Affiliation:
1. Japan Advanced Institute of Science and Technology Ishikawa, Japan
2. Shinshu University Nagano, Japan
Abstract
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 Lov´asz) 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.
Subject
Applied Mathematics,Computational Mathematics
Cited by
3 articles.
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