Despite intense research over many decades and sometimes even centuries, there are numerous number theoretic problems for which efficient solutions continue to elude us. Moreover, such solutions are generally not even known to exist. For example, it is unkown whether it is possible to find solutions to Pell equations and other norm equations quickly. Furthermore, to date, no efficient algorithm for factoring a large randomly chosen number into its prime factors is known, and the true complexity of the integer factorization problem is not even clear. Nevertheless, the popular RSA cryptosystem is based on the assumed difficulty of this problem.

In general, the security of most public-key cryptographic systems relies on the believed difficulty of a certain number theoretic problem. In exploring such problems, researchers face mathematical as well as computational and algorithmic difficulties. This workshop is intended to address the manifold computational challenges arising in number theoretic algorithms and cryptographic applications. Questions to be explored may include, but are by no means limited to:

• discrete logarithm problems in various settings, such as finite fields
  of various forms, algebraic curves and tori, and others
• integer factorization
• primality proving
• lattice problems
• algebraic number theory computations, including methods for computing
  class groups and class numbers, regulators, and fundamental units
• efficient arithmetic in various algebraic structures, such as the
  integers, finite fields, polynomial rings, algebraic curves, algebraic
  number fields, and others
• sieving techniques
• linear algebra techniques