SECURITY & APPLIED LOGIC

Unwinding of proofs
2021-03-04 10:00 - 12:00 (Europe/Bucharest)
Title: Unwinding of proofs
Speaker: Pedro Pinto (TU Darmstadt)

Abstract:
The unwinding of proofs program dates back to Kreisel in the fifties and rests on the following broad question: “What more do we know if we have proved a theorem by restricted means than if we merely know that it is true?”

This research program has since been dubbed proof mining and has been greatly developed during the last two decades and emerged as a new form of applied proof theory [1,2]. Through the use of proof-theoretical tools, the proof mining program is concerned with the unveil of hidden finitary and combinatorial content from proofs that use infinitary noneffective principles.

In this talk, we set out to give a brief introduction to the proof mining program, focusing on the following points:

functional interpretations in an introductory way;
the bounded functional interpretation [3,4];
a concrete translation example: the metric projection argument.

We finish with a brief discussion of some recent results [5,6].
References:

[1] U. Kohlenbach. Applied Proof Theory: Proof Interpretations and their Use in Mathematics. Springer Monographs in Mathematics. Springer-Verlag Berlin Heidelberg, 2008.
[2] U. Kohlenbach. Proof-theoretic methods in nonlinear analysis. In M. Viana B. Sirakov, P. Ney de Souza, editor, Proceedings of the International Congress of Mathematicians – Rio de Janeiro 2018, Vol. II: Invited lectures, pages 61–82. World Sci. Publ., Hackensack, NJ, 2019.
[3] F. Ferreira and P. Oliva. Bounded functional interpretation. Annals of Pure and Applied Logic, 135:73-112, 2005.
[4] F. Ferreira. Injecting uniformities into Peano arithmetic. Annals of Pure and Applied Logic, 157:122-129, 2009.
[5] B. Dinis and P. Pinto. Effective metastability for a method of alternating resolvents. arXiv:2101.12675 [math.FA], 2021.
[6] U. Kohlenbach and P. Pinto. Quantitative translations for viscosity approximation methods in hyperbolic spaces. arXiv:2102.03981 [math.FA], 2021.

References:

Exponential Diophantine equations over ℚ
2021-03-11 10:00 - 12:00
Title: Exponential Diophantine equations over ℚ
Speaker: Mihai Prunescu (University of Bucharest & IMAR)

Abstract:

In a previous exposition [1] we have seen that the solvability over ℚ is undecidable for systems of exponential Diophantine equations. We now show that the solvability of individual exponential Diophantine equations is also undecidable, and that this happens as well for some narrower families of exponential Diophantine equations.
References:

[1] M. Prunescu, The exponential Diophantine problem for ℚ. The Journal of Symbolic Logic, Volume 85, Issue 2, 671–672, 2020.

A proof mining case study on the unit interval
2021-03-18 10:00 - 12:00
Title: A proof mining case study on the unit interval
Speaker: Andrei Sipoș (University of Bucharest & IMAR)

Abstract:

In 1991, Borwein and Borwein proved [1] the following: if L>0, f : [0,1] → [0,1] is L-Lipschitz, (xn), (tn) ⊆ [0,1] are such that for all n, xn+1=(1-tn)xn+tnf(xn) and there is a δ>0 such that for all n, tn≤(2-δ)/(L+1), then the sequence (xn) converges.
The relevant fact here is that the main argument used in their proof is of a kind that hasn’t been analyzed yet from the point of view of proof mining, and thus it may serve as an illustrative new case study. We shall present our work [2] on the proof, showing how to extract a uniform and computable rate of metastability for the above family of sequences.
References:

[1] D. Borwein, J. Borwein, Fixed point iterations for real functions. J. Math. Anal. Appl. 157, no. 1, 112–126, 1991.
[2] A. Sipoș, Rates of metastability for iterations on the unit interval. arXiv:2008.03934 [math.CA], 2020.

Regular matching problems for infinite trees
2021-03-25 10:00 - 12:00
Title: Regular matching problems for infinite trees
Speaker: Mircea Marin (West University of Timișoara)

Abstract:
We study the matching problem “∃σ:σ(L)⊆R?” where L and R are regular tree languages over finite ranked alphabets X and Σ respectively, and σ is a substitution such that σ(x) is a set of trees in T(Σ∪H)∖H for all x∈X. Here, H denotes a set of holes which are used to define a concatenation of trees. Conway studied this problem in the special case for languages of finite words in his classical textbook Regular algebra and finite machines and showed that if L and R are regular, then the problem “∃σ:∀x∈X:σ(x)≠∅∧σ(L)⊆R?” is decidable. Moreover, there are only finitely many maximal solutions, which are regular and effectively computable. We extend Conway’s results when L and R are regular languages of finite and infinite trees, and language substitution is applied inside-out. We show that if L⊆T(X) and R⊆T(Σ) are regular tree languages then the problem “∃σ∀x∈X:σ(x)≠∅∧σio(L)⊆R?” is decidable. Moreover, there are only finitely many maximal solutions, which are regular and effectively computable. The corresponding question for the outside-in extension σoi remains open, even in the restricted setting of finite trees. Our main result is the decidability of “∃σ:σio(L)⊆R?” if R is regular and L belongs to a class of tree languages closed under intersection with regular sets. Such a special case pops up if L is context-free.
This is joint work with Carlos Camino, Volker Diekert, Besik Dundua and Géraud Sénizergues.

References:
[1] C. Camino, V. Diekert, B. Dundua, M. Marin, G. Sénizergues, Regular matching problems for infinite trees. arXiv:2004.09926 [cs.FL], 2021.

An Introduction to Protocols in Dynamic Epistemic Logic
2021-04-01 10:00 - 12:00
Title: An Introduction to Protocols in Dynamic Epistemic Logic
Speaker: Alexandru Dragomir (University of Bucharest)

Abstract:
Dynamic epistemic logics are useful in reasoning about knowledge and acts of learning, seen as epistemic actions. However, not all epistemic actions are allowed to be executed in an initial epistemic model, and this is where the concept of a protocol comes in: a protocol stipulates what epistemic actions are allowed to be performed in a model. The aim of my presentation is to introduce the audience to two accounts of protocols in DEL: Hoshi’s [1], and Wang’s [2].

References:
[1] T. Hoshi, Epistemic dynamics and protocol information. PhD thesis, Stanford, CA, USA, 2009.
[2] Y. Wang, Epistemic Modelling and Protocol Dynamics. PhD thesis, University of Amsterdam, 2010.

Kernelization, Proof Complexity and Social Choice
2021-04-22 10:00 - 12:00
Title: Kernelization, Proof Complexity and Social Choice
Speaker: Gabriel Istrate (West University of Timișoara)

Abstract:

We display an application of the notions of kernelization and data reduction from parameterized complexity to proof complexity: Specifically, we show that the existence of data reduction rules for a parameterized problem having (a) a small-length reduction chain, and (b) small-size (extended) Frege proofs certifying the soundness of reduction steps implies the existence of subexponential size (extended) Frege proofs for propositional formalizations of the given problem. We apply our result to infer the existence of subexponential Frege and extended Frege proofs for a variety of problems. Improving earlier results of Aisenberg et al. (ICALP 2015), we show that propositional formulas expressing (a stronger form of) the Kneser-Lovasz Theorem have polynomial size Frege proofs for each constant value of the parameter k. Previously only quasipolynomial bounds were known (and only for the ordinary Kneser-Lovasz Theorem). Another notable application of our framework is to impossibility results in computational social choice: we show that, for any fixed number of agents, propositional translations of the Arrow and Gibbard-Satterthwaite impossibility theorems have subexponential size Frege proofs.
This is joint work with Cosmin Bonchiș and Adrian Crăciun.

Active Defense in Cybersecurity
2021-05-26 16:00 - 20:00 | online (via Teams)
Title: Active Defense in Cybersecurity
Speaker: Sergiu Bogdan Meseșan & Andreea Drugă, Cybersecurity Specialists at ENEA

Agenda:

Active Defense Mechanisms – Notions, principles and Active Defense mechanisms (ca.1h)

Practical Application for Honeypot Analytics and Attacks Data Collection – Presentation of a platform implemented by ENEA specially for this lecture, a practical demo of Active Defense (ca.1h)

Active Defense DIY – Workshop installation, running, Internet access for a Honeypot type VM using an open source platform (Telekom Tpot CE) (ca.1h-1.5h)

For the students interested to attend the meeting: please contact Ruxandra Olimid (ruxandra.olimid@fmi.unibuc.ro)

Introduction in Quantum Computing
2026-03-06 09:00 - 10:00 | Facultatea de Matematica si Informatica, sala S.211
Title: Introduction in Quantum Computing
Speaker: Mihai Prunescu (UB)

Abstract: Basing QC notions are presented: superposition, wave-function and probability, qubit, independence, entanglement.

Acknowledgement: This seminar talk is (in part) due to Q-FENCE, Programme HORIZON.2.3 – Civil Security for Society, grant agreement ID: 101225708.

This project has received funding from the European Unions Horizon Europe research and innovation programme under grant agreement No. 101225708 as well as the Swiss State Secretariat for Education, Research and Innovation (SERI).

Introduction in Quantum Computing (II)
2026-03-27 09:00 - 10:00 | Facultatea de Matematica si Informatica, sala S.213
Title: Introduction in Quantum Computing (II)
Speaker: Mihai Prunescu (UB)

Abstract: We continue the discussion on QC.

Acknowledgement: This seminar talk is (in part) due to Q-FENCE, Programme HORIZON.2.3 – Civil Security for Society, grant agreement ID: 101225708.

This project has received funding from the European Unions Horizon Europe research and innovation programme under grant agreement No. 101225708 as well as the Swiss State Secretariat for Education, Research and Innovation (SERI).

Cybersecurity of Industrial Control Systems
2026-04-02 14:00 - 16:00 | 503 PBT
Title: Cybersecurity of Industrial Control Systems
Speaker: Stéphane Mocanu (INRIA)

Abstract: In this talk, we discuss the state of the art of industrial control systems cybersecurity. Based on classical events, we analyse the typical threats and the vulnerabilities that they exploit. In the second part of the talk, we present the security architectures and security practices as recommended by international standards (ISO 27000, IEC 62443) and NIST Cybersecurity Framework).

Introduction in Quantum Computing (III)
2026-04-03 09:00 - 10:00 | Facultatea de Matematica si Informatica, sala S.213
Title: Introduction in Quantum Computing (III)
Speaker: Mihai Prunescu (UB)

Abstract: We continue the discussion on QC.

Acknowledgement: This seminar talk is (in part) due to Q-FENCE, Programme HORIZON.2.3 – Civil Security for Society, grant agreement ID: 101225708.

This project has received funding from the European Unions Horizon Europe research and innovation programme under grant agreement No. 101225708 as well as the Swiss State Secretariat for Education, Research and Innovation (SERI).

Hidden Subgroup Problem
2026-06-15 10:00 - 11:00 | Facultatea de Matematica si Informatica, sala S.213
Title: Hidden subgroup problem
Speaker: Mihai Prunescu (UB)

Abstract:A subgroup H of G = F2 x …. x F2 is implicitly given by a function rho on G. The function rho is constant on classes H+x. A classical quantum algorithm is able to find a generating set of H.

Acknowledgement: This seminar talk is (in part) due to Q-FENCE, Programme HORIZON.2.3 – Civil Security for Society, grant agreement ID: 101225708.

This project has received funding from the European Unions Horizon Europe research and innovation programme under grant agreement No. 101225708 as well as the Swiss State Secretariat for Education, Research and Innovation (SERI).

Making zkSNARKs Non-Malleable
2026-06-23 14:30 - 16:00 | Facultatea de Matematica si Informatica, sala S.512, Romania
Title: Making zkSNARKs Non-Malleable
Speaker: Antonio Faonio (Eurecom)

Abstract: Zero-knowledge SNARKs (zkSNARKs) are cryptographic proof systems that allow a prover to convince a verifier that a statement is true, with very small proofs and fast verification, without revealing the underlying witness. The standard security notion for SNARKs is knowledge soundness, which guarantees that any prover who convinces the verifier must “know” a valid witness. A stronger notion is simulation extractability, which ensures that even an adversary who has seen simulated proofs cannot create a new valid proof without actually knowing a witness, and in particular implies non-malleability. This stronger guarantee is especially important in distributed and adversarial settings, where proof malleability can become a real threat. In this talk, we revisit simulation extractability for universal zkSNARKs in the PIOP-to-SNARK paradigm. We discuss how this property can be achieved and analyzed in systems used in practice, with particular attention to optimizations such as the linearization trick. We also place these results in a broader context, reviewing existing approaches to simulation extractability in the literature and highlighting alternative techniques and trade-offs. The goal is to give a unified and accessible picture of how simulation extractability can be obtained in modern zkSNARK constructions, and what design choices are needed to ensure it in practice.

Acknowledgement: This seminar talk is due to the PATTERN CHIST-ERA project https://chistera-pattern.github.io/ ; https://sites.google.com/unibuc.ro/patternub

PATTERN receives funding from the French National Research Agency under Grant Agreement No. ANR-23-CHR4-0008, the Luxembourg National Fund under Grant Agreement No. INTER/CHIST23/17931746, and the Romanian Ministry of Research, Innovation and Digitization, CNCS/CCCDI – UEFISCDI, project number ERANET-CHISTERA-IV-PATTERN, within PNCDI IV.

Quantum Key Distribution - Transitioning to Future Cryptography
2026-06-29 09:30 - 22:30 | Facultatea de Matematica si Informatica, sala S.512, Romania
Title: Quantum Key Distribution – Transitioning to Future Cryptography
Speaker: Andrei Andries (masterand SAL, UB)

Abstract: The talk discusses Quantum Key Distribution (QKD), which marks the transition from mathematics-based to physics-based cryptography. While QKD is in continuous development, there are still unsolved issues (such as long-distance transmission and hardware limitations).
