CORDIS
EU research results

CORDIS

English EN
Algebraic Methods for Stronger Crypto

Algebraic Methods for Stronger Crypto

Objective

Our field is cryptology. Our overarching objective is to advance significantly the frontiers in
design 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 on
the 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
Leaflet | Map data © OpenStreetMap contributors, Credit: EC-GISCO, © EuroGeographics for the administrative boundaries

Host institution

STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN

Address

Van Vollenhovenlaan 659
3527 Jp Utrecht

Netherlands

Activity type

Research Organisations

EU Contribution

€ 2 447 439

STICHTING CENTRUM VOOR WISKUNDE EN INFORMATICA

Address

Science Park 123
1098xg Amsterdam

Netherlands

Activity type

Research Organisations

Beneficiaries (2)

Sort alphabetically

Sort by EU Contribution

Expand all

STICHTING CENTRUM VOOR WISKUNDE EN INFORMATICA

Netherlands

STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN

Netherlands

EU Contribution

€ 2 447 439

Project information

Grant agreement ID: 740972

Status

Ongoing project

  • Start date

    1 October 2017

  • End date

    30 September 2022

Funded under:

H2020-EU.1.1.

  • Overall budget:

    € 2 447 439

  • EU contribution

    € 2 447 439

Hosted by:

STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN

Netherlands