TALK #1:

By: Ramiro Martínez, MAK-UPC

Title: RLWE-based Zero-Knowledge Proofs for linear and multiplicative relations

Abstract: Ring Learning With Errors (RLWE) samples are pairs of polynomials in $\\mathbb{Z}_q\[x\]/(x^{n}+1)$, obtained from a distribution that depends on a secret polynomial. RLWE samples are computationally indistinguishable from uniformly random pairs of polynomials. We present efficient Zero-Knowledge Proofs of Knowledge (ZKPoK) for linear and multiplicative relations among secret messages hidden as RLWE samples. Our proposed protocols for a ZKPoK are based on the celebrated paper by Stern on identification schemes using coding problems (Crypto'93). Our 5-move protocol achieves a soundness error slightly above 1/2 and perfect Zero-Knowledge.

As an application we present ZKPoK of relations between committed messages. The resulting commitment scheme is perfectly binding with overwhelming probability over the choice of the public key, and computationally hiding under the RLWE assumption. Compared with previous Stern-based commitment scheme proofs we decrease computational complexity, improve the size of the parameters and reduce the soundness error of each round.

TALK #2:

By: Carla Ràfols, UPF

Title: A survey on SNARKs

Abstract: Zero-Knowledge proofs are among the oldest and most useful cryptographic primitives. Efficient proofs for "simple" languages (non NP complete) have been known for a long time, in different security models and based on various different computational assumptions. SNARKs or Succint Non-Interactive Arguments of Knowledge, proposed by Groth in 2010, allow to prove circuit satisfiability in zero-knowledge. The most efficient constructions are not only succinct (independent of the witness size) but also very efficient concretely. SNARKs have had a major impact in cryptographic research and practice, partly due to their application to anonymous financial transactions in cryptocurrencies. In this talk, I will survey some of the main results, techniques and applications in the area.

TALK #1:

By: Michael Olugbenga Bamiloshin, URV Tarragona

Title: Common Information, Matroid Representation, and Secret Sharing for Matroid Ports

Abstract: A secret sharing scheme is a method by which a dealer distributes shares to parties such that only authorized subsets of parties can reconstruct the secret. The information ratio of a secret sharing scheme is the size in bits of the largest share of the scheme divided by the size of the secret. Farràs, Kaced, Martín and Padró presented an improvement in the linear programming technique to derive lower bounds on the information ratio of the schemes for an access structure that use the Ahlswede-Körner lemma and the common information of random variables, avoiding the use of explicit non-Shannon information inequalities (EUROCRYPT 2018). In this work we apply this linear programming technique to the classification of matroids on eight and nine points. Namely, we apply this technique to check if a matroid is multilinearly representable, algebraic or almost entropic. We also present some hitherto unknown non-representable matroids and new bounds on the information ratio of schemes for ports of non-representable matroids.

This is a joint work with Aner Ben-Efraim, Oriol Farràs and Carles Padró.

TALK #2:

By: Victor Peña-Macias, Universidad Nacional de Colombia

Title: Characteristic-Dependent Linear Rank Inequalities and Applications to Network Coding

Abstract: In Linear Algebra over finite fields, a characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over fields with other characteristic. In this talk, we show a new method to produce these inequalities. We also discuss some results of application to Network Coding, among these, for each finite or co-finite set of primes P, we show that there exists a sequence of networks (N(t)) in which each member is linearly solvable over a field if and only if the characteristic of the field is in P; and the linear capacity, over fields whose characteristic is not in P, tends to 0 as t tends to infinity.

Incripció:
https://gcice.upc.edu/fitxa_cursos.asp?id=54476

Two talks in this session:

TALK #1:

By: Chen Yuan, CWI Amsterdam
Title: Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary

Abstract: Robust secret sharing enables the reconstruction of a secret-shared message in the presence of up to t (out of n) incorrect shares. The most challenging case is when n = 2t + 1, which is the largest t for which the task is still possible, up to a small error probability and with some overhead in the share size. In this work,we propose a new robust secret sharing scheme that offers full security against a rushing adversary. We also answer the open question posed by Cevallos et al.(Eurocrypt 2012) who proposed a scheme with overhead of O(n+K) and asked whether the linear dependency on n was necessary or not.

This is a joint work with Serge Fehr.

TALK #2:

By: Oriol Farras, URV Tarragona
Title: Secret-Sharing Schemes for General Access Structures

Abstract: A secret-sharing scheme allows some authorized sets of parties to reconstruct a secret; the collection of authorized sets is called the access structure. For over 30 years, it was known that any (monotone) collection of authorized sets can be realized by a secret-sharing scheme whose shares are of size $2^{n−o(n)}$ and until recently no better scheme was known. In a recent breakthrough, Liu and Vaikuntanathan (STOC 2018) reduced the share size to $O(2^{0.994n})$. We improved the general construction, obtaining a share size $O(2^{0.892n})$. For the special case of linear secret-sharing schemes, we get an exponent of $0.942$ (compared to $0.999$ of Liu and Vaikuntanathan).

This result was included in the paper "Secret-Sharing Schemes for General and Uniform Access Structures", a joint work with Benny Applebaum, Amos Beimel, Oded Nir and Naty Peter presented in Eurocrypt 2019.

Més informació a:

http://www.crm.cat/en/Activities/Curs_2019-2020/Pages/Women-in-Geometry-and-Topology.aspx

El director de l’ETSETB, Sr. Josep Pegueroles, el degà de la FIB, Sr. Josep Fernández i el degà de la FME, Sr. Jaume Franch, es complauen a convidar-vos a la inauguració del Curs 2019/20 del Grau en Ciència i Enginyeria de Dades, que tindrà lloc el dia 17 de setembre, a les 13h, a l’Auditori de l’edifici Vèrtex del Campus Nord de la UPC (plaça Eusebi Güell, 6 Barcelona).

ORDRE DE L’ACTE

Obre l’acte el  Sr. Josep Pegueroles, director de l’ETSETB.

• Paraules del Rector de la UPC, Sr. Francesc Torres.
• Lliçó inaugural: “Com serà el món quan us gradueu” i “Els científics de dades ja pronostiquen el temps”, a càrrec del Sr. Tomàs Molina, Cap de Meteorologia de TV3.
• Lliurament millor expedient acadèmic de la Fase Inicial del curs 2018/19.
• Paraules del representant dels estudiants.
• Cloenda a càrrec del Sr. Josep Pegueroles, director de l’ETSETB

Les conferències en aquesta ocasió, estaran a càrrec d'investigadors i investigadores postdoctorals que estan actualment a la UPC: Öznur Yaşar Diner, Gyula Csato, Stefano Pasquali i Juan Margalef. Durant el coffeee break farem una sessió de pòsters.

Més informació sobrel el programa:

https://mat.upc.edu/ca/shared/jornadaderecerca2019.pdf

OBJECTIUS

En aquesta jornada es vol:

• Presentar una nova eina que permetrà al docent tenir guardats tots els dissenys d’assignatures i coordinacions, desvinculats dels estudiants: El maletí del professor/a.
• Fer un tastet de dissenys d’assignatures de la UPC a ATENEA de professors de diferents centres i diferents tipologies de cursos per tal de conèixer com es pot gestionar a través d’ATENEA l’activitat del docent en cursos grans, mitjans o petits, per exemple, o com es pot organitzar el material, quines eines d’ATENEA són útils i quines mancances i limitacions es troben en cada cas.
• Fer un anàlisi i discussió de cap on ha d’evolucionar ATENEA, per tal de poder dedicar esforços en la millora de la plataforma en el sentit correcte.

La convocatoria es troba a l'enllaç:

https://gcice.upc.edu/fitxa_cursos.asp?id=54396

El dimecres 26 de juny tindrà lloc la 4a Jornada Docent del Departament, amb el títol "La perspectiva de gènere en la pràctica de les Matemàtiques".  Hi haurà dues conferències plenàries, a càrrec de C. Grima (U. Sevilla) i A. Susín i dos tallers (J. Saludes i F. Aguiló).

La Jornada compta amb el suport de la Facultat de Matemàtiques i Estadística i de l'Institut de Ciències de l'Educació.

Programa

Podeu inscriure-us a l'enllaç:

https://gcice.upc.edu/fitxa_cursos.asp?id=54398

Aquesta jornada ofereix 8 conferències sobre temes relacionats amb xarxes, teoria de grafs, geometria computacional, matemàtica discreta. Està organitzat dins del projecte H2020-MSCA-RISE-734922 CONNECT.