arXiv subjects

Regis Freguin Babindamana

Publications and source records attributed to Regis Freguin Babindamana.

4 recordsLinked to original sources

arXiv2026

GuardSec: A Multi-Modal Web Platform for Real-Time Digital Fraud Detection, Entity Verification, and Connection Security Analysis in the African Context

Online fraud in Africa has reached an epidemic scale. The few cybersecurity tools that exist are out of reach for ordinary citizens, built almost exclusively for SOC analysts and technically literate users sitting on stable broadband. That mismatch isn't accidental. It's what happens when a research culture rewards benchmark numbers and treats deployability, accessibility, and local threat context as someone else's problem. We present \textit{GuardSec}, a production-deployed web platform for real-time multi-modal threat verification, built from the start around the African user. Anyone with a browser can assess the legitimacy of URLs, websites, phone numbers, email addresses, and business entities in under five seconds. No registration. No API key. No prerequisite knowledge of cybersecurity. The platform's most distinctive component is \textit{Mon Empreinte} (My Footprint), a real-time audit of the user's own connection and digital exposure: it analyses the visitor's IP address, geolocation, ISP identity, connection type, device fingerprint, browser configuration, and twelve security indicators covering network integrity, tracking exposure, and anonymisation status. With this in hand, GuardSec becomes more than a passive checker; the user can see whether their own connection is being tracked or exposed, not just whether some external entity is dangerous. The platform also embeds \textit{Gilda}, a context-aware conversational security assistant that answers questions about digital threats in plain language and offers personalised recommendations on demand.

cs.CR↗

arXiv2025

Integer Factorization: Another perspective

Integer factorization is a fundamental problem in algorithmic number theory and computer science. It is considered as a one way or trapdoor function in the (RSA) cryptosystem. To date, from elementary trial division to sophisticated methods like the General Number Field Sieve, no known algorithm can break the problem in polynomial time, while its proved that Shor's algorithm could on a quantum computer. In this paper, we recall some factorization algorithms and then approach the problem under different angles. Firstly, we take the problem from the ring $\displaystyle\left(\mathbb{Z}, \text{+}, \cdot\right)$ to the Lebesgue space $\mathcal{L}^{1}\left(X\right)$ where $X$ can be $\mathbb{Q}$ or any given interval setting. From this first perspective, integer factorization becomes equivalent to finding the perimeter of a rectangle whose area is known. In this case, it is equivalent to either finding bounds of integrals or finding primitives for some given bounds. Secondly, we take the problem from the ring $\displaystyle\left(\mathbb{Z}, \text{+}, \cdot\right) $ to the ring of matrices $\left( M_{2}\text{(}\mathbb{Z}\text{)}, \ \text{+} \ \cdot\right)$ and show that this problem is equivalent to matrix decomposition, and therefore present some possible computing algorithms, particularly using Gröbner basis and through matrix diagonalization. Finally, we address the problem depending on algebraic forms of factors and show that this problem is equivalent to finding small roots of a bivariate polynomial through coppersmith's method. The aim of this study is to propose innovative methodological approaches to reformulate this problem, thereby offering new perspectives.

math.NT↗

arXiv2023

A Continued Fraction-Hyperbola based Attack on RSA cryptosystem

In this paper we present new arithmetical and algebraic results following the work of Babindamana and al. on hyperbolas and describe in the new results an approach to attacking a RSA-type modulus based on continued fractions, independent and not bounded by the size of the private key $d$ nor the public exponent $e$ compared to Wiener's attack. When successful, this attack is bounded by $\displaystyle\mathcal{O}\left( b\log{α_{j4}}\log{(α_{i3}+α_{j3})}\right)$ with $b=10^{y}$, $α_{i3}+α_{j3}$ a non trivial factor of $n$ and $α_{j4}$ such that $(n+1)/(n-1)=α_{i4}/α_{j4}$. The primary goal of this attack is to find a point $\displaystyle X_α=\left(-α_{3}, \ α_{3}+1 \right) \in \mathbb{Z}^{2}_{\star}$ that satisfies $\displaystyle\left\langle X_{α_{3}}, \ P_{3} \right\rangle =0$ from a convergent of $\displaystyle\frac{α_{i4}}{α_{j4}}+δ$, with $P_{3}\in \mathcal{B}_{n}(x, y)_{\mid_{x\geq 4n}}$. We finally present some experimental examples. We believe these results constitute a new direction in RSA Cryptanalysis using continued fractions independently of parameters $e$ and $d$.

cs.CR↗

arXiv2023

A New Hyperbola based Approach to factoring Integers

From the results in the literature, the algebraic set of the hyperbola with parameter $n$ defined by $\mathcal{B}_{n}(X, Y, Z)_{\mid_{x\geq 4n}}= \displaystyle \lbrace \left(X: Y: Z\right)\in \mathbb{P}^{2}(\mathbb{Q}) \ \vert \ \displaystyle Y^{2}=X^{2}-4nXZ \rbrace$ where $n$ is a semiprime is proved to be in relation with prime factors of $n$. In the affine space over $\mathbb{Z}_{\geqslant 4n}\times \mathbb{Z}_{\geqslant 0}$, this set has exactly 5 points $\displaystyle\lbrace P_{0}, P_{1}, P_{2}, P_{3}, P_{4} \rbrace$ with $P_{2}+P_{3}=P_{1}+2P_{2}=P_{4}$ for which knowledge of $P_{2}$ or $P_{3}$ yields the factorization of $n$. However, The non cyclicity of this group structure over rationals and integers and moreover its non good reduction over finite fields constitute the main difficulty in finding its solutions. In this paper we describe an approach to finding $P_{2}$ and $P_{3}$. We introduce the concept of Hyperbola X-root and Y-root that the solution's greatest common divisors with $n$ reveal prime factors of $n$. We prove that $P_{2}$ and $P_{3}$ can be found on a singular Weierstrass curve isomorphic to a Jacobi quartic using the Hyperbola X-root and Y-root. We present the mathematical framework for this approach.

math.NT↗