The American Mathematical Society's annual Congressional Briefing was given on December 9, 2015 by AMS President Elect Kenneth Ribet (University of California, Berkeley). In his briefing, "From right triangles to modern cryptography," Ribet recounted his experience studying the arithmetic of elliptic curves as a graduate student and then lecturing on elliptic curves in Berkeley's upper-division undergraduate course in cryptography.

Professor Ribet explained that a great deal of contemporary cryptography depends on the apparent difficulty of computing discrete logarithms in the group of non-zero integers modulo a sufficiently large prime number. To guard against "index calculus" algorithms for computing discrete logarithms, the prime number needs to be taken so large that the calculations needed for everyday cryptography tax the batteries and processing power of small devices like smartphones.

If one replaces the group of non-zero numbers mod a prime by the group of points of an elliptic curve over a finite field, one avoids the index calculus attacks and therefore may work with smaller numbers than would be needed otherwise.

Ribet went on to say that the study of elliptic curves is ongoing and that companies like Microsoft use them in all sorts of products to provide security. The National Institute of Standards and Technology (NIST) even has a list of recommended elliptic curves.

The AMS holds annual congressional briefings as a means to communicate information to policymakers. Speakers discuss the importance of mathematics research and present their work in layman's terms to Congressional staff as a way to inform Members of Congress of how mathematics impacts today's important issues.

**Previous AMS Congressional Briefings:**

- December 2014,
*"The Future of Mathematics: Education & Innovation"*presented by Robert Ghrist, Andrea Mitchell University Professor of Mathematics and Electrical/Systems Engineering at the University of Pennsylvania. - December 2013,
*"How Math Fuels the Knowledge Economy"*presented by Mark L. Green, professor emeritus at the University of California-Los Angeles. - December 2012,
*"Chaos and Avalanches in Science and Socio-Political Systems"*presented by James A. Yorke, professor of mathematics and physics at the University of Maryland. - December 2011,
*"Mathematics: Leading the Way for New Options in the Treatment of Coronary Artery Disease"*presented by Suncica Canic, professor of mathematics at the University of Houston. - October 2010,
*The Gulf Oil Spill: How Can We Protect our Beaches in the Future?*presented by Andrea Bertozzi, professor of mathematics at UCLA. - October 2009,
*The Movies, the Markets and Mathematics,*presented by Stuart Geman, professor of applied mathematics at Brown University. - September 2008,
*Can Mathematics Cure Leukemia?*presented by Doron Levy, associate professor of mathematics at the University of Maryland, College Park. - September 2007,
*Mathematics of Ice to Aid Global Warming Forecasts*, presented by Ken Golden, professor of mathematics at the University of Utah. - November 2006,
*The Necessity of Mathematics: From Google to Counterterrorism to Sudoku*, presented by Amy Langville, professor of mathematics at the College of Charleston. - November 2005,
*From Katrina Forward: How Mathematics Helps Predict Storm Surges*, presented by Clint Dawson, professor at the University of Texas and a member of the Center for Subsurface Modeling in the Institute for Computational Engineering and Sciences; and James Westerink, associate professor of civil engineering and geological sciences at the University of Notre Dame. - September 2004,
*Homeland Security: What Can Mathematics Do?*presented by Fred Roberts, professor of mathematics and director of the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University. - July 2003,
*Mathematics is Biology's Next Microscope, Only Better; Biology is Mathematics' Next Physics, Only Better*presented by Joel E. Cohen, Laboratory of Populations, Rockefeller and Columbia Universities. - February 2002,
*Mathematics, Patterns and Homeland Security*, presented by Ingrid Daubechies, Princeton University. - July 2001,
*Adding It Up: Helping Children Learn Mathematics*, a briefing on this National Research Council Report presented by Deborah Loewenberg Ball and Hyman Bass, University of Michigan and by Roger Howe, Yale University. - Other previous briefings include:

*What Does Water Know About Mathematics*, by Mary Fannett Wheeler, The University of Texas at Austin

*Calculating the Secrets of Life: Mathematics in Medicine*by DeWitt Sumners, Florida State University

*Eavesdropping on the Internet: Mathematics and Policy*by Carl Pomerance, University of Georgia

*Mathematical Transcriptions of the Real World: Fingerprints, Magnetic Resonance and Video*by Ronald Coifman, Yale University