking for pure math fun and enrichment, to move up the math ladder and advance your honors and AP (and beyond) academic standing, or to train for mathematics competitions, there’s a CTY course that’s right for you.
Join the exciting world of competitive math
Participate in the High School Math Club or enroll in 6 IP courses: Middle School Competitive Math I, Middle School Competitive Math II, Middle School Competitive Math III, Competitive Mathematics Prep, Competitive Mathematics I, Competitive Mathematics II.