Discrete Geometry: Cryptography in the Braid Group

Event Date: 

Wednesday, April 30, 2014 - 2:00pm to 3:00pm

Event Location: 

  • 4607B South Hall

Event Contact: 

Michael Dougherty

Email: dougherty@math.ucsb.edu

Abstract: Since the introduction of algorithms such as RSA and the Diffie-Hellman key exchange in the 1970s, modern cryptography has been dominated by the exploration of computationally difficult problems. The most popular of these subjects - prime factorization, discrete logarithms, and elliptic curves - originate from number theory and thus reside in abelian groups. In the hopes of developing more robust options, several non-abelian cryptosystems have been proposed, with focus on the braid group.

In this talk, we will discuss some existing braid-based algorithms, their weaknesses, and directions for future research. We will not assume any background in either cryptography or braids.