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The discrete logarithm problem over prime fields: the safe prime case. The Smart attack, non-canonical lifts and logarithmic derivatives

Gopalakrishna Hejmadi Gadiyar, Ramanathan Padma (2018)

Czechoslovak Mathematical Journal

We connect the discrete logarithm problem over prime fields in the safe prime case to the logarithmic derivative.

The formulas for the coefficients of the sum and product of p-adic integers with applications to Witt vectors

Kejian Xu, Zhaopeng Dai, Zongduo Dai (2011)

Acta Arithmetica

The reduced ideals of a special order in a pure cubic number field

Abdelmalek Azizi, Jamal Benamara, Moulay Chrif Ismaili, Mohammed Talbi (2020)

Archivum Mathematicum

Let $K = ℚ (θ)$ be a pure cubic field, with $θ^{3} = D$ , where $D$ is a cube-free integer. We will determine the reduced ideals of the order $𝒪 = ℤ [θ]$ of $K$ which coincides with the maximal order of $K$ in the case where $D$ is square-free and $\neg \equiv \pm 1 (mod 9)$ .

Windmill Polynomials Over Fields of Characteristic Two.

Stephen D. Cohen (1989)

Monatshefte für Mathematik

Yet more projective curves over $𝔽_{2}$ .

Lomont, Chris (2002)

Experimental Mathematics

Z-modules

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama (2012)

Formalized Mathematics

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].