Organizers: Lubjana Beshaj, United States Military Academy, West Point, USA Jaime Gutierrez, University of Cantabria, Santander, Spain
Overview: There has been a continued interest on computational algebra during the last few decades. Such interest is especially growing when it comes to connections and applications of computational algebra in cryptography. The goal of this session is to bring together people from computational algebra, computational number theory, computational algebraic geometry, and cryptography. Topics of the session include, but are not limited to: Computational number theory. Primality and integer factorization. Schemes based on group theory and algebraic coding theory. Multivariate polynomial cryptosystems. Gröbner Bases. Resultants. Pseudorandom number generators. Lattice Problems Algebraic Curves Divisors and Picard groups Abelian varieties Endomorphisms and isogenies Torsion points and Tate modules l-adic representations and characteristic polynomials Hyperelliptic and superelliptic Jacobians Division polynomials for higher genus Modular polynomials for higher genus Diffie-Hellman Key Exchange on Abelian varieties Index calculus Isogenies of Jacobians via Correspondences Modular correspondences Correspondences via modular groups Elliptic Curve Cryptography Point Counting Supersingular Isogeny Based Cryptography Abelian surfaces Computing isogenies of genus 2 Jacobians Picard groups of curves of genus 3 Isogenies via $S_4$ covers Others
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