Counting points on hyperelliptic curves over finite fields

International audienceWe describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They include several methods for obtaining the result modulo small primes and prime powers, in particular an algorithm à la Schoof for genus 2 using Cantor's division polynomials. These are combined with a birthday paradox algorithm to calculate the cardinality. Our methods are practical and we give actual results computed using our current implementation. The Jacobian groups we handle are larger than those previously reported in the literature

The Emergence of Partnership Networks in the Enterprise Application Development Industry: A Global Corporation Perspective

Currently, dramatic changes are happening in the IS development industry. The incumbent system developers (hubs) are embracing partnerships with less well established companies (spokes), acting in specific niches. This paper seeks to establish a better understanding of the motives for this strategy. Relying on existing work on strategic alliance formation, it is argued that partnering is particularly attractive, if these small companies possess certain capabilities that are difficult to obtain through other arrangements than partnering. Again drawing on the literature, three categories of capabilities are identified: the capability to innovate within their niche, the capability to provide a specific functionality that can be integrated with the incumbents’ systems, and the capability to address novel markets. These factors are analyzed through a case study. The case represents a market leader in the global IS development industry, which fosters a network of smaller partner firms. The study reveals that temporal dynamics between the identified factors are playing a dominant role in these networks. A cyclical partnership model is developed that attempts to explain the life cycle of a partnership within such a network