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Consortium for Mathematics and its Applications

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April 17, 2025
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Written on . Posted in Math Curriculum, Math Modeling.

What a Caesar Cipher Can Teach Students About Cryptography

When you hear the word cryptography, your mind might jump to secret agents, spy movies, or encrypted texts that only hackers can decode. What you probably don’t expect is to find your students playing the roles of 1st-century Roman soldiers passing secret messages across the classroom.

And yet, that’s exactly what happens with COMAP’s Introduction to Cryptography module. It’s an engaging, free resource that uses classic codes and modern mathematics to teach computational thinking in a way that sticks. It is also one of a series of related modules.

Why Start with Caesar?

The module kicks off with the Caesar cipher, a simple letter-shifting code used by Julius Caesar himself. It’s fast to learn, easy to implement, and just puzzling enough to spark curiosity. Students try encoding and decoding real quotes (some from Einstein, others from Yoda) and in the process, they get a firsthand look at how even basic encryption works.

But here’s where the real magic happens: as they decode and deliver messages, students also start asking deeper questions. What makes a code secure? How easy is it to break a cipher if the method is known? Could a modern spy crack this in five minutes?

Turns out… yes. And that realization leads straight into substitution ciphers, frequency analysis, and eventually, RSA encryption.

Computational Thinking without the Overhead

This module doesn’t require advanced math. A solid understanding of algebra is enough to get started. Students are introduced to modular arithmetic, algorithms, and mathematical concepts like prime numbers and inverses. It starts to feel less like a math class and more like solving a mystery!

Better yet, the module doesn’t just teach technical skills. It encourages problem solving and computational thinking by organizing data logically, exploring different solution paths, and working through ambiguity (that often happens with productive struggle in math). Students learn how to approach open-ended problems, a skill that’s as useful in everyday life as it is in STEM fields.

Why It Works

The activities are hands-on and collaborative. Roles like coders, messengers, and spies bring an interactive, game-like structure to the classroom, which means students are actively moving, decoding, and thinking rather than sitting passively.

It’s a fun way to teach complex concepts, and it works. The lessons build up from historical ciphers to the RSA algorithm, all while reinforcing the idea that modern security systems rely on the same core principles found in ancient codes.

Explore the full module: Introduction to Cryptography

Whether the module or pieces of it are used as a one-week unit or a single-day teaser, this module proves that cryptography isn’t just about codes; it’s about curiosity, critical thinking, and the surprisingly fun side of applied mathematics.

And if you like exploring aspects of computational thinking without the need for programming or advanced mathematics, check out the rest of the modules in the series.

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COMAP

The Consortium for Mathematics and Its Applications is an award-winning non-profit organization whose mission is to improve mathematics education for students of all ages. Since 1980, COMAP has worked with teachers, students, and business people to create learning environments where mathematics is used to investigate and model real issues in our world.