# Ilaria Zappatore

Post-Doc at LIX

INRIA Saclay, team GRACE

Hi everyone!

I am Ilaria Zappatore, a Post-Doc at LIX, *Laboratoire d’informatique de l’École polytechnique*, INRIA Saclay. I am a member of the GRACE team.

My research interests are in the fields of Algebraic Coding Theory, Computer Algebra and Cryptography.

I got my Ph.D in Computer Science in October 2020. I was a member of the ECO team at the Laboratory of Informatics, Robotics and Microelectronics of Montpellier (LIRMM), in France.

I am a very curious and enthusiastic person. I enjoy learning new things and challenging myself.

This webpage contains information about my professional experiences, my studies and publications.

Here you can find my latest CV.

## Education

**From October 2017 until October 2020**

Ph.D student at LIRMM (Montpellier, France)

- LIRMM, University of Montpellier, CNRS
- Supervisors: Laurent Imbert, Eleonora Guerrini, Romain Lebreton
- Exact Computing (ECO) team, ECO
- My research activity is mainly based on Coding Theory and Computer Algebra.

**2017**

Master Degree in Mathematics: curriculum Coding Theory and Cryptography

- University of Trento, Italy
- Final mark: 110/110 cum laude
- Thesis: “Primitivity of generalized translation based block ciphers.”

*In this thesis we introduce a new model of block ciphers, the generalized translation based block ciphers. This model is a generalization of translation based block ciphers, i.e. a class of ciphers that includes some famous block ciphers such as AES, SERPENT and PRESENT. We also prove the primitivity of the algebraic group generated by the round functions of this new class of ciphers. This means that these kind of block ciphers are resistant to some attacks that exploit their algebraic structure.* You can download my thesis here.

**2014**

Bachelor Degree in Mathematics

- University of Bari, Italy
- Final mark: 106/110
- Thesis: “Primality tests and factorization algorithms: a cryptographic approach.”

**2009**

High School Diploma (Science studies)

- Liceo Scientifico Battaglini, Taranto, Italy
- Final mark: 100/100

## Ph.D. Defense

My Ph.D. defense entitled *“Simultaneous Rational Function Reconstruction and applications to Algebraic Coding Theory” *took place on October 16 at 10:30 a.m., at the Salle de Séminaire, Bat. 4, LIRMM, Montpellier, France.

Here you can also find the updated version of my thesis.

**Jury**

- Daniel AUGOT,
*Directeur de Recherche, Inria Saclay***(Rapporteur)**, - Clément PERNET,
*Maître de Conférences, Université Grenoble Alpes, LJK, Grenoble***(Rapporteur)**, - Magali BARDET,
*Maître de Conférences, Université de Rouen, LITIS, Rouen***(Examinatrice)**, - Elisa GORLA,
*Professeur, Université de Neuchâtel, Switzerland***(Examinatrice)**, - Gilles VILLARD,
*Directeur de Recherche CNRS, LIP, Lyon***(Président).** - Laurent IMBERT, Directeur de Recherche CNRS, LIRMM, Montpellier
**(Directeur)**, - Eleonora GUERRINI,
*Maître de Conférences, Université de Montpellier, LIRMM, Montpellier***(Co-encadrante)**, - Romain LEBRETON
*Maître de Conférences, Université de Montpellier, LIRMM, Montpellier***(Co-encadrant)**.

**Abstract**

*This thesis deals with a Computer Algebra problem which has significant consequences in Algebraic Coding Theory and Error Correcting Codes: the simultaneous rational function reconstruction. Indeed, an accurate analysis of this problem leads to interesting results in both these scientific domains.*

*More precisely, the simultaneous rational function reconstruction is the problem of reconstructing a vector of rational functions with the same denominator given its evaluations (or more generally given its remainders modulo different polynomials). The peculiarity of this problem consists in the fact that the common denominator constraint reduces the number of evaluation points needed to guarantee the existence of a solution, possibly losing the uniqueness. One of the main contribution of this work consists in the proof that uniqueness is guaranteed for almost all instances of this problem.*

*This result was obtained by elaborating some other contributions and techniques derived by the applications of SRFR, from the polynomial linear system solving to the decoding of Interleaved Reed-Solomon codes.*

*In this work, we will also study and present another application of the SRFR problem, concerning the problem of constructing fault-tolerant algorithms: algorithms resilients to computational errors. These algorithms are constructed by introducing redundancy and using error correcting codes tools to detect and possibly correct errors which occur during computations. In this application context, we improve an existing fault-tolerant technique for polynomial linear system solving by interpolation-evaluation, by focusing on the SRFR problem related to it.*

## Publications

##### Proceedings

###### 2021

Eleonora Guerrini, Romain Lebreton, Ilaria Zappatore. *Polynomial Linear System Solving with Random Errors: new bounds and early termination technique. **Proceedings of ISSAC’21, 2021*

###### 2020

Eleonora Guerrini, Romain Lebreton, Ilaria Zappatore. *On the Uniqueness of the Simultaneous Rational Function Reconstruction. Proceedings of ISSAC’20, 2020*

###### 2019

Eleonora Guerrini, Romain Lebreton, Ilaria Zappatore. *Polynomial Linear System Solving with Errors by Simultaneous Polynomial Reconstruction of Interleaved Reed-Solomon Codes.**Proceedings of ISIT’19*, 2019. Corrected version arXiv, HAL.

##### Journals

###### 2019

Riccardo Aragona, Marco Calderini, Roberto Civino, Massimiliano Sala, Ilaria Zappatore. *Wave-shaped round functions and primitive groups*, Advances in Mathematics of Communications **13**, 1.

##### Preprints, work in progress

###### 2021

Daniel Augot, François Morain, Ilaria Zappatore. *Computing the Discrete Logarithm over Finite Fields* *using Reed-Solomon codes* (in progress).

###### 2020

Eleonora Guerrini, Romain Lebreton, Ilaria Zappatore. *Enhancing the simultaneous rational function recovery: adaptive error correction capability and new bounds for applications. *arXiv

##### Talks

###### 2021

**Polynomial Linear System Solving with Errors: new bounds and Early Termination Technique.** JNCF 2021 , CIRM, Luminy (France), 1st Mars 2021.

**Simultaneous Rational Function Reconstruction and applications to Coding Theory**

- Séminaire Limousin de Calcul Formel, XLIM, Limoges (France), 25th Mars 2021.
- PolSys SpecFun Seminar, LIP6, Sorbonne Université, Paris (France) 19th February 2021.

###### 2020

**Décodage des codes Reed-Solomon classiques et entrelacés du point de vue du Calcul Formel : le problème de la Reconstruction Rationnelle**, Groupe de Travail de (post) doctorants de l’equipe GRACE, Inria-Saclay (France) 27th November and 4th December 2020.

**Algorithm-based Fault Tolerant Technique for Polynomial Linear System Solving by Evaluation-Interpolation**,

- Groupe de Travail de l’équipe GRACE, Inria-Saclay (France), 1st December 2020
- Journées C2 virtuelles, 6th November 2020.

**On the Uniqueness of the Simultaneous Rational Function Reconstruction,**

- Séminaire CASC, Laboratoire Jean Kuntzmann, Grenoble (France)
- JNCF 2020, CIRM, Luminy (France), 2nd Mars 2020

###### 2019

**Polynomial Linear System Solving with Errors by Simultaneous Polynomial Reconstruction of Interleaved Reed Solomon Codes, **

- Séminaire IMATH, Laboratoire IMATH-CPT-COSMER, Université de Toulon (France) 22th Mars 2019
- JNCF 2019, CIRM, Luminy (France), 7th February 2019

###### 2018

**Polynomial Linear System Solving with Errors by Simultaneous Polynomial Reconstruction of Interleaved Reed Solomon Codes, **Journées C2 , 10th October 2018, Aussois (France)

##### Awards

Student travel grant – ISIT 2019

Merit Award 2018 – University of Trento

## Teachings

###### 2019-2020, University of Montpellier

- HLIN101 Introduction à l’algorithmique et à la programmation, TD and TP, L1;
- HLIN406 Modélisation et programmation objet 1, TD and TP, L2.

###### 2018-2019, University of Montpellier

- HLIN101 Introduction à l’algorithmique et à la programmation, TD and TP, L1;
- HLIN606 Programmation Linéaire, TP, L3.

###### 2017-2018, University of Montpellier

- HLIN606 Programmation Linéaire, TP, L3;
- HLIN403 Programmation Applicative, TP, L2;
- HLIN202 Programmation Impérative, TP, L1.

## Work Experiences

**2016, Internship **

at AliasLab S.p.a., Mantova, Italy.

During this stage I studied and analyzed the Bitcoin blockchain and other Altchains, like Ethereum, Bigchain DB and Multichain, aiming to integrate this technology to the company’s existing products.

I also implemented some smart contracts in the Ethereum blockchain using the Solidity language.

#### Contacts

Laboratoire d’Informatique de l’École Polytechnique

1 rue Honoré d’Estien d’Orves

Campus de l’École Polytechnique

91120 Palaiseau

France

e-mails: ilaria.zappatore@gmail.com, ilaria.zappatore@inria.fr