Project acronym ACROSS
Project 3D Reconstruction and Modeling across Different Levels of Abstraction
Researcher (PI) Leif Kobbelt
Host Institution (HI) RHEINISCH-WESTFAELISCHE TECHNISCHE HOCHSCHULE AACHEN
Call Details Advanced Grant (AdG), PE6, ERC-2013-ADG
Summary "Digital 3D models are gaining more and more importance in diverse application fields ranging from computer graphics, multimedia and simulation sciences to engineering, architecture, and medicine. Powerful technologies to digitize the 3D shape of real objects and scenes are becoming available even to consumers. However, the raw geometric data emerging from, e.g., 3D scanning or multi-view stereo often lacks a consistent structure and meta-information which are necessary for the effective deployment of such models in sophisticated down-stream applications like animation, simulation, or CAD/CAM that go beyond mere visualization. Our goal is to develop new fundamental algorithms which transform raw geometric input data into augmented 3D models that are equipped with structural meta information such as feature aligned meshes, patch segmentations, local and global geometric constraints, statistical shape variation data, or even procedural descriptions. Our methodological approach is inspired by the human perceptual system that integrates bottom-up (data-driven) and top-down (model-driven) mechanisms in its hierarchical processing. Similarly we combine algorithms operating on different levels of abstraction into reconstruction and modeling networks. Instead of developing an individual solution for each specific application scenario, we create an eco-system of algorithms for automatic processing and interactive design of highly complex 3D models. A key concept is the information flow across all levels of abstraction in a bottom-up as well as top-down fashion. We not only aim at optimizing geometric representations but in fact at bridging the gap between reconstruction and recognition of geometric objects. The results from this project will make it possible to bring 3D models of real world objects into many highly relevant applications in science, industry, and entertainment, greatly reducing the excessive manual effort that is still necessary today."
Summary
"Digital 3D models are gaining more and more importance in diverse application fields ranging from computer graphics, multimedia and simulation sciences to engineering, architecture, and medicine. Powerful technologies to digitize the 3D shape of real objects and scenes are becoming available even to consumers. However, the raw geometric data emerging from, e.g., 3D scanning or multi-view stereo often lacks a consistent structure and meta-information which are necessary for the effective deployment of such models in sophisticated down-stream applications like animation, simulation, or CAD/CAM that go beyond mere visualization. Our goal is to develop new fundamental algorithms which transform raw geometric input data into augmented 3D models that are equipped with structural meta information such as feature aligned meshes, patch segmentations, local and global geometric constraints, statistical shape variation data, or even procedural descriptions. Our methodological approach is inspired by the human perceptual system that integrates bottom-up (data-driven) and top-down (model-driven) mechanisms in its hierarchical processing. Similarly we combine algorithms operating on different levels of abstraction into reconstruction and modeling networks. Instead of developing an individual solution for each specific application scenario, we create an eco-system of algorithms for automatic processing and interactive design of highly complex 3D models. A key concept is the information flow across all levels of abstraction in a bottom-up as well as top-down fashion. We not only aim at optimizing geometric representations but in fact at bridging the gap between reconstruction and recognition of geometric objects. The results from this project will make it possible to bring 3D models of real world objects into many highly relevant applications in science, industry, and entertainment, greatly reducing the excessive manual effort that is still necessary today."
Max ERC Funding
2 482 000 €
Duration
Start date: 2014-03-01, End date: 2019-02-28
Project acronym ADAPT
Project Life in a cold climate: the adaptation of cereals to new environments and the establishment of agriculture in Europe
Researcher (PI) Terence Austen Brown
Host Institution (HI) THE UNIVERSITY OF MANCHESTER
Call Details Advanced Grant (AdG), SH6, ERC-2013-ADG
Summary "This project explores the concept of agricultural spread as analogous to enforced climate change and asks how cereals adapted to new environments when agriculture was introduced into Europe. Archaeologists have long recognized that the ecological pressures placed on crops would have had an impact on the spread and subsequent development of agriculture, but previously there has been no means of directly assessing the scale and nature of this impact. Recent work that I have directed has shown how such a study could be carried out, and the purpose of this project is to exploit these breakthroughs with the goal of assessing the influence of environmental adaptation on the spread of agriculture, its adoption as the primary subsistence strategy, and the subsequent establishment of farming in different parts of Europe. This will correct the current imbalance between our understanding of the human and environmental dimensions to the domestication of Europe. I will use methods from population genomics to identify loci within the barley and wheat genomes that have undergone selection since the beginning of cereal cultivation in Europe. I will then use ecological modelling to identify those loci whose patterns of selection are associated with ecogeographical variables and hence represent adaptations to local environmental conditions. I will assign dates to the periods when adaptations occurred by sequencing ancient DNA from archaeobotanical assemblages and by computer methods that enable the temporal order of adaptations to be deduced. I will then synthesise the information on environmental adaptations with dating evidence for the spread of agriculture in Europe, which reveals pauses that might be linked to environmental adaptation, with demographic data that indicate regions where Neolithic populations declined, possibly due to inadequate crop productivity, and with an archaeobotanical database showing changes in the prevalence of individual cereals in different regions."
Summary
"This project explores the concept of agricultural spread as analogous to enforced climate change and asks how cereals adapted to new environments when agriculture was introduced into Europe. Archaeologists have long recognized that the ecological pressures placed on crops would have had an impact on the spread and subsequent development of agriculture, but previously there has been no means of directly assessing the scale and nature of this impact. Recent work that I have directed has shown how such a study could be carried out, and the purpose of this project is to exploit these breakthroughs with the goal of assessing the influence of environmental adaptation on the spread of agriculture, its adoption as the primary subsistence strategy, and the subsequent establishment of farming in different parts of Europe. This will correct the current imbalance between our understanding of the human and environmental dimensions to the domestication of Europe. I will use methods from population genomics to identify loci within the barley and wheat genomes that have undergone selection since the beginning of cereal cultivation in Europe. I will then use ecological modelling to identify those loci whose patterns of selection are associated with ecogeographical variables and hence represent adaptations to local environmental conditions. I will assign dates to the periods when adaptations occurred by sequencing ancient DNA from archaeobotanical assemblages and by computer methods that enable the temporal order of adaptations to be deduced. I will then synthesise the information on environmental adaptations with dating evidence for the spread of agriculture in Europe, which reveals pauses that might be linked to environmental adaptation, with demographic data that indicate regions where Neolithic populations declined, possibly due to inadequate crop productivity, and with an archaeobotanical database showing changes in the prevalence of individual cereals in different regions."
Max ERC Funding
2 492 964 €
Duration
Start date: 2014-02-01, End date: 2019-01-31
Project acronym ALEXANDRIA
Project "Foundations for Temporal Retrieval, Exploration and Analytics in Web Archives"
Researcher (PI) Wolfgang Nejdl
Host Institution (HI) GOTTFRIED WILHELM LEIBNIZ UNIVERSITAET HANNOVER
Call Details Advanced Grant (AdG), PE6, ERC-2013-ADG
Summary "Significant parts of our cultural heritage are produced on the Web, yet only insufficient opportunities exist for accessing and exploring the past of the Web. The ALEXANDRIA project aims to develop models, tools and techniques necessary to archive and index relevant parts of the Web, and to retrieve and explore this information in a meaningful way. While the easy accessibility to the current Web is a good baseline, optimal access to Web archives requires new models and algorithms for retrieval, exploration, and analytics which go far beyond what is needed to access the current state of the Web. This includes taking into account the unique temporal dimension of Web archives, structured semantic information already available on the Web, as well as social media and network information.
Within ALEXANDRIA, we will significantly advance semantic and time-based indexing for Web archives using human-compiled knowledge available on the Web, to efficiently index, retrieve and explore information about entities and events from the past. In doing so, we will focus on the concurrent evolution of this knowledge and the Web content to be indexed, and take into account diversity and incompleteness of this knowledge. We will further investigate mixed crowd- and machine-based Web analytics to support long- running and collaborative retrieval and analysis processes on Web archives. Usage of implicit human feedback will be essential to provide better indexing through insights during the analysis process and to better focus harvesting of content.
The ALEXANDRIA Testbed will provide an important context for research, exploration and evaluation of the concepts, methods and algorithms developed in this project, and will provide both relevant collections and algorithms that enable further research on and practical application of our research results to existing archives like the Internet Archive, the Internet Memory Foundation and Web archives maintained by European national libraries."
Summary
"Significant parts of our cultural heritage are produced on the Web, yet only insufficient opportunities exist for accessing and exploring the past of the Web. The ALEXANDRIA project aims to develop models, tools and techniques necessary to archive and index relevant parts of the Web, and to retrieve and explore this information in a meaningful way. While the easy accessibility to the current Web is a good baseline, optimal access to Web archives requires new models and algorithms for retrieval, exploration, and analytics which go far beyond what is needed to access the current state of the Web. This includes taking into account the unique temporal dimension of Web archives, structured semantic information already available on the Web, as well as social media and network information.
Within ALEXANDRIA, we will significantly advance semantic and time-based indexing for Web archives using human-compiled knowledge available on the Web, to efficiently index, retrieve and explore information about entities and events from the past. In doing so, we will focus on the concurrent evolution of this knowledge and the Web content to be indexed, and take into account diversity and incompleteness of this knowledge. We will further investigate mixed crowd- and machine-based Web analytics to support long- running and collaborative retrieval and analysis processes on Web archives. Usage of implicit human feedback will be essential to provide better indexing through insights during the analysis process and to better focus harvesting of content.
The ALEXANDRIA Testbed will provide an important context for research, exploration and evaluation of the concepts, methods and algorithms developed in this project, and will provide both relevant collections and algorithms that enable further research on and practical application of our research results to existing archives like the Internet Archive, the Internet Memory Foundation and Web archives maintained by European national libraries."
Max ERC Funding
2 493 600 €
Duration
Start date: 2014-03-01, End date: 2019-02-28
Project acronym ALEXANDRIA
Project Large-Scale Formal Proof for the Working Mathematician
Researcher (PI) Lawrence PAULSON
Host Institution (HI) THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE
Call Details Advanced Grant (AdG), PE6, ERC-2016-ADG
Summary Mathematical proofs have always been prone to error. Today, proofs can be hundreds of pages long and combine results from many specialisms, making them almost impossible to check. One solution is to deploy modern verification technology. Interactive theorem provers have demonstrated their potential as vehicles for formalising mathematics through achievements such as the verification of the Kepler Conjecture. Proofs done using such tools reach a high standard of correctness.
However, existing theorem provers are unsuitable for mathematics. Their formal proofs are unreadable. They struggle to do simple tasks, such as evaluating limits. They lack much basic mathematics, and the material they do have is difficult to locate and apply.
ALEXANDRIA will create a proof development environment attractive to working mathematicians, utilising the best technology available across computer science. Its focus will be the management and use of large-scale mathematical knowledge, both theorems and algorithms. The project will employ mathematicians to investigate the formalisation of mathematics in practice. Our already substantial formalised libraries will serve as the starting point. They will be extended and annotated to support sophisticated searches. Techniques will be borrowed from machine learning, information retrieval and natural language processing. Algorithms will be treated similarly: ALEXANDRIA will help users find and invoke the proof methods and algorithms appropriate for the task.
ALEXANDRIA will provide (1) comprehensive formal mathematical libraries; (2) search within libraries, and the mining of libraries for proof patterns; (3) automated support for the construction of large formal proofs; (4) sound and practical computer algebra tools.
ALEXANDRIA will be based on legible structured proofs. Formal proofs should be not mere code, but a machine-checkable form of communication between mathematicians.
Summary
Mathematical proofs have always been prone to error. Today, proofs can be hundreds of pages long and combine results from many specialisms, making them almost impossible to check. One solution is to deploy modern verification technology. Interactive theorem provers have demonstrated their potential as vehicles for formalising mathematics through achievements such as the verification of the Kepler Conjecture. Proofs done using such tools reach a high standard of correctness.
However, existing theorem provers are unsuitable for mathematics. Their formal proofs are unreadable. They struggle to do simple tasks, such as evaluating limits. They lack much basic mathematics, and the material they do have is difficult to locate and apply.
ALEXANDRIA will create a proof development environment attractive to working mathematicians, utilising the best technology available across computer science. Its focus will be the management and use of large-scale mathematical knowledge, both theorems and algorithms. The project will employ mathematicians to investigate the formalisation of mathematics in practice. Our already substantial formalised libraries will serve as the starting point. They will be extended and annotated to support sophisticated searches. Techniques will be borrowed from machine learning, information retrieval and natural language processing. Algorithms will be treated similarly: ALEXANDRIA will help users find and invoke the proof methods and algorithms appropriate for the task.
ALEXANDRIA will provide (1) comprehensive formal mathematical libraries; (2) search within libraries, and the mining of libraries for proof patterns; (3) automated support for the construction of large formal proofs; (4) sound and practical computer algebra tools.
ALEXANDRIA will be based on legible structured proofs. Formal proofs should be not mere code, but a machine-checkable form of communication between mathematicians.
Max ERC Funding
2 430 140 €
Duration
Start date: 2017-09-01, End date: 2022-08-31
Project acronym ALGAME
Project Algorithms, Games, Mechanisms, and the Price of Anarchy
Researcher (PI) Elias Koutsoupias
Host Institution (HI) THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Call Details Advanced Grant (AdG), PE6, ERC-2012-ADG_20120216
Summary The objective of this proposal is to bring together a local team of young researchers who will work closely with international collaborators to advance the state of the art of Algorithmic Game Theory and open new venues of research at the interface of Computer Science, Game Theory, and Economics. The proposal consists mainly of three intertwined research strands: algorithmic mechanism design, price of anarchy, and online algorithms.
Specifically, we will attempt to resolve some outstanding open problems in algorithmic mechanism design: characterizing the incentive compatible mechanisms for important domains, such as the domain of combinatorial auctions, and resolving the approximation ratio of mechanisms for scheduling unrelated machines. More generally, we will study centralized and distributed algorithms whose inputs are controlled by selfish agents that are interested in the outcome of the computation. We will investigate new notions of mechanisms with strong truthfulness and limited susceptibility to externalities that can facilitate modular design of mechanisms of complex domains.
We will expand the current research on the price of anarchy to time-dependent games where the players can select not only how to act but also when to act. We also plan to resolve outstanding questions on the price of stability and to build a robust approach to these questions, similar to smooth analysis. For repeated games, we will investigate convergence of simple strategies (e.g., fictitious play), online fairness, and strategic considerations (e.g., metagames). More generally, our aim is to find a productive formulation of playing unknown games by drawing on the fields of online algorithms and machine learning.
Summary
The objective of this proposal is to bring together a local team of young researchers who will work closely with international collaborators to advance the state of the art of Algorithmic Game Theory and open new venues of research at the interface of Computer Science, Game Theory, and Economics. The proposal consists mainly of three intertwined research strands: algorithmic mechanism design, price of anarchy, and online algorithms.
Specifically, we will attempt to resolve some outstanding open problems in algorithmic mechanism design: characterizing the incentive compatible mechanisms for important domains, such as the domain of combinatorial auctions, and resolving the approximation ratio of mechanisms for scheduling unrelated machines. More generally, we will study centralized and distributed algorithms whose inputs are controlled by selfish agents that are interested in the outcome of the computation. We will investigate new notions of mechanisms with strong truthfulness and limited susceptibility to externalities that can facilitate modular design of mechanisms of complex domains.
We will expand the current research on the price of anarchy to time-dependent games where the players can select not only how to act but also when to act. We also plan to resolve outstanding questions on the price of stability and to build a robust approach to these questions, similar to smooth analysis. For repeated games, we will investigate convergence of simple strategies (e.g., fictitious play), online fairness, and strategic considerations (e.g., metagames). More generally, our aim is to find a productive formulation of playing unknown games by drawing on the fields of online algorithms and machine learning.
Max ERC Funding
2 461 000 €
Duration
Start date: 2013-04-01, End date: 2019-03-31
Project acronym AlgoRNN
Project Recurrent Neural Networks and Related Machines That Learn Algorithms
Researcher (PI) Juergen Schmidhuber
Host Institution (HI) UNIVERSITA DELLA SVIZZERA ITALIANA
Call Details Advanced Grant (AdG), PE6, ERC-2016-ADG
Summary Recurrent neural networks (RNNs) are general parallel-sequential computers. Some learn their programs or weights. Our supervised Long Short-Term Memory (LSTM) RNNs were the first to win pattern recognition contests, and recently enabled best known results in speech and handwriting recognition, machine translation, etc. They are now available to billions of users through the world's most valuable public companies including Google and Apple. Nevertheless, in lots of real-world tasks RNNs do not yet live up to their full potential. Although universal in theory, in practice they fail to learn important types of algorithms. This ERC project will go far beyond today's best RNNs through novel RNN-like systems that address some of the biggest open RNN problems and hottest RNN research topics: (1) How can RNNs learn to control (through internal spotlights of attention) separate large short-memory structures such as sub-networks with fast weights, to improve performance on many natural short-term memory-intensive tasks which are currently hard to learn by RNNs, such as answering detailed questions on recently observed videos? (2) How can such RNN-like systems metalearn entire learning algorithms that outperform the original learning algorithms? (3) How to achieve efficient transfer learning from one RNN-learned set of problem-solving programs to new RNN programs solving new tasks? In other words, how can one RNN-like system actively learn to exploit algorithmic information contained in the programs running on another? We will test our systems existing benchmarks, and create new, more challenging multi-task benchmarks. This will be supported by a rather cheap, GPU-based mini-brain for implementing large RNNs.
Summary
Recurrent neural networks (RNNs) are general parallel-sequential computers. Some learn their programs or weights. Our supervised Long Short-Term Memory (LSTM) RNNs were the first to win pattern recognition contests, and recently enabled best known results in speech and handwriting recognition, machine translation, etc. They are now available to billions of users through the world's most valuable public companies including Google and Apple. Nevertheless, in lots of real-world tasks RNNs do not yet live up to their full potential. Although universal in theory, in practice they fail to learn important types of algorithms. This ERC project will go far beyond today's best RNNs through novel RNN-like systems that address some of the biggest open RNN problems and hottest RNN research topics: (1) How can RNNs learn to control (through internal spotlights of attention) separate large short-memory structures such as sub-networks with fast weights, to improve performance on many natural short-term memory-intensive tasks which are currently hard to learn by RNNs, such as answering detailed questions on recently observed videos? (2) How can such RNN-like systems metalearn entire learning algorithms that outperform the original learning algorithms? (3) How to achieve efficient transfer learning from one RNN-learned set of problem-solving programs to new RNN programs solving new tasks? In other words, how can one RNN-like system actively learn to exploit algorithmic information contained in the programs running on another? We will test our systems existing benchmarks, and create new, more challenging multi-task benchmarks. This will be supported by a rather cheap, GPU-based mini-brain for implementing large RNNs.
Max ERC Funding
2 500 000 €
Duration
Start date: 2017-10-01, End date: 2022-09-30
Project acronym ALGSTRONGCRYPTO
Project Algebraic Methods for Stronger Crypto
Researcher (PI) Ronald John Fitzgerald CRAMER
Host Institution (HI) STICHTING NEDERLANDSE WETENSCHAPPELIJK ONDERZOEK INSTITUTEN
Call Details Advanced Grant (AdG), PE6, ERC-2016-ADG
Summary 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
Summary
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
Max ERC Funding
2 447 439 €
Duration
Start date: 2017-10-01, End date: 2022-09-30
Project acronym ALLEGRO
Project Active large-scale learning for visual recognition
Researcher (PI) Cordelia Schmid
Host Institution (HI) INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE
Call Details Advanced Grant (AdG), PE6, ERC-2012-ADG_20120216
Summary A massive and ever growing amount of digital image and video content
is available today, on sites such as
Flickr and YouTube, in audiovisual archives such as those of BBC and
INA, and in personal collections. In most cases, it comes with
additional information, such as text, audio or other metadata, that forms a
rather sparse and noisy, yet rich and diverse source of annotation,
ideally suited to emerging weakly supervised and active machine
learning technology. The ALLEGRO project will take visual recognition
to the next level by using this largely untapped source of data to
automatically learn visual models. The main research objective of
our project is the development of new algorithms and computer software
capable of autonomously exploring evolving data collections, selecting
the relevant information, and determining the visual models most
appropriate for different object, scene, and activity categories. An
emphasis will be put on learning visual models from video, a
particularly rich source of information, and on the representation of
human activities, one of today's most challenging problems in computer
vision. Although this project addresses fundamental research
issues, it is expected to result in significant advances in
high-impact applications that range from visual mining of the Web and
automated annotation and organization of family photo and video albums
to large-scale information retrieval in television archives.
Summary
A massive and ever growing amount of digital image and video content
is available today, on sites such as
Flickr and YouTube, in audiovisual archives such as those of BBC and
INA, and in personal collections. In most cases, it comes with
additional information, such as text, audio or other metadata, that forms a
rather sparse and noisy, yet rich and diverse source of annotation,
ideally suited to emerging weakly supervised and active machine
learning technology. The ALLEGRO project will take visual recognition
to the next level by using this largely untapped source of data to
automatically learn visual models. The main research objective of
our project is the development of new algorithms and computer software
capable of autonomously exploring evolving data collections, selecting
the relevant information, and determining the visual models most
appropriate for different object, scene, and activity categories. An
emphasis will be put on learning visual models from video, a
particularly rich source of information, and on the representation of
human activities, one of today's most challenging problems in computer
vision. Although this project addresses fundamental research
issues, it is expected to result in significant advances in
high-impact applications that range from visual mining of the Web and
automated annotation and organization of family photo and video albums
to large-scale information retrieval in television archives.
Max ERC Funding
2 493 322 €
Duration
Start date: 2013-04-01, End date: 2019-03-31
Project acronym AlmaCrypt
Project Algorithmic and Mathematical Cryptology
Researcher (PI) Antoine Joux
Host Institution (HI) SORBONNE UNIVERSITE
Call Details Advanced Grant (AdG), PE6, ERC-2014-ADG
Summary Cryptology is a foundation of information security in the digital world. Today's internet is protected by a form of cryptography based on complexity theoretic hardness assumptions. Ideally, they should be strong to ensure security and versatile to offer a wide range of functionalities and allow efficient implementations. However, these assumptions are largely untested and internet security could be built on sand.
The main ambition of Almacrypt is to remedy this issue by challenging the assumptions through an advanced algorithmic analysis.
In particular, this proposal questions the two pillars of public-key encryption: factoring and discrete logarithms. Recently, the PI contributed to show that in some cases, the discrete logarithm problem is considerably weaker than previously assumed. A main objective is to ponder the security of other cases of the discrete logarithm problem, including elliptic curves, and of factoring. We will study the generalization of the recent techniques and search for new algorithmic options with comparable or better efficiency.
We will also study hardness assumptions based on codes and subset-sum, two candidates for post-quantum cryptography. We will consider the applicability of recent algorithmic and mathematical techniques to the resolution of the corresponding putative hard problems, refine the analysis of the algorithms and design new algorithm tools.
Cryptology is not limited to the above assumptions: other hard problems have been proposed to aim at post-quantum security and/or to offer extra functionalities. Should the security of these other assumptions become critical, they would be added to Almacrypt's scope. They could also serve to demonstrate other applications of our algorithmic progress.
In addition to its scientific goal, Almacrypt also aims at seeding a strengthened research community dedicated to algorithmic and mathematical cryptology.
--
Summary
Cryptology is a foundation of information security in the digital world. Today's internet is protected by a form of cryptography based on complexity theoretic hardness assumptions. Ideally, they should be strong to ensure security and versatile to offer a wide range of functionalities and allow efficient implementations. However, these assumptions are largely untested and internet security could be built on sand.
The main ambition of Almacrypt is to remedy this issue by challenging the assumptions through an advanced algorithmic analysis.
In particular, this proposal questions the two pillars of public-key encryption: factoring and discrete logarithms. Recently, the PI contributed to show that in some cases, the discrete logarithm problem is considerably weaker than previously assumed. A main objective is to ponder the security of other cases of the discrete logarithm problem, including elliptic curves, and of factoring. We will study the generalization of the recent techniques and search for new algorithmic options with comparable or better efficiency.
We will also study hardness assumptions based on codes and subset-sum, two candidates for post-quantum cryptography. We will consider the applicability of recent algorithmic and mathematical techniques to the resolution of the corresponding putative hard problems, refine the analysis of the algorithms and design new algorithm tools.
Cryptology is not limited to the above assumptions: other hard problems have been proposed to aim at post-quantum security and/or to offer extra functionalities. Should the security of these other assumptions become critical, they would be added to Almacrypt's scope. They could also serve to demonstrate other applications of our algorithmic progress.
In addition to its scientific goal, Almacrypt also aims at seeding a strengthened research community dedicated to algorithmic and mathematical cryptology.
--
Max ERC Funding
2 403 125 €
Duration
Start date: 2016-01-01, End date: 2021-12-31
Project acronym ALPHA
Project Alpha Shape Theory Extended
Researcher (PI) Herbert Edelsbrunner
Host Institution (HI) INSTITUTE OF SCIENCE AND TECHNOLOGYAUSTRIA
Call Details Advanced Grant (AdG), PE6, ERC-2017-ADG
Summary Alpha shapes were invented in the early 80s of last century, and their implementation in three dimensions in the early 90s was at the forefront of the exact arithmetic paradigm that enabled fast and correct geometric software. In the late 90s, alpha shapes motivated the development of the wrap algorithm for surface reconstruction, and of persistent homology, which was the starting point of rapidly expanding interest in topological algorithms aimed at data analysis questions.
We now see alpha shapes, wrap complexes, and persistent homology as three aspects of a larger theory, which we propose to fully develop. This viewpoint was a long time coming and finds its clear expression within a generalized
version of discrete Morse theory. This unified framework offers new opportunities, including
(I) the adaptive reconstruction of shapes driven by the cavity structure;
(II) the stochastic analysis of all aspects of the theory;
(III) the computation of persistence of dense data, both in scale and in depth;
(IV) the study of long-range order in periodic and near-periodic point configurations.
These capabilities will significantly deepen as well as widen the theory and enable new applications in the sciences. To gain focus, we concentrate on low-dimensional applications in structural molecular biology and particle systems.
Summary
Alpha shapes were invented in the early 80s of last century, and their implementation in three dimensions in the early 90s was at the forefront of the exact arithmetic paradigm that enabled fast and correct geometric software. In the late 90s, alpha shapes motivated the development of the wrap algorithm for surface reconstruction, and of persistent homology, which was the starting point of rapidly expanding interest in topological algorithms aimed at data analysis questions.
We now see alpha shapes, wrap complexes, and persistent homology as three aspects of a larger theory, which we propose to fully develop. This viewpoint was a long time coming and finds its clear expression within a generalized
version of discrete Morse theory. This unified framework offers new opportunities, including
(I) the adaptive reconstruction of shapes driven by the cavity structure;
(II) the stochastic analysis of all aspects of the theory;
(III) the computation of persistence of dense data, both in scale and in depth;
(IV) the study of long-range order in periodic and near-periodic point configurations.
These capabilities will significantly deepen as well as widen the theory and enable new applications in the sciences. To gain focus, we concentrate on low-dimensional applications in structural molecular biology and particle systems.
Max ERC Funding
1 678 432 €
Duration
Start date: 2018-07-01, End date: 2023-06-30