Students decipher cryptography

Lincoln Laboratory recently unveiled LLCipher, a new outreach program for high school students. LLCipher is a one-week cryptography workshop that provides an introduction to modern cryptography — a math-based, theoretical approach to securing data.

Lessons in abstract algebra, number theory, and complexity theory provide students with the foundational knowledge needed to understand theoretical cryptography. Students build on that knowledge to construct provably secure encryption and digital signature schemes. On the last day, the students learn about some less mainstream developments in cryptography. Guest speakers cover various techniques that enable multiple entities to exchange data without disclosing to one another more data than necessary to perform a particular function. These include zero-knowledge proofs (proving a statement is true without revealing any information beyond the truth of the statement) and multiparty computation (computing a function over multiple parties’ inputs while keeping the inputs private).”

The course, held at Lincoln Laboratory’s Beaver Works facility near MIT campus, came about with the help of Bradley Orchard of the laboratory’s Advanced Sensor Systems and Test Beds Group and Sophia Yakoubov, Emily Shen, and David Wilson, all of the Secure Resilient Systems and Technology Group.

Orchard conceived the idea for LLCipher while teaching high-school students at the Russian School of Mathematics in Lexington, Massachusetts. He noticed a significant need for additional learning opportunities beyond what is offered in even the best high schools. Orchard noticed some very bright students were ready for material beyond calculus. “I thought it would be fun to offer a short introductory summer course for advanced high-school students,” he said. “I naturally thought of cryptography because it combines beautiful mathematics with powerful, useful, and fun techniques, and most importantly, aspects of cryptography are very accessible to advanced students.”

To design the course, Orchard asked for help from the laboratory’s management; John Wilkinson, leader of the Cyber Systems Assessments Group; and cryptography experts including Yakoubov, who, knowing how much she enjoyed teaching the CyberPatriot students, was eager to get involved.

“I cannot emphasize how difficult it is to design a short course that is effective, interesting, and fun for high-school students,” Orchard said. “Sophia did a superb job accomplishing this task, as evidenced by the enthusiasm and participation of the students. The students were engaged, asking questions, and demonstrating that they understood the material, and, most importantly, having fun.”

Chiamaka Agbasi-Porter of the Communications and Community Outreach Office handled the student applications and class logistics. Agbasi-Porter indicated that each of the 16 selected students were able to express their enjoyment of math through independent projects in their application to be a part of LLCipher. She felt the students for this pilot class were smart and enthusiastic. Yakoubov agreed: “The class was very interactive and the students were engaged in the topic; their questions and ideas made them a pleasure to teach.”

The first thing covered in class was encryption. The instructors started by explaining the one-time pad, which is a perfectly secure encryption scheme, meaning that an eavesdropping adversary cannot learn anything about the encrypted message no matter how much computing power he or she has. Perfectly secure encryption schemes have a significant drawback, however: The secret key shared by the message sender (typically called “Alice” in the industry) and message receiver (referred to as “Bob”) has to be at least as long as the message itself. Alice might want to send Bob very long messages, and might not know in advance how long these messages will be, so establishing a sufficiently long key might be problematic.