The research areas of OLCRYPT are the mathematical and algorithmic foundations of cryptography, explicit number theory and computer algebra. The focus lies on theoretical and computational aspects of algebraic curves, abelian varieties and number fields, real-world applications and implementations of cryptographic algorithms.

Some sample research topics include ...

• Abelian varieties, isogeny graphs and endomorphism rings, complex multiplication
• Construction of families of curves with many rational points
• Numerical verification of conjectures from arithmetic geometry in examples
• Numerical and symbolic methods for Riemann surfaces and complex Jacobians with applications in number theory and theoretical physics
• Elliptic curves and other number theoretic objects in cryptographic applications
• Applications of computer algebra