Modern Cryptography

About the Course

Modern Cryptography

Grades 7-10
CTY-Level
LIVE
Mathematics

In the age of digital surveillance, apps boasting end-to-end encryption such as WhatsApp and Telegram have flourished. What are these tools, and how do they work? How have developments in modern computing and mathematics affected the field of cryptography and impacted privacy and safety in modern society?

Explore modern cryptographical tools such as ElGamal encryption and the Diffie-Hellman key exchange or the RSA cryptosystem with a focus on the interplay between privacy and security, including how governments and law enforcement agencies respond to new technological developments. As you and your peers develop your own cryptosystems or product ideas that solve an issue in modern cryptography, you simultaneously consider the technological and social implications of your work by looking deeply into its potential long-term impacts on cryptography and how it may complicate the balance between privacy and security.

Fall and Spring Time Commitment: 4-5 hours per week (1-hour of class time, 3-4 hours of independent work).
Summer Time Commitment: 12-15 hours per week (3-hours of class time, 9-12 hours of independent work).

Course Overview

What we'll do

The primary goals of the course are to extend students’ knowledge and understanding of mathematics and computer science and apply it to solve problems in modern society related to privacy and security. The course consists of nine units. Each unit includes a synchronous group meeting held on Zoom. Each unit also contains asynchronous activities, including assigned readings, videos, written assignments, labs, and projects.

What we’ll learn

Mathematics can be used to encrypt and decrypt data securely
Mathematics and computer science have constant interplay, especially in the field of cryptography, and this interplay can be used to maximize the privacy and security of a cipher
In mathematics, processes that can be done, can often, but not always, be undone with absolute certainty
Cryptography can be applied to the fields of cybersecurity, government, technology, business, law enforcement, IT, archaeology, and more

By the end of this course, you will be able to:

Identify problems in modern society related to privacy and security, and offer mathematical and/or digital solutions
Evaluate the efficiency of a variety of cryptosystems, accurately referencing combinatorics and number theory as needed
Use modular arithmetic to encrypt and decrypt messages
Analyze strengths and predict weakness of ciphers based on what is present in the mathematics of each cipher
Describe connections between mathematical cryptography and digital cryptography and examine the interplay between mathematics and computer science
Investigate how privacy and security are affected by various mathematical strategies used in specific cryptosystems
Create research presentations evaluating the efficiency, strengths, weaknesses, privacy, and security of a mathematical and/or digital strategy in cryptography

How we'll measure learning

There are two main summative assessments in this course:

Mini-presentation on digital cryptography: Students will work in pairs or a group of three to investigate a topic in digital cryptography and provide an overview to the class.
Final Project on privacy and security: Students will identify a problem in modern privacy and security and use topics from the course to design a potential solution for this problem.

This course is

ungraded.

Classes

Register for an Online course by selecting an open class below. If no open classes are listed, then course enrollment is currently closed. Note: You will need to have an active CTY Account to complete registration through MyCTY.

Mondays, Wednesdays, and Fridays

Jun 16 - Jul 3

12:00 p.m. (ET)

$1,365

Enroll

Testing and Prerequisites

	Math	Verbal
Required Level	CTY-Level	Not required

Check your eligibility using existing test scores If you do not have existing test scores:

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.

Course Prerequisites

Modern Cryptography requires:

1 prerequisite

Algebra I

Cost and Financial Aid

Tuition
- Varies
Application fee
- Nonrefundable Application Fee - $15 (Waived for financial aid applicants)
- Nonrefundable International Fee - $20 (outside US only)

Financial Aid

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.

Learn More

Course Materials

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 Code Book
Author: Simon Singh
ISBN: 978-0385495325

(Optional) Book Title: An Introduction to Mathematical Cryptography
Author: Hoffstein, Pipher, and Silverman
ISBN: 978-0387779935

Materials:

Colored cardstock paper* (required cardstock-friendly printer, *colored paper can be used as a substitute)

Technical Requirements

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.

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.

New math enrichment courses available!

Explore our new math enrichment courses, including Excursions in Pre-algebra and Introduction to Logic and Proofs.

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.

Meet our Mathematics Instructors

I love that through CTY, I get the chance to work with gifted students from all over the world. I consider it an honor to be part of their journey!

Amanda Broton

Mathematics Instructor

I love helping students understand difficult topics and make connections between them. Understanding Calculus is what makes advanced engineering applications possible, so it is extremely relevant to today's world and to the inventions of tomorrow.

Donna Miller

Mathematics Instructor

I am so excited when students are able to persevere and decode a very challenging cipher in the course! I love that Cryptology teaches patience and dedication, and that mathematics is so much more than just the study of numbers and equations.

Jillian Green

Mathematics Instructor

Online Programs