Objective Our field is cryptology. Our overarching objective is to advance significantly the frontiers indesign and analysis of high-security cryptography for the future generation. Particularly, we wish to enhance the efficiency, functionality, and, last-but-not-least, fundamental understanding of cryptographic security against very powerful adversaries.Our approach here is to develop completely novel methods by deepening, strengthening and broadening the algebraic foundations of the field.Concretely, our lens builds onthe arithmetic codex. This is a general, abstract cryptographic primitive whose basic theory we recently developed and whose asymptotic part, which relies on algebraic geometry, enjoys crucial applications in surprising foundational results on constant communication-rate two-party cryptography. A codex is a linear (error correcting) code that, when endowing its ambient vector space just with coordinate-wise multiplication, can be viewed as simulating, up to some degree, richer arithmetical structures such as finite fields (or products thereof), or generally, finite-dimensional algebras over finite fields. Besides this degree, coordinate-localities for which simulation holds and for which it does not at all are also captured.Our method is based on novel perspectives on codices which significantly widen their scope and strengthen their utility. Particularly, we bring symmetries, computational- and complexity theoretic aspects, and connections with algebraic number theory, -geometry, and -combinatorics into play in novel ways. Our applications range from public-key cryptography to secure multi-party computation.Our proposal is subdivided into 3 interconnected modules:(1) Algebraic- and Number Theoretical Cryptanalysis(2) Construction of Algebraic Crypto Primitives(3) Advanced Theory of Arithmetic Codices Fields of science natural sciencescomputer and information sciencescomputer securitycryptographynatural sciencesmathematicspure mathematicsarithmeticsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-2016-ADG - ERC Advanced Grant Call for proposal ERC-2016-ADG See other projects for this call Funding Scheme ERC-ADG - Advanced Grant Coordinator STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN Net EU contribution € 2 447 439,00 Address Winthontlaan 2 3526 KV Utrecht Netherlands See on map Region West-Nederland Utrecht Utrecht Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 Beneficiaries (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN Netherlands Net EU contribution € 2 447 439,00 Address Winthontlaan 2 3526 KV Utrecht See on map Region West-Nederland Utrecht Utrecht Activity type Research Organisations Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
