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Nearly Sparse Linear Algebra and application to Discrete Logarithms Computations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Joux, Antoine Pierrot, Cécile |
| Copyright Year | 2016 |
| Abstract | In this article1, we propose a method to perform linear algebra on a matrix with nearly sparse properties. More precisely, although we require the main part of the matrix to be sparse, we allow some dense columns with possibly large coefficients. This is achieved by modifying the Block Wiedemann algorithm. Under some precisely stated conditions on the choices of initial vectors in the algorithm, we show that our variation not only produces a random solution of a linear system but gives a full basis of the set of solutions. Moreover, when the number of heavy columns is small, the cost of dealing with them becomes negligible. In particular, this eases the computation of discrete logarithms in medium and high characteristic finite fields, where nearly sparse matrices naturally occur. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://eprint.iacr.org/2015/930.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Block Wiedemann algorithm Choice Behavior Coefficient Column (database) Computation (action) Discrete logarithm Linear algebra Linear system Solutions Sparse matrix The Matrix |
| Content Type | Text |
| Resource Type | Article |
