基本信息
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职业迁徙
个人简介
My research involves three complementary areas:
Algorithms and complexity in exact linear algebra, and its applications.
My work concerns the computational aspects of linear algebra problems in general, and more specifically problems in exact linear alebra related to the matrix multiplication, rank (rank profile, rank structure), the characteristic polynomial and matrix normal forms. My two major contributions in the field are:
a new matrix invariant, the rank profile matrix, and a characterization of the conditions on pivoting for a Gaussian elimination to reveal it. It finds a natural application in the field of rank structured matrices;
a reduction of the complexity for computing the characteristic polynomial to that of matrix multiplication, with a probabilistic algorithm, and more recently a deterministic one.
Security of outsourced computing
In the context of outsourced or multi-party computations, I develop protocols to ensure security in the broad sense (trust, privacy, proof of correctness, etc) of these computations. My approach focuses on efficiency in practice, by developing problem specific approaches to avoid overheads of the generic approaches. More precisely I contribute to
Coding theory applied to Algorithm Based Fault Tolerance.
Interactive proofs, applied to two party verification protocols.
Secure Multi-party Computations in linear algebra.
Proof of retrievability.
Mathematic software development.
I seek to develop algorithms combining theoretical and practical efficiency, and therefore propose in a rather systematic way, their implementations in largely distributed, mainstream libraries and software. I am mainly working on 3 open-source software projects: FFLAS-FFPACK, a package of routines for dense linear algebra over a finite field; LinBox, a library for exact linear algebra over a finite field or integers; SageMath, a general purpose mathematic software.
Algorithms and complexity in exact linear algebra, and its applications.
My work concerns the computational aspects of linear algebra problems in general, and more specifically problems in exact linear alebra related to the matrix multiplication, rank (rank profile, rank structure), the characteristic polynomial and matrix normal forms. My two major contributions in the field are:
a new matrix invariant, the rank profile matrix, and a characterization of the conditions on pivoting for a Gaussian elimination to reveal it. It finds a natural application in the field of rank structured matrices;
a reduction of the complexity for computing the characteristic polynomial to that of matrix multiplication, with a probabilistic algorithm, and more recently a deterministic one.
Security of outsourced computing
In the context of outsourced or multi-party computations, I develop protocols to ensure security in the broad sense (trust, privacy, proof of correctness, etc) of these computations. My approach focuses on efficiency in practice, by developing problem specific approaches to avoid overheads of the generic approaches. More precisely I contribute to
Coding theory applied to Algorithm Based Fault Tolerance.
Interactive proofs, applied to two party verification protocols.
Secure Multi-party Computations in linear algebra.
Proof of retrievability.
Mathematic software development.
I seek to develop algorithms combining theoretical and practical efficiency, and therefore propose in a rather systematic way, their implementations in largely distributed, mainstream libraries and software. I am mainly working on 3 open-source software projects: FFLAS-FFPACK, a package of routines for dense linear algebra over a finite field; LinBox, a library for exact linear algebra over a finite field or integers; SageMath, a general purpose mathematic software.
研究兴趣
论文共 66 篇作者统计合作学者相似作者
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CoRR (2024)
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CoRR (2024)
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JOURNAL OF COMPLEXITY (2024): 101803-101803
arxiv(2023)
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HAL (Le Centre pour la Communication Scientifique Directe) (2023)
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Proc. Priv. Enhancing Technol.no. 3 (2023): 354-374
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Gaspard Anthoine,Jean-Guillaume Dumas, Melanie de Jonghe,Aude Maignan,Clement Pernet,Michael Hanling,Daniel S. Roche
PROCEEDINGS OF THE 30TH USENIX SECURITY SYMPOSIUM (2021): 537-554
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