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We connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.
Let be a pure cubic field, with , where is a cube-free integer. We will determine the reduced ideals of the order of which coincides with the maximal order of in the case where is square-free and .
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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