Finite and infinite collections of multiplication modules.
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In this article, we formalize Z-module, that is a module over integer ring. Z-module is necassary for lattice problems, LLL (Lenstra-Lenstra-Lovász) base reduction algorithm and cryptographic systems with lattices [11].
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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...
Ali, Majid M., Smith, David J. (2004)
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In this article we formalize a quotient module of Z-module and a vector space constructed by the quotient module. We formally prove that for a Z-module V and a prime number p, a quotient module V/pV has the structure of a vector space over Fp. Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz) base reduction algorithm and cryptographic systems with lattices [14]. Some theorems in this article are described by translating theorems in [20] and [19] into theorems...
Ali, Majid M. (2006)
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