We are pleased to announce that Jill Pipher (Elisha Benjamin Andrews Professor of Mathematics at Brown University) will deliver the inaugural UConn Mathematics Distinguished Lecture on Friday, April 19th at 3:30pm in the Schenker Lecture Hall.

Mathematical ideas in public key cryptography

Jill Pipher
Elisha Benjamin Andrews Professor of Mathematics, Brown University
President, American Mathematical Society

The problem solved by public key encryption is this: how can we create secure communication over an insecure channel (like the internet) between two people who have never met or shared a secret? The model application, unknown at the time of its invention, is you and any of your online vendors.

The concept of public key encryption was introduced in the famous 1976 paper “New Directions in Cryptography” by Diffie and Hellman. At the time it was indeed a “solution in search of a problem”: the application of encryption and authentication on a mass scale had yet to emerge from the Arpanet. In that paper, Diffie and Hellman posed an extraordinarily challenging mathematical problem and laid the foundation for a new field of mathematics/computer science. Then, in 1978, Rivest, Shamir and Adelman produced the first published example of a public key cryptosystem; their RSA encryption is still widely used for secure communication.

This lecture will provide some historical background on the subject of private and public key, encryption and explain some of the ideas involved in several different encryption systems. Particular attention will be focused on lattiice-based encryption schemes such as NTRU, an efficient public key system due to Hoffstein, Pipher, and Silverman, first disseminated in1996, which continues to remain secure against the potential speed-ups of quantum computers. In the last couple of years, national agencies and large financial institutions have recognized the urgent need for post-quantum cryptography; NIST has initiated a process to solicit, evaluate, and standardize one or more quantum-resistant public-key cryptographic algorithms. We will indicate some of the applications of lattice-based cryptosystems like NTRU to post-quantum computing and to cloud computing on private data.

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On October 25th, 2018 the UConn graduate student chapter of the AMS held their Second Annual Integration Bee, where undergraduates of varying levels of mathematical background came together to test their knowledge of integrals. Students took turns in groups of six, going to the blackboard to compute various integrals on the spot. In each round a student had four minutes to compute an integral, and if time ran out or the answer was incorrect a student received a strike. After two strikes a student was out of the competition.

After an hour and half there were two finalists and five other students competing for third place. The rivalry was pretty intense among students for third place. They all stayed in the competition for round round after round until they were asked to integrate cos(ln(1/x)). Only Nick Juricic evaluated it correctly and he got third place.

The two finalists were Samuel Degnan-Morgenstern and Zhongwei Wang. The final battle between them was very dramatic and exhausting for both. After about another hour Samuel was the winner for successfully integrating 1/(e^2-x^2). Contestants who scored in the top three won prizes that were generously donated from our sponsors: Cengage, Lizzie’s Curbside Catering, and Moe’s Southwest Grill.

Although there were only three winners who officially won prizes, all students attending the Integration Bee received a nice meal compliments of the AMS and the joy of solving math problems.

Pictured from left to right: Samuel Degnan-Morgenstern (1st place), Zhongwei Wang (2nd place), and Nick Juricic (3rd place).

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On April 19, 2018, UConn’s graduate student chapter of the American Mathematical Society (AMS) organized the math department’s first annual integration bee, in which undergraduates came together to test their skill at (indefinite) integration.

After welcoming remarks by department head Ambar Sengupta and the AMS Graduate Student Chapter officers, the students got to work. In the first round each student was given 5 minutes to compute 3 integrals. In later rounds students came up to the blackboard in groups of four to compute an integral in four minutes. A wrong answer or no answer was a strike against a student and, unlike in baseball, after 2 strikes the student was out.

After three hours the four remaining contenders were Nick Juricic, Grace Lauber, Zhongwei Wang, and Zerun Zhao. Grace and Zerun competed for third place, with Grace clutching that position with only seconds to spare. In the last round Nick and Zhongwei competed to compute the integral of cot(x)sec^2(x), which Nick figured out to take first place.

The winners received gift certificates from several area businesses: Bonchon Chicken, Gansett Wraps, Kathmandu Kitchen, Lizzie’s Curbside, Moe’s Southwest Grill, Starbucks, and Subway. All participants received a free meal compliments of the AMS and the brain nourishment that comes from solving math problems.

The AMS graduate student chapter thanks all the participants and volunteers for their help making this event a success and it looks forward to organizing the Integration Bee again next year.

Pictured above, from left to right, Nick Juricic (1st place), Zhongwei Wang (2nd place), Grace Lauber (3rd place), and Zerun Zhao (4th place).