The discovery of a new paradigm in cryptography -- public-key cryptography [DiHe76] -- represented by the popular RSA cryptosystem [AdRiSh78], caused a renewed interest for number theory and more importantly for computations. Among the problems that naturally arose, we find integer factorisation or primality proving. To tackle such problems, one needs to find good, efficient and fast algorithms. This caused the growth of the

There is a strong connection between the high-brow mathematics used
(such as elliptic curves, numbers fields, etc.) and the use of modern
computing means (parallelism, networks). These two main streams are
represented at **LIX**.