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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