Algorithmic Methods for Generating Primes for Cryptographic Systems

Abstract: This talk discusses algorithmic methods for generating prime parameters used in cryptographic systems based on finite abelian groups. The main objective is to generate primes that allow the construction of groups containing large prime-order subgroups while keeping the subgroup index small and ensuring computational efficiency. We consider this problem for multiplicative groups of finite fields, elliptic curves over finite fields, and pairing-friendly elliptic curves. Particular attention is given to generating pairs of primes satisfying prescribed divisibility, congruence, and algebraic conditions. We also discuss the complexity of the corresponding probabilistic algorithms, including expected polynomial-time results in several of these settings.

number theory

Audience: researchers in the topic

The Graduate Center Arithmetic Geometry Seminar

Series comments: The Graduate Center Arithmetic Geometry Seminar covers a wide range of topics in Arithmetic Geometry and Number Theory. The purpose of this seminar is to provide a venue for researchers in the NYC area to connect with new research and with other number theorists and arithmetic geometers. The seminar will be conducted in a hybrid format in order to increase access.