Math Circles Fun – Learning Cryptography

March is fraud prevention month. The stats are fascinating: according to internet security experts, it takes a hacker only a fraction of a millisecond to crack a simple password like “abcdefg”. Add just one more character and the time increases to five hours. Nine-character passwords typically take five days to break, and ten characters, four months to crack. The timing was right on Wednesday, March 30, for Dalhousie’s Virtual Math Circles event that explored cryptography, the science of encryption and security behind applications like banking transaction cards, computer passwords, and e-commerce transactions. The presenter was Dr. Frank Fu, a postdoctoral researcher, who showed us encryption methods used to safeguard the digital world. Encryption and decryption were defined, and specific encoding methods were explored. Caesar encryption, a shift cipher, was one of the easiest encryption techniques to learn. Each letter of the message is “shifted” a fixed number of positions (key) down the alphabet. For example, if the key is “2”, the word “MAGIC” would be encrypted to “OCIKE”. Dr. Fu pointed out that when trying to break a code, a frequency analysis of letters is beneficial. A bar graph demonstrated that the letter “e” occurs most frequently, and much more so than the letter “q”. With this in mind, participants were challenged to decrypt “ALIIP”.  Substituting a probable double “e” for the double “I”, leads to an encryption key of “-4”. Moving four letters back from the original letters results in the word “WHEEL”.  Did you get it? The seminar continued to explore more complicated encryption protocols.

I commend Ellie ’24 and Lillian Blois ‘27, Zoë Steeves ‘25, Will Larder ‘26, Anthony Wheeler ‘27, Owen Xu ‘27 and Abby '28 and Isaac Woodworth '27 for their participation and contributions. I congratulate Lillian for winning the 7:00 Math Circles participant draw. The choice of an Amazon or Indigo gift card is hers. Congratulations, Lillian!  Math Circles are a great form of math enrichment for students of all grades.