Crack the Code: Mathematics, Ciphers & Encryption

What Will You Do?

• Encrypt and exchange messages using Caesar shifts and substitution ciphers

• Use letter-counting spreadsheets to investigate patterns in encrypted text

• Create grid ciphers and encode messages with Vigenère keywords

• Apply clock-style arithmetic, matrices, and prime numbers to cipher problems

• Work through guided RSA encryption and decryption exercises

• Develop and present an original cryptography capstone with supporting evidence

Learning Outcomes

By the end of the course, students will be able to:

• Apply mathematical rules to encrypt and decrypt a message

• Use patterns and letter frequencies to explain a cipher’s possible weaknesses

• Present and evaluate a cryptography project using evidence and clear reasoning

You’ll leave with your cryptography capstone and a clearer sense of which puzzles, mathematical methods, or coding ideas you want to explore next.

Why Cryptography Skills Matter

A codebreaking guess has to survive a test. Counting letters, comparing patterns, and checking a decoded message help students distinguish a promising idea from one that only seems right. When a method fails, the error gives them a reason to revise their approach.

Cryptography also makes abstract mathematics easier to picture. A remainder can determine a letter, and a matrix can scramble a message. Explaining those steps to classmates develops precision and patience. Students practice showing how they reached a conclusion, useful habits for mathematics, science, and any problem that needs a defensible answer.

Who Should Attend?

For students who have completed 5th, 6th, 7th, or 8th grade.

If you enjoy puzzles, hidden messages, or asking how something works, cryptography gives you plenty to investigate. You’ll work through mathematical examples, compare approaches with classmates, and develop a project you can explain. No prior coding or advanced mathematics experience is required; comfort with algebra is helpful. Students should bring a compatible laptop, charger, headphones, and a scientific calculator or device with a calculator app.

Institute for the Gifted eligibility requirements apply; see the program FAQ. A completed program application is required.

Based on students surveyed in Summer Discovery’s 2026 Cornell program.

Cornell’s Ithaca setting gives elementary and middle school students an adventurous first experience of campus life, surrounded by Finger Lakes gorges, waterfalls, and a landscape shaped by research, agriculture, and invention. The setting makes learning feel different from an ordinary school day and gives students plenty to notice and explore.

The program combines active academics with friendships, campus activities, clear routines, and support as students become more comfortable in a new environment. Students can try challenging ideas, share interests with peers, and enjoy the fun of living and learning on a university campus. For families, Cornell offers a structured middle-school experience that balances learning and discovery with community, support, and growing independence.

Cryptography appears whenever information needs protection: a message sent online, a payment, or access to an account. People who design security systems have to consider who can read a message, which information an observer can see, and how a system might be attacked. Historians ask related questions when studying intercepted messages and the choices made around them.

The course offers several ways to keep exploring those questions. You might investigate a historical cipher, try a codebreaking challenge, or make a tool that explains encryption to someone else. Each direction combines a mathematical method with a practical reason for using it.