- Grades 7-11
- Advanced CTY-Level
Cryptology is the study of the codes and ciphers used to create secret writing. This math course explores many early techniques in cryptology, such as cipher wheels, the Caesar shift, polyalphabetic substitution, and the Vigenère cipher, as well as modern techniques like RSA public key cryptography. You and your classmates will learn how data transmitted by computers can be secured with digital encryption, and how the vulnerabilities of each encryption system enable hackers to attack and decrypt messages using techniques such as frequency analysis and cribbing. You’ll apply concepts while encrypting and decrypting your own secret messages. Though the course’s central focus is on the mathematics of cryptology, you’ll also learn the historical context of cryptography and cryptographic devices like the Enigma Machine—one of the most important cryptographic devices in history—so you develop a deep understanding of this branch of mathematics and its applications in the world.
Typical Class Size: 16-18
- Apply modular arithmetic, group theory and cycle structure to coding theory and cryptography
- Create schemes to encipher, decipher, and crypto-analyze in order to use cryptography to defend systems
- Test coding and decoding methods using frequency analysis and different ciphers
- Analyze the rudiments of elementary number theory to apply to Vigenére, substitution, and Enigma cracks, among others
- Formulate monoalphabetic and combinatorial exercises to solve ciphers
- Model affine ciphers and division algorithms by conducting labs to show their effectiveness
- Construct discrete log problems to formulate and solve pseudorandom numbers and modern cryptography schemes
Summer Dates & Locations
Testing and Prerequisites
|Required Level||Advanced 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
Cost and Financial Aid
- Nonrefundable Application Fee - $50 (Waived for financial aid applicants)
- Nonrefundable International Fee - $250 (outside US only)
Financial Aid is available
We are committed to serving all talented youth regardless of financial circumstances. Financial assistance is available based on need.
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].
These titles have been featured in past sessions of the course, and may be included this summer. CTY provides students with all texts; no purchase is required.
- The Code Book, Simon Singh
About Mathematics at CTY
Explore the study of shapes
Many of our courses allow students to describe the world around them in basic and profound ways. Our younger students learn about shape, scale, and proportion in Geometry and Spatial Sense. Middle School students explore beautiful real-world applications of lines; analyze data based on curves that fit a uniform, symmetric and bell-shaped, or skewed pattern in Data and Chance. And advanced students explore the underlying mathematics and fundamental characteristics of shapes, distance, and continuous deformations in our proof-based Topology course.
Dive deep into logic and reasoning
Our courses in formal logic give you the tools to question the world around you. Inductive and Deductive Reasoning introduces younger students to different types of reasoning, as well as the strengths and weaknesses inherent in various forms of critical analysis. Older students explore how logical reasoning can explain (or fail to explain) counter-intuitive results in Paradoxes and Infinities, or take a more rigorous approach to formal logic in Mathematical Logic.