arXiv subjects

Pascal Lafourcade

Publications and source records attributed to Pascal Lafourcade.

16 recordsLinked to original sources

arXiv2026

Lozenge Tiling by Computing Distances

The Calisson puzzle is a tiling puzzle in which one must tile a triangular grid inside a hexagon with lozenges, under the constraint that certain prescribed edges remain tile boundaries and that adjacent lozenges along these edges have different orientations. We present the first polynomial-time algorithm for this problem, with cubic running time. This algorithm, called the advancing surface algorithm, can be executed in a simple and intuitive way, even by hand with a pencil and an eraser. Its apparent simplicity conceals a deeper algorithmic reinterpretation of the classical ideas of John Conway and William Thurston, revisited here from a theoretical computer science perspective. We introduce a graph-theoretic overlay based on directed cuts and systems of difference constraints that complements Thurston's theory of lozenge tilings and makes its algorithmic structure explicit. In Thurston's approach, lozenge tilings are lifted to monotone stepped surfaces in the three-dimensional cubic lattice and projected back to the plane using height functions, reducing tilability to the computation of heights. We show that selecting a monotone surface corresponds to selecting a directed cut in a periodic directed graph, while height functions arise as solutions of a system of difference constraints. In this formulation, a region is tilable if and only if the associated weighted directed graph contains no cycle of strictly negative weight. This additional graph layer shows that the Bellman-Ford algorithm suffices to decide feasibility and compute solutions. In particular, our framework allows one to decide whether the infinite triangular grid can be tiled while respecting a finite set of prescribed local constraints, even in the absence of boundary conditions.

cs.CG↗

arXiv2024

Accuracy Limits as a Barrier to Biometric System Security

Biometric systems are widely used for identity verification and identification, including authentication (i.e., one-to-one matching to verify a claimed identity) and identification (i.e., one-to-many matching to find a subject in a database). The matching process relies on measuring similarities or dissimilarities between a fresh biometric template and enrolled templates. The False Match Rate FMR is a key metric for assessing the accuracy and reliability of such systems. This paper analyzes biometric systems based on their FMR, with two main contributions. First, we explore untargeted attacks, where an adversary aims to impersonate any user within a database. We determine the number of trials required for an attacker to successfully impersonate a user and derive the critical population size (i.e., the maximum number of users in the database) required to maintain a given level of security. Furthermore, we compute the critical FMR value needed to ensure resistance against untargeted attacks as the database size increases. Second, we revisit the biometric birthday problem to evaluate the approximate and exact probabilities that two users in a database collide (i.e., can impersonate each other). Based on this analysis, we derive both the approximate critical population size and the critical FMR value needed to bound the likelihood of such collisions occurring with a given probability. These thresholds offer insights for designing systems that mitigate the risk of impersonation and collisions, particularly in large-scale biometric databases. Our findings indicate that current biometric systems fail to deliver sufficient accuracy to achieve an adequate security level against untargeted attacks, even in small-scale databases. Moreover, state-of-the-art systems face significant challenges in addressing the biometric birthday problem, especially as database sizes grow.

cs.CR↗

arXiv2023

The Calissons Puzzle

In 2022, Olivier Longuet, a French mathematics teacher, created a game called the \textit{calissons puzzle}. Given a triangular grid in a hexagon and some given edges of the grid, the problem is to find a calisson tiling such that no input edge is overlapped and calissons adjacent to an input edge have different orientations. We extend the puzzle to regions $R$ that are not necessarily hexagonal. The first interesting property of this puzzle is that, unlike the usual calisson or domino problems, it is solved neither by a maximal matching algorithm, nor by Thurston's algorithm. This raises the question of its complexity. We prove that if the region $R$ is finite and simply connected, then the puzzle can be solved by an algorithm that we call the \textit{advancing surface algorithm} and whose complexity is $O(|\partial R|^3)$ where $\partial R|$ is the size of the boundary of the region $R$. In the case where the region is the entire infinite triangular grid, we prove that the existence of a solution can be solved with an algorithm of complexity $O(|X|^3)$ where $X$ is the set of input edges. To prove these theorems, we revisit William Thurston's results on the calisson tilability of a region $R$. The solutions involve equivalence between calisson tilings, stepped surfaces and certain DAG cuts that avoid passing through a set of edges that we call \textit{unbreakable}. It allows us to generalize Thurston's theorem characterizing tilable regions by rewriting it in terms of descending paths or absorbing cycles. Thurston's algorithm appears as a distance calculation algorithm following Dijkstra's paradigm. The introduction of a set $X$ of interior edges introduces negative weights that force a Bellman-Ford strategy to be preferred. These results extend Thurston's legacy by using computer science structures and algorithms.

cs.CG↗

arXiv2023

Conflict Optimization for Binary CSP Applied to Minimum Partition into Plane Subgraphs and Graph Coloring

CG:SHOP is an annual geometric optimization challenge and the 2022 edition proposed the problem of coloring a certain geometric graph defined by line segments. Surprisingly, the top three teams used the same technique, called conflict optimization. This technique has been introduced in the 2021 edition of the challenge, to solve a coordinated motion planning problem. In this paper, we present the technique in the more general framework of binary constraint satisfaction problems (binary CSP). Then, the top three teams describe their different implementations of the same underlying strategy. We evaluate the performance of those implementations to vertex color not only geometric graphs, but also other types of graphs.

cs.CG↗

arXiv2022

Near-collisions and their Impact on Biometric Security

Biometric recognition encompasses two operating modes. The first one is biometric identification which consists in determining the identity of an individual based on her biometrics and requires browsing the entire database (i.e., a 1:N search). The other one is biometric authentication which corresponds to verifying claimed biometrics of an individual (i.e., a 1:1 search) to authenticate her, or grant her access to some services. The matching process is based on the similarities between a fresh and an enrolled biometric template. Considering the case of binary templates, we investigate how a highly populated database yields near-collisions, impacting the security of both the operating modes. Insight into the security of binary templates is given by establishing a lower bound on the size of templates and an upper bound on the size of a template database depending on security parameters. We provide efficient algorithms for partitioning a leaked template database in order to improve the generation of a master-template-set that can impersonates any enrolled user and possibly some future users. Practical impacts of proposed algorithms are finally emphasized with experimental studies.

cs.CR↗

arXiv2021

Authentication Attacks on Projection-based Cancelable Biometric Schemes

Cancelable biometric schemes aim at generating secure biometric templates by combining user specific tokens, such as password, stored secret or salt, along with biometric data. This type of transformation is constructed as a composition of a biometric transformation with a feature extraction algorithm. The security requirements of cancelable biometric schemes concern the irreversibility, unlinkability and revocability of templates, without losing in accuracy of comparison. While several schemes were recently attacked regarding these requirements, full reversibility of such a composition in order to produce colliding biometric characteristics, and specifically presentation attacks, were never demonstrated to the best of our knowledge. In this paper, we formalize these attacks for a traditional cancelable scheme with the help of integer linear programming (ILP) and quadratically constrained quadratic programming (QCQP). Solving these optimization problems allows an adversary to slightly alter its fingerprint image in order to impersonate any individual. Moreover, in an even more severe scenario, it is possible to simultaneously impersonate several individuals.

cs.CR↗

arXiv2021

Shadoks Approach to Low-Makespan Coordinated Motion Planning

This paper describes the heuristics used by the Shadoks team for the CG:SHOP 2021 challenge. This year's problem is to coordinate the motion of multiple robots in order to reach their targets without collisions and minimizing the makespan. It is a classical multi agent path finding problem with the specificity that the instances are highly dense in an unbounded grid. Using the heuristics outlined in this paper, our team won first place with the best solution to 202 out of 203 instances and optimal solutions to at least 105 of them. The main ingredients include several different strategies to compute initial solutions coupled with a heuristic called Conflict Optimizer to reduce the makespan of existing solutions.

cs.CG↗

arXiv2020

A Faster Cryptographer's Conspiracy Santa

In Conspiracy Santa, a variant of Secret Santa, a group of people offer each other Christmas gifts, where each member of the group receives a gift from the other members of the group. To that end, the members of the group form conspiracies, to decide on appropriate gifts, and usually divide the cost of each gift among all participants of that conspiracy. This requires to settle the shared expenses per conspiracy, so Conspiracy Santa can actually be seen as an aggregation of several shared expenses problems. First, we show that the problem of finding a minimal number of transaction when settling shared expenses is NP-complete. Still, there exist good greedy approximations. Second, we present a greedy distributed secure solution to Conspiracy Santa. This solution allows a group of n people to share the expenses for the gifts in such a way that no participant learns the price of his gift, but at the same time notably reduces the number of transactions to 2 $\times$ n + 1 with respect to a na{\"i}ve aggregation of n $\times$ (n -- 2). Furthermore, our solution does not require a trusted third party, and can either be implemented physically (the participants are in the same room and exchange money using envelopes) or, over Internet, using a cryptocurrency.

cs.CR↗

arXiv2020

Optimal Threshold Padlock Systems

In 1968, Liu described the problem of securing documents in a shared secret project. In an example, at least six out of eleven participating scientists need to be present to open the lock securing the secret documents. Shamir proposed a mathematical solution to this physical problem in 1979, by designing an efficient $k$-out-of-$n$ secret sharing scheme based on Lagrange's interpolation. Liu and Shamir also claimed that the minimal solution using physical locks is clearly impractical and exponential in the number of participants. In this paper we relax some implicit assumptions in their claim and propose an optimal physical solution to the problem of Liu that uses physical padlocks, but the number of padlocks is not greater than the number of participants. Then, we show that no device can do better for $k$-out-of-$n$ threshold padlock systems as soon as $k\geq{\sqrt{2n}}$, which holds true in particular for Liu's example. More generally, we derive bounds required to implement any threshold system and prove a lower bound of $\mathcal{O}{\log(n)}$ padlocks for any threshold larger than $2$. For instance we propose an optimal scheme reaching that bound for $2$-out-of-$n$ threshold systems and requiring less than $2\log_2(n)$ padlocks. We also discuss more complex access structures, a wrapping technique, and other sublinear realizations like an algorithm to generate $3$-out-of-$n$ systems with $2.5\sqrt{n}$ padlocks. Finally we give an algorithm building $k$-out-of-$n$ threshold padlock systems with only $\mathcal{O}{\log(n)^{k-1}}$ padlocks. Apart from the physical world, our results also show that it is possible to implement secret sharing over small fields.

cs.CR↗

arXiv2019

Infinite Grid Exploration by Disoriented Robots

We deal with a set of autonomous robots moving on an infinite grid. Those robots are opaque, have limited visibility capabilities, and run using synchronous Look-Compute-Move cycles. They all agree on a common chirality, but have no global compass. Finally, they may use lights of different colors, but except from that, robots have neither persistent memories, nor communication mean. We consider the infinite grid exploration (IGE) problem. For this problem we give two impossibility results and three algorithms, including one which is optimal in terms of number of robots. In more detail, we first show that two robots are not sufficient in our settings to solve the problem, even when robots have a common coordinate system. We then show that if the robots' coordinate systems are not self-consistent, three or four robots are not sufficient to solve the problem. Finally, we present three algorithms that solve the IGE problem in various settings. The first algorithm uses six robots with constant colors and a visibility range of one. The second one uses the minimum number of robots, i.e., five, as well as five modifiable colors, still under visibility one. The last algorithm requires seven oblivious anonymous robots, yet assuming visibility two. Notice that the two last algorithms also satisfy achieve exclusiveness.

cs.DC↗

arXiv2016

Private Multi-party Matrix Multiplication and Trust Computations

This paper deals with distributed matrix multiplication. Each player owns only one row of both matrices and wishes to learn about one distinct row of the product matrix, without revealing its input to the other players. We first improve on a weighted average protocol, in order to securely compute a dot-product with a quadratic volume of communications and linear number of rounds. We also propose a protocol with five communication rounds, using a Paillier-like underlying homomorphic public key cryptosystem, which is secure in the semi-honest model or secure with high probability in the malicious adversary model. Using ProVerif, a cryptographic protocol verification tool, we are able to check the security of the protocol and provide a countermeasure for each attack found by the tool. We also give a randomization method to avoid collusion attacks. As an application, we show that this protocol enables a distributed and secure evaluation of trust relationships in a network, for a large class of trust evaluation schemes.

cs.CR↗

arXiv2016

Physical Zero-Knowledge Proofs for Akari, Takuzu, Kakuro and KenKen

Akari, Takuzu, Kakuro and KenKen are logic games similar to Sudoku. In Akari, a labyrinth on a grid has to be lit by placing lanterns, respecting various constraints. In Takuzu a grid has to be filled with 0's and 1's, while respecting certain constraints. In Kakuro a grid has to be filled with numbers such that the sums per row and column match given values; similarly in KenKen a grid has to be filled with numbers such that in given areas the product, sum, difference or quotient equals a given value. We give physical algorithms to realize zero-knowledge proofs for these games which allow a player to show that he knows a solution without revealing it. These interactive proofs can be realized with simple office material as they only rely on cards and envelopes. Moreover, we formalize our algorithms and prove their security.

cs.CR↗

arXiv2012

Brandt's Fully Private Auction Protocol Revisited

Auctions have a long history, having been recorded as early as 500 B.C. Nowadays, electronic auctions have been a great success and are increasingly used. Many cryptographic protocols have been proposed to address the various security requirements of these electronic transactions, in particular to ensure privacy. Brandt developed a protocol that computes the winner using homomorphic operations on a distributed ElGamal encryption of the bids. He claimed that it ensures full privacy of the bidders, i.e. no information apart from the winner and the winning price is leaked. We first show that this protocol -- when using malleable interactive zero-knowledge proofs -- is vulnerable to attacks by dishonest bidders. Such bidders can manipulate the publicly available data in a way that allows the seller to deduce all participants' bids. Additionally we discuss some issues with verifiability as well as attacks on non-repudiation, fairness and the privacy of individual bidders exploiting authentication problems.

cs.CR↗

arXiv2010

Benaloh's Dense Probabilistic Encryption Revisited

In 1994, Josh Benaloh proposed a probabilistic homomorphic encryption scheme, enhancing the poor expansion factor provided by Goldwasser and Micali's scheme. Since then, numerous papers have taken advantage of Benaloh's homomorphic encryption function, including voting schemes, computing multi-party trust privately, non-interactive verifiable secret sharing, online poker... In this paper we show that the original description of the scheme is incorrect, possibly resulting in ambiguous decryption of ciphertexts. We give a corrected description of the scheme and provide a complete proof of correctness. We also compute the probability of failure of the original scheme. Finally we analyze several applications using Benaloh's encryption scheme. We show in each case the impact of a bad choice in the key generation phase of Benaloh's scheme. For instance in the application of e-voting protocol, it can inverse the result of an election, which is a non negligible consequence.

cs.CR↗

arXiv2010

How to prevent type-flaw attacks on security protocols under algebraic properties

Type-flaw attacks upon security protocols wherein agents are led to misinterpret message types have been reported frequently in the literature. Preventing them is crucial for protocol security and verification. Heather et al. proved that tagging every message field with it's type prevents all type-flaw attacks under a free message algebra and perfect encryption system. In this paper, we prove that type-flaw attacks can be prevented with the same technique even under the ACUN algebraic properties of XOR which is commonly used in "real-world" protocols such as SSL 3.0. Our proof method is general and can be easily extended to other monoidal operators that possess properties such as Inverse and Idempotence as well. We also discuss how tagging could be used to prevent type-flaw attacks under other properties such as associativity of pairing, commutative encryption, prefix property and homomorphic encryption.

cs.CR↗

arXiv2008

The NAO humanoid: a combination of performance and affordability

This article presents the design of the autonomous humanoid robot called NAO that is built by the French company Aldebaran-Robotics. With its height of 0.57 m and its weight about 4.5 kg, this innovative robot is lightweight and compact. It distinguishes itself from its existing Japanese, American, and other counterparts thanks to its pelvis kinematics design, its proprietary actuation system based on brush DC motors, its electronic, computer and distributed software architectures. This robot has been designed to be affordable without sacrificing quality and performance. It is an open and easy-to-handle platform where the user can change all the embedded system software or just add some applications to make the robot adopt specific behaviours. The robot's head and forearms are modular and can be changed to promote further evolution. The comprehensive and functional design is one of the reasons that helped select NAO to replace the AIBO quadrupeds in the 2008 RoboCup standard league.

cs.RO↗