Publicly Verifiable Secret Sharing Using Non-Abelian Groups

Computational and Combinatorial Group Theory and Cryptography AMS Special Sessions: Computational Algebra, Groups, and Applications April 30–May 1, 2011 University of Nevada, Las Vegas, NV Mathematical Aspects of Cryptography and Cyber Security September 10–11, 2011 Cornell University, Ithaca, NY

Preface: This volume consists of contributions by participants and speakers at special sessions at two AMS Conferences. These conferences concerned Computational and Combinatorial Group Theory as well as various aspects of Group-Based Cryptography. One of these sessions was at Cornell University in September of 2011 and the other was the University of Nevada, Las Vegas in May of 2011. Over the past twenty years Combinatorial and Infinite Group Theory has been energized by three developments: the emergence of Geometric and Asymptotic Group Theory, the development of Algebraic Geometry over Groups leading to the solution of the Tarski problems, and the development of Group-Based Cryptography. These three areas in turn have had an impact on computational algebra and complexity theory. The papers in this volume, both survey and research, exhibit the tremendous vitality that is at the heart of Group Theory in the beginning of the twenty-first century as well as the diversity of interests in the field. We are grateful to the American Mathematical Society for their help in publication of this volume. In particular, we