Mystery Hunters: Cracking Secret Enigmas

"A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.” — Alan Turing

This time, the LUMS Math Circles delved into the intriguing world of Cryptography with an engaging session. The circle was aptly titled "Mystery Hunters: Cracking Secret Enigmas" and was expertly conducted by the dynamic duo of Dr. Waqas Ali Azhar (Adjunct Faculty, Mathematics) and Dr. Imran Anwar (Associate Professor, Mathematics) on October 06, 2023.

The adventure began with a simple yet thought-provoking question posed by Dr. Waqas, "How many languages do you speak?". The room echoed with responses ranging from "Two" to "Three." Dr. Waqas continued, "What if I tell you that you can create an infinite number of languages from a single one, using the power of Mathematics?" The kids were immediately captivated, their curiosity piqued. Dr. Imran chimed in, "What if I told you that these languages could also be secret ones, known only to you and your partner?" He playfully demonstrated this concept by speaking in "Fey ki Boli," evoking a mix of laughter and bewilderment. Several volunteers, proficient in languages like Arabic, French, and Pashto, joined the discussion to illustrate how a language becomes a secret code when unfamiliar to others.

The instructors probed further, asking, "Why might you need secret languages?" A girl responded, "Wars?" Dr. Imran nodded approvingly, "Yes, excellent." Dr. Waqas followed up, "Anywhere else?" A boy chimed in, "During exams!" Laughter once again filled the room.

Example of an Anagram

The instructors transitioned into the first activity, saying, "Let's begin by teaching you how to create secret languages." This initial exercise involved Anagrams, where letters of a word were rearranged to form another word, and the challenge was to decipher the original words. The kids quickly conquered this task. Dr. Imran explained, "Anagrams are a way to construct a secret message, where you need to put in effort to unlock the hidden meaning." Dr. Waqas added, "But we face a small problem—they're quite easy to crack." The instructors then introduced the kids to the "Caesar's Cipher," providing a brief historical context about its origins.

Dr. Waqas and Dr. Imran adeptly explained Caesar's Cipher, using an analogy of numbers in different bases, drawing parallels with a clock. This approach brilliantly introduced modular arithmetic to the young minds. In simple terms, modular arithmetic is like counting on a clock. Imagine if the clock only had numbers from 1 to 12. When you reach 12, it starts again at 1. So, if you're at 10 and want to add 3, you don't get 13; you wrap back to 1, ending up at 1. It's a way of doing math with this "wrapping around" idea, and it's used in things like telling time, computer coding, and even secret codes. Soon, the kids were encoding and decoding a wide range of texts using Caesar's Cipher while gaining a deeper understanding of this cipher and cryptography.

Julius Caesar's secret code: The ancient encryption that shielded Rome's intrigues!

Once the participants gained an understanding of the Caeser's Cipher, Dr. Waqas inquired from the class, "Is it easy to crack/decipher the Caeser's encrypted text?" After a brief silence, someone enthusiastically responded, "Yes," emphasizing how it took only 25 attempts to uncover all the possibilities. Dr. Imran acknowledged the response and further clarified the simplicity of cracking this code.

At that point, the instructors then moved on to the next, more robust cipher—the Vigenère Cipher. They provided insight into this cipher's intricacies, using modular arithmetic to explain encoding and decoding while highlighting its difficulty to crack.

The grand finale of the day was a Scavenger Hunt. The room was divided into five teams, each handed a clue encoded with Caesar's Cipher. Deciphering it would lead to the next clue, ultimately unveiling the key to a shiny locked box prominently displayed for all to see. In a matter of minutes, shouts of excitement filled the air as one team successfully cracked all the codes and claimed Dr. Waqas's magic hat as the final code. From the hat, they retrieved the key and unlocked the box brimming with chocolates. To ensure fairness, Dr. Imran and Dr. Waqas revealed several other hidden key locations.

Overall, it was a thrilling event characterized by exceptional pedagogy and enjoyable games. It was an experience that the participants would cherish for a long time. The session concluded with the distribution of certificates, an honor bestowed by SBASSE's esteemed faculty member, Dr. Haniya Azam.