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AMS Holds Congressional Briefing

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.

Prof. Kenneth Ribet, University of California, Berkeley

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