Séminaire de Théorie Algorithmique des Nombres

We discuss the computational problem of finding pairs of consecutive smooth integers, also known as smooth twins. Such twins have had some relevance in isogeny-based cryptography and reducing the smoothness bound of these twins aids the performance of these cryptosystems. However searching for such twins with a small smoothness bound is the most challenging aspect of this problem especially since the set of smooth twins with a fixed smoothness bound is finite. This talk presents new large smooth twins which have a smaller smoothness bound compared to twins found with prior approaches.