Description: The security of encrypted computer protocols such as credit card transactions depends on unproven mathematical assumptions concerning the limits of computation. The central assumption is the conjecture known as ‘P vs NP’, which is one of the “million dollar questions” listed by the Clay Mathematics Institute. I will explain the conjecture, and how our world could be very different if it turns out to be false. This lecture is co-sponsored by the Fields Institute for Research in Mathematical Sciences (www.fields.utoronto.ca).