Efficiency and security of pre and post quantum cryptographic methods: theory and applications

Abstract

Cryptography is at the basis of virtually every existing security solution for information systems. Its study has blossomed into a full-fledged area in the intersection of Mathematics, Statistics, Computing and Engineering, bringing together Algebra, Geometry, Number Theory, Complexity Theory, and quantum-specialized versions of these fields. Research in efficient and secure cryptographic algorithms and protocols is built upon layers of theoretical science mixed with technological issues. Even symmetric cryptography, usually less reliant on algorithm complexity, has benefited from interactions with finite fields and algebra. Accordingly, this proposal aims precisely at strengthening ties among researchers of these cryptography-affine areas, in order to exploit research challenges in Pre- and Post-quantum Cryptography (especially Lattice and Code-based), areas rich in interactions of Finite Fields, Number Theory and Computer Science. Our proposal leverages on the ongoing FAPESP Thematic Project "Security and Reliability of Information: Theory and Practice", which intermingles Math, CS and Engineering as a basis for Information Security and Cryptography. For the UNICAMP group, Carleton's researchers will be a great boost for its world-class expertise in areas as Finite Fields, Coding, Combinatorics and Finite Geometry; for the Carleton group, it will be an excellent opportunity to expand its research horizons to include Pre- and Post-quantum Crvptoqraphv, which have been the focus of part of the UNICAMP group for over 20 years. (AU)