Name
Abstract | ||
|---|---|---|
In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems-LLL (Lenstra, Lenstra and Lovasz) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this article are described by translating theorems in [11] into theorems of Z-module, however their proofs are different. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.2478/forma-2013-0029 | FORMALIZED MATHEMATICS |
Keywords | Field | DocType |
free Z-module, submodule of free Z-module | Discrete mathematics,Vector space,Free module,Lattice (order),Cryptography,Lattice problem,Mathematical proof,Mathematics | Journal |
Volume | Issue | ISSN |
21 | 4 | 1898-9934 |
Citations | PageRank | References |
2 | 0.58 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuichi Futa | 1 | 23 | 15.08 |
| Hiroyuki Okazaki | 2 | 2 | 0.58 |
| Yasunari Shidama | 3 | 166 | 72.47 |