Complex Multiplication: Class invariants and cryptographic applications

• Applicant: Professor Dr. Florian Heß
• Subject Area: Mathematics
• Term: from 2013 to 2017
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 239407529

With the emergence of computer algebra and the need for explicit calculations, the theory of complex multiplication has become subject to algorithmic investigations with a view towards applications in algorithmic algebraic number theory and cryptography. Among the applications are of particular interest primarily proving, explicit classified theory, and curve and pairing based cryptography. A central aspect of algorithmic CM theory is the interplay between numerical and symbolic computations describing discrete objects by analytic means. This project investigates the following three main topics: Class invariants for quadratic and quartic CM-fields, pairing based cryptography and aspects of algorithmic number theory.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1489: Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory
• International Connection: France, Luxembourg, Turkey, United Kingdom
• Participating Persons: Privatdozent Dr. Andreas Enge; Professor Dr. David Kohel; Professor Dr. Omer Kucuksakalli; Professor Dr. Franck Leprévost; Professor Dr. Michael E. Pohst; Dr. Marco Streng; Dr. Emmanuel Thome