A cipher—or secret code—uses mathematics to disguise high-level communication between or within organizations. The ciphers are unreadable without the key. Government agencies, diplomatic forces and information-heavy businesses employ ciphers to help protect confidential documentation.
In her sophomore year at Elizabethtown College applied mathematics major Kayla Novak was encouraged by professors to conduct research. Professor of Mathematics Tim McDevitt suggested the College’s Summer Scholarship, Creative Arts and Research Projects program, which supports independent student research under the sponsorship of a faculty mentor.
Novak understood the leg-up this research could give her as she applied to graduate schools.
She asked Nicolette Siermine, another sophomore applied math major, to share in the research. Neither had worked with ciphers before, Novak said. Nor had they used Mathematica or the Java computer languages.
You gain more knowledge with interdisciplinary research.”
Ciphers, at all levels of complexity, have been around for eons, said McDevitt, as have people skilled at cracking them.
The Hill Cipher, Novak said, is one of the more advanced elementary ciphers. It uses letters assigned numerical designations. These numbers are multiplied in a matrix—an array of numbers, symbols or expressions, arranged in rows and columns.
The Hill Cipher had been cryptanalyzed for smaller matrices, but Novak and Siermine wanted to break it faster, more easily—in a few hours rather than days.
The students had the assistance of computer science professor Tom Leap who helped set up computer programs to process large amount of information. “We used multiple computers to speed up the computation,” Leap said. “Just as two heads are better than one, two computers are 1.7 times better.”
The students also attempted to increase the difficulty of the cipher by using larger and larger matrices. The cipher had been solved for a 4-by-4 matrix, but, with they were able to take the cipher to an 8-by-8.
“The Hill Cipher is not one you would generally use, because it is breakable,” said Leap. It’s more for learning purposes.
However, “it’s surprisingly strong for how simple it is,” noted McDevitt, adding that an efficient cryptanalysis of the Hill cipher is difficult to teach at the undergraduate level but “it was good experience for the students. They have research experience and a publication under their belts.”
Their research was published in Cryptologia, a journal read by computer scientists and mathematicians. Now, as Novak applies to Northeastern and Georgetown, among others, she knows she’ll stand out over other applicants. Also, she said, being already published makes work on her honors thesis a bit less challenging. “I already know what is expected.”
“I definitely learned to work well with a team. We really put our minds together. … You gain more knowledge with interdisciplinary research.”
Siermine also sees the research as a “resume booster” as she looks for work in operations research. “It shows we can dedicate a chunk of our time to a particular study. It shows discipline and dedication.”