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Section: New Results
Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries
In [15] we present new results for efficient arithmetic
operations in a number field
Overall Objectives
Scientific Foundations
Application Domains
New Results
- The complexity of solving quadratic boolean systems is better than exhaustive search
- Improving the Complexity of Index Calculus Algorithms in Elliptic Curves over Binary Fields
- On the relation between the MXL family of algorithms and Gröbner basis algorithms
- On the Complexity of the BKW Algorithm on LWE
- On the Complexity of the Arora-Ge algorithm against LWE
- On enumeration of polynomial equivalence classes and their application to MPKC
- Cryptanalysis of HFE, Multi-HFE and Variants for Odd and Even Characteristic
- Solving Polynomial Systems over Finite Fields: Improved Analysis of the Hybrid Approach
- Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries
- Algebraic Crypanalysis with Side Channels Information
- Worst case complexity of the Continued Fraction (CF) algorithm.
- Local Generic Position for Root Isolation of Zero-dimensional Triangular Polynomial Systems.
- Univariate Real Root Isolation in Multiple Extension Fields
- Mixed volume and distance geometry techniques for counting Euclidean embeddings of rigid graphs.
- Variant Quantifier Elimination
- Global optimization
- Gröbner bases and critical points
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Bibliography
Overall Objectives
Scientific Foundations
Application Domains
New Results
- The complexity of solving quadratic boolean systems is better than exhaustive search
- Improving the Complexity of Index Calculus Algorithms in Elliptic Curves over Binary Fields
- On the relation between the MXL family of algorithms and Gröbner basis algorithms
- On the Complexity of the BKW Algorithm on LWE
- On the Complexity of the Arora-Ge algorithm against LWE
- On enumeration of polynomial equivalence classes and their application to MPKC
- Cryptanalysis of HFE, Multi-HFE and Variants for Odd and Even Characteristic
- Solving Polynomial Systems over Finite Fields: Improved Analysis of the Hybrid Approach
- Efficient Arithmetic in Successive Algebraic Extension Fields Using Symmetries
- Algebraic Crypanalysis with Side Channels Information
- Worst case complexity of the Continued Fraction (CF) algorithm.
- Local Generic Position for Root Isolation of Zero-dimensional Triangular Polynomial Systems.
- Univariate Real Root Isolation in Multiple Extension Fields
- Mixed volume and distance geometry techniques for counting Euclidean embeddings of rigid graphs.
- Variant Quantifier Elimination
- Global optimization
- Gröbner bases and critical points
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Bibliography