**Alice Silverberg, UC Irvine**

**Friday, December 8, 2010**

**Abstract: **When you send your credit card number over the Internet, cryptography helps to ensure that no one can steal the number in transit. Julius Caesar and Mary Queen of Scots used cryptography to send secret messages, in the latter case with ill-fated results. More recently, cryptography is used in electronic voting, and it is also used to "sign" documents electronically. While cryptography has been used for thousands of years, public-key cryptography dates only from the 1970's. Some recent exciting breakthroughs in public-key cryptography include elliptic curve cryptography, pairing-based cryptography, and identity-based cryptography, all of which are based on the number theory of elliptic curves. This talk will give an elementary introduction to cryptography, including elliptic curve and pairing-based cryptography.

**Biography: **Alice Silverberg is a Professor of Mathematics and Computer Science at the University of California, Irvine. Her research interests include number theory and cryptography. She graduated summa cum laude in mathematics from Harvard University, and earned a Certificate of Advanced Study from Cambridge and a PhD and a Master's degree in mathematics from Princeton University. Gender equity issues are a long-standing concern of hers, as an outgrowth of her time spent studying at traditionally male institutions. She was awarded Humboldt, Bunting, Sloan, IBM, and NSF Fellowships, and has held a number of visiting or consulting positions in the US and abroad, including at IBM, Bell Labs, Xerox PARC, DoCoMo USA Labs, the Mathematical Sciences Research Institute in Berkeley, the University of Erlangen and the Max Planck Institute in Germany, the Institut des Hautes Études Scientifiques in France, and Macquarie University in Australia. Silverberg consulted for the TV show NUMB3RS, and occasionally writes mathematically-inspired Scottish country dances.

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