This talk will give an overview of the history of various hard problems in number theory which are used as the basis for cryptosystems. I will survey the evolution of attacks and discuss the upcoming NIST competition to standardize new cryptographic schemes for a post-quantum world. I will present some current proposals for post-quantum systems based on supersingular isogeny graphs of elliptic curves and lattice-based cryptosystems in cyclotomic number fields and give the ideas behind some recent attacks.
Kristin Lauter is a Principal Researcher and Research Manager for the Cryptography group at Microsoft Research. She directs the group’s research activities in theoretical and applied cryptography and in the related math fields of number theory and algebraic geometry. Her personal research interests include algorithmic number theory, elliptic curve, pairing-based, and lattice-based cryptography, homomorphic encryption, and cloud security and privacy, including privacy for healthcare.
Lauter is currently serving as President of the Association for Women in Mathematics, and on the Council of the American Mathematical Society. She was selected to be a Fellow of the American Mathematical Society in 2014. She is on the Editorial Board for the SIAM Journal on Applied Algebra and Geometry (SIAGA), Journal of Mathematical Cryptology, and International Journal of Information and Coding Theory. She was a co-founder of the Women In Numbers Network, a research collaboration community for women in number theory, and she serves on the Scientific Advisory Board for BIRS, the Banff International Research Station. Lauter is also an Affiliate Professor in the Department of Mathematics at the University of Washington. She received her BA, MS, and PhD, all in mathematics, from the University of Chicago, in 1990, 1991, and 1996, respectively. She was T.H. Hildebrandt Assistant Professor of Mathematics at the University of Michigan (1996-1999), and a Visiting Scholar at Max Planck Institut fur Mathematik in Bonn, Germany (1997), and at Institut de Mathematiques Luminy in France (1999). In 2008, Lauter, together with her coauthors, was awarded the Selfridge Prize in Computational Number Theory.
The Dr. Carl “C.J.” Maxson Endowed Lecture Series honors Professor Emeritus Carl Maxson, a member of the Texas A&M Mathematics Faculty from 1969 until his retirement in 2002, and was established in October 2005 by Dr. Ponnamal Natarajan ’74, Maxson’s first doctoral student and the first woman ever to receive a Ph.D. in Mathematics from Texas A&M (an all-male university until 1963). This annual event features experts in areas of current interest in algebra, number theory, and theoretical computer science.