arXiv subjects

Carlos Pinzón

Publications and source records attributed to Carlos Pinzón.

13 recordsLinked to original sources

arXiv2026

Dual-Layer Optical Security Framework for Cryptogram Camouflage Using Circular Harmonic Components

Protecting confidential information requires not only preventing unauthorized access to encrypted data but also concealing the very existence of the protected information. In this work, we propose a computational dual-layer optical security framework that integrates optical encryption and steganographic camouflage into a unified strategy. The proposed method is based on a 4F optical architecture and employs two two-dimensional private keys: a phase-only key represented through Circular Harmonic Components (CHC) and a periodic amplitude mask acting as a second secret key. Their combined action generates visually diverse steganograms from encrypted RGB images while preserving the correct recovery of the original information by authorized users. Unlike conventional optical encryption methods that produce easily recognizable cryptograms, the proposed approach disguises the encrypted information within camouflage patterns, providing an additional layer of protection before any decryption process is attempted. Numerical simulations demonstrate successful encryption, camouflage, and image recovery while showing that different steganographic appearances can be generated by modifying the private key and the periodic-mask parameters. Furthermore, a prospective optical implementation based on a Mach--Zehnder interferometer and digital holographic recording is presented, providing a feasible path toward future experimental realization. The proposed methodology is introduced as a proof of concept of the dual-layer optical security framework; a comprehensive cryptanalytic evaluation is beyond the scope of this first study and is left for future work.

physics.optics↗

arXiv2026

Minimal Effort to Consensus (MEC) polarization measure

We introduce the Minimum Effort to Consensus (MEC), a measure that quantifies polarization as resistance to consensus: a population is highly polarized when much effort is needed to bring its members to a common position, and weakly polarized when little is needed. Given an opinion distribution, MEC is the minimum effort required to turn it into a consensus distribution, taken over all consensus points, and it returns both a scalar value and an endogenous optimal consensus point. In the basic case MEC equals the 1-Wasserstein distance (Earth Mover's Distance) to the nearest consensus configuration, so that polarization becomes proximity to maximum disagreement. A two-parameter family with exponents alpha, beta >= 1 writes MEC as a weighted L^beta cost whose weights are the alpha-power of the group masses, recovering mean absolute deviation and variance-like dispersion as special cases and giving alpha and beta natural readings as identification and alienation. We prove a Shifting Away from Consensus principle, by which displacing a whole group's mass away from the optimal consensus point strictly increases polarization, and use it to show that MEC is maximized by the extremal distribution that splits the population equally between the two extremes, establishing that MEC is a polarization measure in the standard sense. We also obtain a Minority Principle and a Tipping Point method, showing that polarization is not monotone in extremism. MEC further satisfies the three axioms of Esteban and Ray with a central-split monotonicity property. Empirically, MEC[2,1.15] attains Kendall's tau near 0.89 against a sixty-expert benchmark, matching the strongest Esteban-Ray parametrization and outperforming the Van der Eijk and Tastle-Wierman measures, and it is computable by bisection in O(n log(1/epsilon)) time.

cs.CY↗

arXiv2026

Information Leakage Envelopes

We study privacy guarantees in the framework of pointwise maximal leakage (PML) that satisfy two requirements: they are robust under post-processing and upper bound the failure probability, i.e., the probability that the information leakage exceeds a given threshold. We first examine two candidate definitions inspired by (approximate) differential privacy and show that neither one satisfies both requirements simultaneously. We then introduce the notion of the PML envelope, which quantifies the largest amount of information leakage about a secret after arbitrary post-processing of a mechanism's output. By construction, the PML envelope satisfies both requirements. We discuss basic structural properties of the envelope, such as monotonicity, and derive general upper and lower bounds. We further analyze the envelope for two widely used privacy mechanisms: the PML-extremal mechanisms in the high-privacy regime and randomized response. Overall, this work establishes the PML envelope as a natural and operationally meaningful definition for providing privacy guarantees that are preserved under arbitrary downstream transformations.

cs.CR↗

arXiv2025

Uniform Distributions on p-Balls and the Singular Role of $p=1,2,\infty$ in p-Norm Geometry

This paper studies the relationship between volume and surface uniform measures on n-dimensional p-balls under the p-norm. It is proved that for p=1, p=2 and p=infinity, and only for these values of p, radial projection maps a volumetrically uniform distribution to a surface-uniform distribution. Algorithms for uniform sampling on p-balls and p-spheres are provided, together with empirical illustrations.

math.ST↗

arXiv2025

Jeffrey's update rule as a minimizer of Kullback-Leibler divergence

In this paper, we show a more concise and high level proof than the original one, derived by researcher Bart Jacobs, for the following theorem: in the context of Bayesian update rules for learning or updating internal states that produce predictions, the relative entropy between the observations and the predictions is reduced when applying Jeffrey's update rule to update the internal state.

stat.ML↗

arXiv2024

Causal Discovery Under Local Privacy

Differential privacy is a widely adopted framework designed to safeguard the sensitive information of data providers within a data set. It is based on the application of controlled noise at the interface between the server that stores and processes the data, and the data consumers. Local differential privacy is a variant that allows data providers to apply the privatization mechanism themselves on their data individually. Therefore it provides protection also in contexts in which the server, or even the data collector, cannot be trusted. The introduction of noise, however, inevitably affects the utility of the data, particularly by distorting the correlations between individual data components. This distortion can prove detrimental to tasks such as causal discovery. In this paper, we consider various well-known locally differentially private mechanisms and compare the trade-off between the privacy they provide, and the accuracy of the causal structure produced by algorithms for causal learning when applied to data obfuscated by these mechanisms. Our analysis yields valuable insights for selecting appropriate local differentially private protocols for causal discovery tasks. We foresee that our findings will aid researchers and practitioners in conducting locally private causal discovery.

cs.CR↗

arXiv2023

Frequency Estimation of Evolving Data Under Local Differential Privacy

Collecting and analyzing evolving longitudinal data has become a common practice. One possible approach to protect the users' privacy in this context is to use local differential privacy (LDP) protocols, which ensure the privacy protection of all users even in the case of a breach or data misuse. Existing LDP data collection protocols such as Google's RAPPOR and Microsoft's dBitFlipPM can have longitudinal privacy linear to the domain size k, which is excessive for large domains, such as Internet domains. To solve this issue, in this paper we introduce a new LDP data collection protocol for longitudinal frequency monitoring named LOngitudinal LOcal HAshing (LOLOHA) with formal privacy guarantees. In addition, the privacy-utility trade-off of our protocol is only linear with respect to a reduced domain size $2\leq g \ll k$. LOLOHA combines a domain reduction approach via local hashing with double randomization to minimize the privacy leakage incurred by data updates. As demonstrated by our theoretical analysis as well as our experimental evaluation, LOLOHA achieves a utility competitive to current state-of-the-art protocols, while substantially minimizing the longitudinal privacy budget consumption by up to k/g orders of magnitude.

cs.CR↗

arXiv2022

Counting and Computing Join-Endomorphisms in Lattices (Revisited)

Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. We study the cardinality of the set $\mathcal{E}(L)$ of all join-endomorphisms of a given finite lattice $L$. In particular, we show for $\mathbf{M}_n$, the discrete order of $n$ elements extended with top and bottom, $| \mathcal{E}(\mathbf{M}_n) | =n!\mathcal{L}_n(-1)+(n+1)^2$ where $\mathcal{L}_n(x)$ is the Laguerre polynomial of degree $n$. We also study the following problem: Given a lattice $L$ of size $n$ and a set $S\subseteq \mathcal{E}(L)$ of size $m$, find the greatest lower bound ${\large\sqcap}_{\mathcal{E}(L)} S$. The join-endomorphism ${\large\sqcap}_{\mathcal{E}(L)} S$ has meaningful interpretations in epistemic logic, distributed systems, and Aumann structures. We show that this problem can be solved with worst-case time complexity in $O(mn)$ for distributive lattices and $O(mn + n^3)$ for arbitrary lattices. In the particular case of modular lattices, we present an adaptation of the latter algorithm that reduces its average time complexity. We provide theoretical and experimental results to support this enhancement. The complexity is expressed in terms of the basic binary lattice operations performed by the algorithm.

cs.MA↗

arXiv2022

On the Computation of Distributed Knowledge as the Greatest Lower Bound of Knowledge

Let $L$ be a finite lattice and $\mathcal{E}(L)$ be the set of join endomorphisms of $L$. We consider the problem of given $L$ and $f,g \in \mathcal{E}(L)$, finding the greatest lower bound $f \sqcap_{{\scriptsize \mathcal{E}(L)}} g$ in the lattice $\mathcal{E}(L)$. (1) We show that if $L$ is distributive, the problem can be solved in time $O(n)$ where $n=| L |$. The previous upper bound was $O(n^2)$. (2) We provide new algorithms for arbitrary lattices and give experimental evidence that they are significantly faster than the existing algorithm. (3) We characterize the standard notion of distributed knowledge of a group as the greatest lower bound of the join-endomorphisms representing the knowledge of each member of the group. (4) We show that deciding whether an agent has the distributed knowledge of two other agents can be computed in time $O(n^2)$ where $n$ is the size of the underlying set of states. (5) For the special case of $S5$ knowledge, we show that it can be decided in time $O(nα_{n})$ where $α_{n}$ is the inverse of the Ackermann function.

cs.MA↗

arXiv2022

Minimizing Information Leakage under Padding Constraints

An attacker can gain information of a user by analyzing its network traffic. The size of transferred data leaks information about the file being transferred or the service being used, and this is particularly revealing when the attacker has background knowledge about the files or services available for transfer. To prevent this, servers may pad their files using a padding scheme, changing the file sizes and preventing anyone from guessing their identity uniquely. This work focuses on finding optimal padding schemes that keep a balance between privacy and the costs of bandwidth increase. We consider Rényi-min leakage as our main measure for privacy, since it is directly related with the success of a simple attacker, and compare our algorithms with an existing solution that minimizes Shannon leakage. We provide improvements to our algorithms in order to optimize average total padding and Shannon leakage while minimizing Rényi-min leakage. Moreover, our algorithms are designed to handle a more general and important scenario in which multiple servers wish to compute padding schemes in a way that protects the servers' identity in addition to the identity of the files.

cs.CR↗

arXiv2022

Causal Discovery for Fairness

It is crucial to consider the social and ethical consequences of AI and ML based decisions for the safe and acceptable use of these emerging technologies. Fairness, in particular, guarantees that the ML decisions do not result in discrimination against individuals or minorities. Identifying and measuring reliably fairness/discrimination is better achieved using causality which considers the causal relation, beyond mere association, between the sensitive attribute (e.g. gender, race, religion, etc.) and the decision (e.g. job hiring, loan granting, etc.). The big impediment to the use of causality to address fairness, however, is the unavailability of the causal model (typically represented as a causal graph). Existing causal approaches to fairness in the literature do not address this problem and assume that the causal model is available. In this paper, we do not make such assumption and we review the major algorithms to discover causal relations from observable data. This study focuses on causal discovery and its impact on fairness. In particular, we show how different causal discovery approaches may result in different causal models and, most importantly, how even slight differences between causal models can have significant impact on fairness/discrimination conclusions. These results are consolidated by empirical analysis using synthetic and standard fairness benchmark datasets. The main goal of this study is to highlight the importance of the causal discovery step to appropriately address fairness using causality.

cs.AI↗

arXiv2021

On the impossibility of non-trivial accuracy under fairness constraints

One of the main concerns about fairness in machine learning (ML) is that, in order to achieve it, one may have to trade off some accuracy. To overcome this issue, Hardt et al. proposed the notion of equality of opportunity (EO), which is compatible with maximal accuracy when the target label is deterministic with respect to the input features. In the probabilistic case, however, the issue is more complicated: It has been shown that under differential privacy constraints, there are data sources for which EO can only be achieved at the total detriment of accuracy, in the sense that a classifier that satisfies EO cannot be more accurate than a trivial (i.e., constant) classifier. In our paper we strengthen this result by removing the privacy constraint. Namely, we show that for certain data sources, the most accurate classifier that satisfies EO is a trivial classifier. Furthermore, we study the trade-off between accuracy and EO loss (opportunity difference), and provide a sufficient condition on the data source under which EO and non-trivial accuracy are compatible.

cs.LG↗

arXiv2019

A Random Network Model for the Analysis of Blockchain Designs with Communication Delay

This paper proposes a random network model for blockchains, a distributed hierarchical data structure of blocks that has found several applications in various industries. The model is parametric on two probability distribution functions governing block production and communication delay, which are key to capture the complexity of the mechanism used to synchronize the many distributed local copies of a blockchain. The proposed model is equipped with simulation algorithms for both bounded and unbounded number of distributed copies of the blockchain. They are used to study fast blockchain systems, i.e., blockchains in which the average time of block production can match the average time of message broadcasting used for blockchain synchronization. In particular, the model and the algorithms are useful to understand efficiency criteria associated with fast blockchains for identifying, e.g., when increasing the block production will have negative impact on the stability of the distributed data structure given the network's broadcast delay.

cs.DC↗