8 papers
Definability via the tilting correspondence
Gessica Alecci, Ihsane Hadeg, Franziska Jahnke +2
We show that arithmetic definability of henselian valuations is preserved by the tilting correspondence. Moreover, we show that if a perfectoid valuation is arithmetically definabl…
Linear Code Equivalence via Plücker Coordinates
Gessica Alecci, Giuseppe D'Alconzo
The assumed hardness of the Linear Code Equivalence problem (LCE) lies at the core of the security of the LESS signature scheme and other signature schemes with advanced functional…
Classical Algebraic Geometry and Discrete Integrable Systems
Gessica Alecci, Michele Graffeo, Alexander Stokes
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precis…
On a criterion for algebraic independence and its variants
Gessica Alecci, Carsten Elsner
From around 2010 onward, Elsner et al.,developed and applied a method in which the algebraic independence of n quantities x_1,...,x_n over a field is transferred to further n quant…
On alternative definition of Lucas atoms and their -adic valuations
Gessica Alecci, Piotr Miska, Nadir Murru +1
Lucas atoms are irreducible factors of Lucas polynomials and they were introduced in \cite{ST}. The main aim of the authors was to investigate, from an innovatory point of view, wh…
Some notes on the algebraic structure of linear recurrent sequences
Gessica Alecci, Stefano Barbero, Nadir Murru
Several operations can be defined on the set of all linear recurrent sequences, such as the binomial convolution (Hurwitz product) or the multinomial convolution (Newton product).…
Zeckendorf representation of multiplicative inverses modulo a Fibonacci number
Gessica Alecci, Nadir Murru, Carlo Sanna
Prempreesuk, Noppakaew, and Pongsriiam determined the Zeckendorf representation of the multiplicative inverse of modulo , for every positive integer not divisible by $…
Pell hyperbolas in DLP-based cryptosystems
Gessica Alecci, Simone Dutto, Nadir Murru
We present a study on the use of Pell hyperbolas in cryptosystems with security based on the discrete logarithm problem. Specifically, after introducing the group's structure over…