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Algorithmic Number Theory in Computer Science

Objective

"During the past twenty years, we have witnessed profound technological changes, summarised under the terms of digital revolution or entering the information age. It is evident that these technological changes will have a deep societal impact, and questions of privacy and security are primordial to ensure the survival of a free and open society.

Cryptology is a main building block of any security solution, and at the heart of projects such as electronic identity and health cards, access control, digital content distribution or electronic voting, to mention only a few important applications. During the past decades, public-key cryptology has established itself as a research topic in computer science; tools of theoretical computer science are employed to “prove” the security of cryptographic primitives such as encryption or digital signatures and of more complex protocols. It is often forgotten, however, that all practically relevant public-key cryptosystems are rooted in pure mathematics, in particular, number theory and arithmetic geometry. In fact, the socalled security “proofs” are all conditional to the algorithmic untractability of certain number theoretic problems, such as factorisation of large integers or discrete logarithms in algebraic curves. Unfortunately, there is a large cultural gap between computer scientists using a black-box security reduction to a supposedly hard problem in algorithmic number theory and number theorists, who are often interested in solving small and easy instances of the same problem. The theoretical grounds on which current algorithmic number theory operates are actually rather shaky, and cryptologists are generally unaware of this fact.
The central goal of ANTICS is to rebuild algorithmic number theory on the firm grounds of theoretical computer science."

Field of science

  • /natural sciences/mathematics/pure mathematics/arithmetic

Call for proposal

ERC-2011-StG_20101014
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

Host institution

INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE
Address
Domaine De Voluceau Rocquencourt
78153 Le Chesnay Cedex
France
Activity type
Research Organisations
EU contribution
€ 1 453 507
Principal investigator
Andreas Enge (Dr.)
Administrative Contact
Dominique Salles (Ms.)

Beneficiaries (1)

INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE
France
EU contribution
€ 1 453 507
Address
Domaine De Voluceau Rocquencourt
78153 Le Chesnay Cedex
Activity type
Research Organisations
Principal investigator
Andreas Enge (Dr.)
Administrative Contact
Dominique Salles (Ms.)