René NDOUNDAM

Comptabilité analytique complète pour le codage par blocs épars : écarts d’indice de Fibonacci et contrôles structurels

Stéphane Gaël R. Ekodeck, Ebele, Serge, Alain, Chantal Marguerite Mveh-Abia, Hervé Talé Kalachi, Norbert Djong Wang, René Ndoundam

HAL (Le Centre pour la Communication Scientifique Directe)

We study complete-stream accounting for static additive block formats through FISA 1.0 (Fibonacci Index-gap Shared Alphabet), a byte-exact test format that amortises one gap alphabet over a stream of blocks. The accounting criterion keeps stream-level framing and model bytes, per-block records, and input size in one auditable inequality; we use it as a measurement discipline rather than as a new coding theorem. FISA, a zero-block bitmap, and a boundary-trim format are evaluated as fully serialized, exactly decodable instances. A retrospective offline portfolio bound reports the smallest measured self-contained stream among these formats and raw storage, yielding ratios of 0.8936 on Canterbury and 0.9774 on Silesia. The FISA transform is proved bijective; a compiled implementation verifies decode round-trips on Canterbury, Silesia, and the 100 MB enwik8 benchmark, and the supplied test suite passes 10,119 cases. Corpus experiments show that 256-byte blocks average about 815.63 Zeckendorf terms, well above the measured favorable range of 326-392 terms: only 3.70% and 1.94% of blocks satisfy the sufficient local gain condition. A controlled Fibonacci-sparsity threshold experiment provides an internal consistency check on that cost model. For streams whose blocks contain at most 200 Zeckendorf terms, FISA reaches ratios of 0.04-0.62 and is smaller than Zstandard level 19, the tested zero-structure controls, and a new complete binary position-gap baseline. Structural controls on standard corpora attribute the observed savings primarily to zero structure rather than to the Fibonacci basis. The resulting contribution is therefore a reproducible account of where an apparently compact positional transform does and does not survive complete serialization.

• #algorithms and data compression
• #advanced database systems and queries
• #parallel computing and optimization techniques
• #portfolio

Contextual Cloud Steganography(CCS): Breaking the Capacity-Security Trade-Off

Stéphane Willy Mossebo Tcheunteu, Leonel Moyou Metcheka, Hervé Talé Kalachi, Stéphane Gael Raymond Ekodeck, René Ndoundam, Alain Tchana

IEEE Transactions on Cloud Computing

The exponential growth of cloud storage adoption has introduced new attack surfaces and privacy concerns, necessitating advanced methods for secure and covert communication. Traditional steganographic techniques, particularly in distributed settings, often struggle with balancing undetectability, embedding capacity, and security. Recent indirect methods that avoid file modification have improved undetectability but remain constrained by low capacity and reliance on cryptographic secrecy alone. This paper introduces Contextual Cloud Steganography (CCS), a novel framework that replaces traditional base-based encoding with contextual protocols based on deterministic file ordering within cloud directories. CCS leverages pre-established sorting criteria (e.g., cryptographic hashes, creation dates) to embed secret data by selecting files from sorted lists, achieving a multiplicative increase in capacity of 3.2× to 4.3× over state-of-the-art base-B methods. The framework simultaneously enhances security through protocol-dependent protection, making message extraction computationally infeasible without the precise contextual protocol, even if the stego-folder is discovered. We provide formal security proofs under established steganographic models, detailed algorithms with cryptographic enhancements, and extensive experimental evaluation across major cloud platforms (Google Drive, Dropbox, OneDrive) over a 30-day period. Results demonstrate CCS's practical efficiency and robustness in dynamic environments, establishing it as a significant advancement in cloud-based covert communication that breaks the traditional capacity-security trade-off.

• #cloud data security solutions
• #advanced steganography and watermarking techniques
• #cryptography and data security
• #cloud computing

DIGITAL EVIDENCE ACQUISITION FOLLOWING MINING AND NETWORK ATTACKS IN A PRIVATE BLOCKCHAIN

Ali Hamadou, René Ndoundam, Abdoul Aziz Issaka Hassane, Mbopgue Timo Patrick Noel

International Journal of Advanced Research

The rapid adoption of blockchain technology has introduced new cybersecurity challenges, particularly in private blockchain environments where mining and network attacks pose significant threats. This study investigates the digital forensics process within private blockchain environments, with a specific focus on methodologies for acquiring digital evidence following mining and network attacks. In this context, we propose two complementary evidence acquisition models applied to Hyperledger Fabric: a post-mortem model using forensic disk imaging and hash verification (dd, sha256sum), and a live acquisition model using Hyperledger Explorer\\\'s REST API. Attack simulations including Denial-of-Service (DoS), 51%, and selfish mining attacks were conducted to validate the proposed models. The proposed models successfully enabled the identification and collection of user-generated and machine-generated evidence, including cryptographic transactions, node event logs, smart contract interactions, and network traffic metadata, while preserving chain of custody integrity. This work contributes a structured, practical methodology for blockchain forensics in private environments, addressing the unique challenges posed by the decentralized and immutable nature of blockchain systems.

• #digital and cyber forensics
• #blockchain technology applications and security
• #cybercrime and law enforcement studies
• #blockchain

Fisher--Rao Geometric Optimization and Detection for Generative Steganographic Transport

Stéphane Gael Raymond Ekodeck, Prosper Rosaire MAMA ASSANDJE, Serge Ebele, St´ephane Willy Mossebo Tcheunteu, Ewane Ulrich Arthur, Damaris Belle M. Fotso and 1 more

Figshare

This supplementary dataset contains the reproducibility code and numerical outputs supporting the manuscript “Fisher--Rao Geometric Optimization and Detection for Generative Steganographic Transport.”<br>The package provides Python scripts for reproducing the numerical simulations reported in the paper. These simulations cover: (i) Fisher--Rao geodesics on Gaussian statistical manifolds, (ii) natural-gradient versus Euclidean-gradient convergence in diagonal and non-diagonal Gaussian families, (iii) comparisons with adaptive optimizers such as Adam and RMSprop, (iv) curvature estimation on Gaussian-mixture statistical manifolds, (v) geodesic versus Euclidean path comparisons, and (vi) local Fisher-ball volume estimation for representative Gaussian-mixture points.<br>The main script `run_all.py` executes the principal simulations S1--S4 in sequence. Individual scripts are also provided for each experiment: `sim_s1_geodesics.py`, `sim_s2_gradient.py`, `sim_s2_nondiagonal.py`, `sim_s2_adaptive_comparison.py`, `sim_s3_curvature.py`, `sim_s4_path_comparison.py`, and `compute_fisher_ball_volumes.py`.<br>The scripts generate CSV data files, PDF figures, and LaTeX tables used to support the manuscript’s numerical claims. In particular, the Fisher-ball volume script estimates local Fisher-ball volumes for a one-dimensional two-component Gaussian mixture model and outputs `fisher_ball_volumes.csv` and `fisher_ball_volumes.tex`.<br>The supplementary material is intended for academic reproducibility of the theoretical and numerical results. The simulations are performed on low-dimensional Gaussian and Gaussian-mixture statistical manifolds and should not be interpreted as an operational benchmark of a complete image-steganography system.

• #advanced steganography and watermarking techniques
• #chaos-based image/signal encryption
• #internet traffic analysis and secure e-voting
• #gaussian

Fisher--Rao Geometric Optimization and Detection for Generative Steganographic Transport

Stéphane Gael Raymond Ekodeck, Prosper Rosaire MAMA ASSANDJE, Serge Ebele, St´ephane Willy Mossebo Tcheunteu, Ewane Ulrich Arthur, Damaris Belle M. Fotso and 1 more

Figshare

This supplementary dataset contains the reproducibility code and numerical outputs supporting the manuscript “Fisher--Rao Geometric Optimization and Detection for Generative Steganographic Transport.”<br>The package provides Python scripts for reproducing the numerical simulations reported in the paper. These simulations cover: (i) Fisher--Rao geodesics on Gaussian statistical manifolds, (ii) natural-gradient versus Euclidean-gradient convergence in diagonal and non-diagonal Gaussian families, (iii) comparisons with adaptive optimizers such as Adam and RMSprop, (iv) curvature estimation on Gaussian-mixture statistical manifolds, (v) geodesic versus Euclidean path comparisons, and (vi) local Fisher-ball volume estimation for representative Gaussian-mixture points.<br>The main script `run_all.py` executes the principal simulations S1--S4 in sequence. Individual scripts are also provided for each experiment: `sim_s1_geodesics.py`, `sim_s2_gradient.py`, `sim_s2_nondiagonal.py`, `sim_s2_adaptive_comparison.py`, `sim_s3_curvature.py`, `sim_s4_path_comparison.py`, and `compute_fisher_ball_volumes.py`.<br>The scripts generate CSV data files, PDF figures, and LaTeX tables used to support the manuscript’s numerical claims. In particular, the Fisher-ball volume script estimates local Fisher-ball volumes for a one-dimensional two-component Gaussian mixture model and outputs `fisher_ball_volumes.csv` and `fisher_ball_volumes.tex`.<br>The supplementary material is intended for academic reproducibility of the theoretical and numerical results. The simulations are performed on low-dimensional Gaussian and Gaussian-mixture statistical manifolds and should not be interpreted as an operational benchmark of a complete image-steganography system.

• #advanced steganography and watermarking techniques
• #chaos-based image/signal encryption
• #internet traffic analysis and secure e-voting
• #gaussian

High embedding capacity text steganography using optimal color combinations from 24-bit space

Stéphane Willy Mossebo Tcheunteu, Hervé Talé Kalachi, Stéphane Gael Raymond Ekodeck, Leonel Moyou Metcheka, Jean Marsien Ayemidie Moto, René Ndoundam

Journal of Computer Security

The texts "only boats catch connotes ..." and "in the research area of text steganography ...." were not coloured in section 6 (Experimental Evaluation) as in the original manuscript.This article introduces a paradigm-shifting approach to text steganography that fundamentally redefines the capacity limits of covert communication through the synergistic integration of combinatorial color optimization and Huffman compression. By exploiting the combinatorial richness of the 24-bit RGB color space enhanced with lossless compression, we present a framework that achieves unprecedented embedding capabilities—reaching up to 400% effective capacity, representing a 17.9 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>×</mml:mo> </mml:math> improvement over state-of-the-art permutation-based method (Sadie et al., 2023) for n <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mo>=</mml:mo> </mml:math> 10 colors. Our methodology combines optimal color subset selection from 16.7 million possibilities with hybrid combinatorial–permutational encoding and Huffman compression, creating exponential growth in steganographic potential while maintaining format compatibility with standard communication channels. Theoretical analysis confirms <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">O</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mn>24</mml:mn> </mml:msup> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mrow> <mml:mi>k</mml:mi> <mml:mi>n</mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy="false">)</mml:mo> </mml:math> complexity scaling with only 12% compression overhead, while experimental validation demonstrates practical implementation achieving 350 to 400% capacity with only 5 to 8% cover text modification. The compression-enhanced scheme establishes new benchmarks for high-capacity steganography, offering robust security against statistical detection through dynamic palette selection, adaptive encoding strategies, and compression-induced entropy redistribution. This work represents a significant advancement in digital covert communication, providing a scalable, efficient solution for modern security requirements while enhancing both capacity and undetectability beyond existing text-based steganographic systems.

• #advanced steganography and watermarking techniques
• #chaos-based image/signal encryption
• #internet traffic analysis and secure e-voting
• #steganography

Stéganographie d'images neuronale sans canal auxiliaire et prenant en compte la fiabilité, avec récupération autonome de la charge utile

Serge Ebele, Stéphane Gaël R. Ekodeck, Chantal Marguerite Mveh-Abia, Batinyuy, Ngeh, Anna, Arthur Ulrich Ewane, René Ndoundam

HAL (Le Centre pour la Communication Scientifique Directe)

<div> Operational side channels remain a practical source of leakage in some high-capacity image steganography systems. WYSAWIS, a recent coverless indexing method, avoids pixel modification but relies on cloud-carried location information for extraction. We investigate a different operating point: CRC-verified payload recovery from one transmitted image without folder positions, block-index lists, or external location metadata. We propose ETHEGAN, an auxiliarychannel-free neural image steganography framework with a self-contained packet layer containing payload length, CRC32 validation, Reed-Solomon parity, deterministic interleaving, and optional reliability-aware erasure decoding. We further add residual-statistics regularization and a lightweight adversarial residual-domain discriminator to reduce visible and statistical embedding artifacts. On fixed 100-image Caltech101 and COCO val2017 clean-channel subsets at 0.25 nominal bpp, corresponding to 0.185546875 effective user bpp after packet and error-correction overhead, ETHEGAN recovers 100/100 Caltech101 payloads and 93/100 COCO payloads exactly after ECC and CRC validation. Increasing Reed-Solomon parity from 64 to 128 bytes per chunk lowers the effective user payload to 0.123046875 bpp and recovers 100/100 payloads on both datasets. Residual-strength and steganalysis-aware ablations preserve 50/50 exact recovery on both 50-image subsets while improving PSNR relative to the initial residual baseline. A lightweight residual/LSB detector remains effective over three grouped train/test splits, with mean test AUC 0.9835 on Caltech101 and 0.8763 on COCO. JPEG compression, blur, and resizing yield 0/20 exact recoveries in both datasets. A conservative low-payload detectability-gated mode at 0.001953125 effective bpp accepts 10/40 candidate images, recovers all accepted payloads, and yields test AUC 0.58 for the lightweight detector and 0.52 for a SPAM-style residual cooccurrence detector. An AES-256-GCM pre-packet encryption wrapper also passes correct-key, wrong-key, and wrong-associated-data authentication tests. The supported contribution is therefore clean-channel, auxiliary-channel-free payload recovery with effective-capacity accounting, optional confidential payload transport, and detector-bounded passive security only in the lowpayload gated mode; robustness remains unsupported. </div>

• #digital media forensic detection
• #advanced steganography and watermarking techniques
• #internet traffic analysis and secure e-voting
• #payload (computing)

VCUFE-IP : Chiffrement fonctionnel à produit interne vérifiable et actualisable pour les transferts de données dans le cloud auditables

Ebele, Serge, Alain, Stéphane Gaël R. Ekodeck, Chantal Marguerite Mveh-Abia, Atangana Amougou, Clément, Marie, Arthur Ulrich Ewane, René Ndoundam

HAL (Le Centre pour la Communication Scientifique Directe)

<div> Ciphertext-updatable functional encryption lets an authorized party convert a ciphertext from one tag to another without decrypting it. This is useful in cloud data-sharing workflows, but existing ciphertext-updatable functional encryption models assume that the update server performs the conversion correctly. In adversarial deployments, a compromised server may return a malformed ciphertext, omit or misapply an update token, or report a forged functional decryption result. We present VCUFE-IP, a verifiable ciphertext-updatable functional encryption construction for bounded inner products. The construction uses asymmetric bilinear groups and separates fresh and updated ciphertexts into two tag-hash levels. Update tokens are vectors of group elements and updates are deterministic, which makes update verification a public recomputation. We additionally give Fiat-Shamir proof systems for ciphertext well-formedness and delegated result correctness. The public transcript authenticates the encryption bases, functional-key view, and update token before checking group equations. The result proof is formulated over public group elements and is bound to the signed verification view of the issued functional key; it does not require the verifier to know discrete logarithms of ciphertext components or the hidden function vector. We prove algebraic correctness, state explicit game-based confidentiality and verifiability reductions, and provide a reference implementation with executable tests over both an exponenttracing backend and a BLS12-381 backend. The artifact also includes symbolic identity checks, an analytical state-of-the-art comparison, BLS12-381 single-dimension and scaling benchmarks, optimized-pairing measurements, container and CI metadata, and a local reproducibility archive prepared for public deposit. </div>

• #cryptography and data security
• #cloud data security solutions
• #cryptographic implementations and security
• #functional encryption

A high-capacity coverless image steganography approach using block-level hash encoding and sequence category mapping: WYSAWIS

Damaris Belle M. Fotso, Serge Ebele, Stéphane Gael Raymond Ekodeck, René Ndoundam

Multimedia Tools and Applications

• #advanced steganography and watermarking techniques
• #digital media forensic detection
• #chaos-based image/signal encryption
• #hash function

Hybrid Approach for Image Processing Based on Convolutional Neural Network in Facial Recognition System

Ibrahim Aoudou Pouamoun, Justin Moskolaï Ngossaha, René Ndoundam, Francis Yongwa Dtissibe, Abdelhak Mourad Gueroui, Ado Adamou Abba Ari

Lecture notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

• #face and expression recognition
• #image and video stabilization
• #advanced image and video retrieval techniques
• #convolutional neural network

Research in Computer Science

Paulin Melatagia Yonta, Kamel Barkaoui, René Ndoundam, Omer-Blaise Yenke

Communications in computer and information science

• #distributed and parallel computing systems
• #parallel computing and optimization techniques
• #computer science
• #visualization

Threshold Circuit Based on Cyclic Codes

Syril Corneille Tchio Tchichelia, Hervé Talé Kalachi, Waku Kouomou Jules, René Ndoundam

SSRN Electronic Journal

• #coding theory and cryptography
• #machine learning and algorithms
• #dna and biological computing
• #code (set theory)

Binary image steganography based on permutation

Juvet Karnel Sadié, Stéphane Gael Raymond Ekodeck, René Ndoundam

Iran Journal of Computer Science

• #advanced steganography and watermarking techniques
• #chaos-based image/signal encryption
• #digital media forensic detection
• #information hiding

Depth of Threshold Circuit

Syril Corneille Tchio Tchichelia, Hervé Talé Kalachi, Jules Waku, René Ndoundam

SSRN Electronic Journal

• #complexity and algorithms in graphs
• #computational geometry and mesh generation
• #advanced graph theory research
• #geology

Combinatorial-based Steganographic Scheme for PDF File Justified Texts

Stephane Ekodeck, Serge Ebele, René Ndoundam

In this paper, we proposed a method that exploits justified texts of PDF files to embed secret data. The method is inspired by the work of Khosravi et al on "A new method for pdf steganography in justified texts" where they proposed a stegosystem allowing to embed in particular lines called a host line, 4 bits of secret message. We've improved it by exposing a combinatorics-based method able not only to embed 7 bits of secret message in these host lines but also b bits (b&lt;14) in any line containing at least n spaces and m added spaces for (m, n &gt; 0), thus allowing a sender to conceal a bigger message with very few changes made to the cover text.&lt;br&gt;

• #advanced steganography and watermarking techniques
• #chaos-based image/signal encryption
• #biometric identification and security
• #steganography

Combinatorial-based Steganographic Scheme for PDF File Justified Texts

Stephane Ekodeck, Serge Ebele, René Ndoundam

In this paper, we proposed a method that exploits justified texts of PDF files to embed secret data. The method is inspired by the work of Khosravi et al on “A new method for pdf steganography in justified texts” where they proposed a stegosystem allowing to embed in particular lines called a host line, 4 bits of secret message. We’ve improved it by exposing a combinatorics-based method able not only to embed 7 bits of secret message in these host lines but also b bits (b&lt;14) in any line containing at least n spaces and m added spaces for (m, n &gt; 0), thus allowing a sender to conceal a bigger message with very few changes made to the cover text.

• #advanced steganography and watermarking techniques
• #chaos-based image/signal encryption
• #biometric identification and security
• #steganography

Binary Image Steganography based on Permutation

Juvet Karnel Sadié, Stéphane Gael Raymond Ekodeck, René Ndoundam

Research Square

Abstract We propose a steganographic scheme based on permutations, which improves the capacity of embedding information in a series of p host binary images. Given a host binary image block of size m x n bits and any embedding technique T, where T can hide Q(m, n) bits of data in the image; given p images, T can hide p x Q(m, n) bits of data in these images. Our scheme improves the capacity of embedding information in p images such that, instead of p x Q(m, n) bits, it can hide p x log 2 (p) + p x Q(m, n)bits. The results which have been obtained by experiments, show that our model performs a better hiding process in terms of hiding capacity.

• #advanced steganography and watermarking techniques
• #chaos-based image/signal encryption
• #digital media forensic detection
• #steganography

Correlation and dimension relevance in multidimensional networks: a systematic taxonomy

Félicité Gamgne Domgue, Norbert Tsopzé, René Ndoundam

Social Network Analysis and Mining

• #complex network analysis techniques
• #opinion dynamics and social influence
• #advanced graph neural networks
• #relevance (law)

A high capacity text steganography scheme based on permutation and color coding.

Juvet Karnel Sadié, Leonel Moyou Metcheka, René Ndoundam

arXiv (Cornell University)

In this paper, we propose a text steganographic scheme based on color coding and permutation. Given a secret message and a cover text, the proposed scheme embed the secret message in the cover text by making it colored, using a permutation algorithm. The stego-text is then send to the receiver by mail. The results which have been obtained by experiments, show that our model performs a better hiding process in terms of hiding capacity as compared to the scheme of Aruna Malik et al. on which our idea is based.

• #advanced steganography and watermarking techniques
• #chaos-based image/signal encryption
• #internet traffic analysis and secure e-voting
• #steganography

Community structure extraction in directed network using triads

Félicité Gamgne Domgue, Norbert Tsopzé, René Ndoundam

International Journal of General Systems

Community detection in directed networks appears as one of the most relevant topics in the field of network analysis. One of the common themes in its formalizations is information flow clustering in a network. Such clusters can be extracted by using triads, expected to play an important role in the detection of that type of communities since communities could be centered round core nodes called kernels. Triads in directed graphs are directed sub-graphs of three nodes involving at least two links between them. To identify communities in directed networks, this paper proposes an in-seed-centric scheme based on directed triads. We also propose a new metric of the communities' quality based on the triad density of communities. To validate our approach, an experiment was conducted on some networks showing it has better performance on triad-based density over some state-of-the-art methods.

• #complex network analysis techniques
• #peer-to-peer network technologies
• #network security and intrusion detection
• #triad (sociology)

An Efficient Data Analysis based Flood Forecasting System (EDAFFS)

Joel Tanzouak, Blaise Omer Yenké, Ndiouma Bame, René Ndoundam

International Journal of Information Technology and Computer Science

• #hydrological forecasting using ai
• #flood risk assessment and management
• #traffic prediction and management techniques
• #computer science

Détection des structures de communautés dans les graphes orientés à partir des triades

Félicité Gamgne Domgue, Norbert Tsopzé, René Ndoundam

HAL (Le Centre pour la Communication Scientifique Directe)

Community detection in directed networks appears as one of the most relevant topics in the field of network analysis. One common theme in some formalizations is that flows should tend to stay within communities and could be centered round core nodes called "kernels". Hence, we expecttriads to play an important role in the detection of that kind of community. Triads for directed graph are directed sub-graphs of 3 nodes involving at least 2 links between them. To identify communities in directed networks, this paper proposes an undirected edge-weighting scheme based on directed triads. We also propose a new metric on quality of the communities that is based on the triad density of communities. To validate our approach, an experiment was conducted on some networks which show that it has better performance on triad-based density over some state-of-the-art methods.

• #complex network analysis techniques
• #advanced clustering algorithms research
• #network security and intrusion detection
• #triad (sociology)

Quaternion-Based Texture Analysis of Multiband Satellite Images: Application to the Estimation of Aboveground Biomass in the East Region of Cameroon

Cedrigue Boris Djiongo Kenfack, Olivier Monga, Serge Moto Mpong, René Ndoundam

Acta Biotheoretica

• #remote sensing in agriculture
• #remote sensing and lidar applications
• #soil geostatistics and mapping
• #quaternion

A Novel Approach of Pseudorandomly sorted list-based Steganography

René Ndoundam, Stéphane Gael Raymond Ekodeck

arXiv (Cornell University)

We propose a new model of steganography based on a list of pseudo-randomly sorted sequences of characters. Given a list $L$ of $m$ columns containing $n$ distinct strings each, with low or no semantic relationship between columns taken two by two, and a secret message $s \in \{0,1\}^*$, our model embeds $s$ in $L$ block by block, by generating, for each column of $L$, a permutation number and by reordering strings contained in it according to that number. Where, letting $l$ be average bit length of a string, the embedding capacity is given by $[(m-1)*log_2(n!-1)/n*l]$. We've shown that optimal efficiency of the method can be obtained with the condition that $(n &gt;&gt; l)$. The results which has been obtained by experiments, show that our model performs a better hiding process than some of the important existing methods, in terms of hiding capacity.

• #advanced steganography and watermarking techniques
• #internet traffic analysis and secure e-voting
• #digital media forensic detection
• #steganography

PDF steganography based on Chinese Remainder Theorem

Stéphane Gael Raymond Ekodeck, René Ndoundam

Journal of Information Security and Applications

• #advanced steganography and watermarking techniques
• #chaos-based image/signal encryption
• #biometric identification and security
• #ascii

Generalized Period-halving Bifurcation of a Neuronal Recurrence Equation.

René Ndoundam, Serge Alain Ebélé

arXiv (Cornell University)

• #neural networks stability and synchronization
• #nonlinear dynamics and pattern formation
• #stochastic dynamics and bifurcation
• #period (music)

PDF Steganography based on Chinese Remainder Theorem

René Ndoundam, Stéphane Gael Raymond Ekodeck

arXiv (Cornell University)

We propose different approaches of PDF files based steganography, essentially based on the Chinese Remainder Theorem. Here, after a cover PDF document has been released from unnecessary A0, a secret message is hidden in it using one of the proposed approaches, making it invisible to common PDF readers, and the file is then transmitted through a non-secure communication channel. Where each of our methods, ensure the condition that the number of inserted A0 is less than the number of characters of the secret message s.

• #advanced steganography and watermarking techniques
• #chaos-based image/signal encryption
• #cryptography and data security
• #chinese remainder theorem

DISTANCE PRESERVING SUBTREES IN MINIMUM AVERAGE DISTANCE SPANNING TREES

Laurent Lyaudet, Paulin Melatagia Yonta, Maurice Tchuenté, René Ndoundam

Discrete Mathematics Algorithms and Applications

Given an undirected graph G = (V, E) with n vertices and a positive length w(e) on each edge e ∈ E, we consider Minimum Average Distance (MAD) spanning trees i.e., trees that minimize the path length summed over all pairs of vertices. One of the first results on this problem is due to Wong who showed in 1980 that a Distance Preserving (DP) spanning tree rooted at the median of G is a 2-approximate solution. On the other hand, Dankelmann has exhibited in 2000 a class of graphs where no MAD spanning tree is distance preserving from a vertex. We establish here a new relation between MAD and DP trees in the particular case where the lengths are integers. We show that in a MAD spanning tree of G, each subtree H′ = (V′, E′) consisting of a vertex [Formula: see text] and the union of branches of [Formula: see text] that are each of size less than or equal to [Formula: see text], where w + is the maximum edge-length in G, is a distance preserving spanning tree of the subgraph of G induced by V′.

• #advanced graph theory research
• #graph theory and applications
• #graph labeling and dimension problems
• #combinatorics

Collision-resistant hash function based on composition of functions

René Ndoundam, Juvet Karnel Sadié

Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées

A cryptographic hash function is a deterministic procedure that compresses an arbitrary block of numerical data and returns a fixed-size bit string. There exists many hash functions: MD5, HAVAL, SHA, ... It was reported that these hash functions are no longer secure. Our work is focused on the construction of a new hash function based on composition of functions. The construction used the NP-completeness of Three-dimensional contingency tables and the relaxation of the constraint that a hash function should also be a compression function. Une fonction de hachage cryptographique est une procédure déterministe qui compresse un ensemble de données numériques de taille arbitraire en une chaîne de bits de taille fixe. Il existe plusieurs fonctions de hachage : MD5, HAVAL, SHA... Il a été reporté que ces fonctions de hachagene sont pas sécurisées. Notre travail a consisté à la construction d’une nouvelle fonction de hachage basée sur une composition de fonctions. Cette construction utilise la NP-completude des tables de contingence de dimension 3 et une relaxation de la contrainte selon laquelle une fonction de hachage doit être aussi une fonction de compression.

• #cryptographic implementations and security
• #cryptography and data security
• #coding theory and cryptography
• #hash function

MODELING AND ANALYSIS OF HIV AND HEPATITIS C CO-INFECTIONS

Dany Pascal Moualeu-Ngangue, Joseph Mbang, René Ndoundam, Samuel Bowong

Journal of Biological Systems

Infection with the hepatitis C virus (HCV) is the most common coinfection in people with the human immunodeficiency virus (HIV), and hepatitis C is categorized as an HIV-related illness. The study of the joint dynamics of HIV and HCV present formidable mathematical challenges in spite the fact that they share similar routes of transmission. A deterministic model for the co-interaction of HCV and HIV in a community is presented and rigorously analyzed. The disease-free equilibrium is shown to be locally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than the unity. The Centre Manifold theory is used to show that the HCV only and HIV/AIDS only endemic equilibria are locally asymptotically stable when their associated reproduction numbers are greater than the unity. We compute two coexistence thresholds for the stability of boundary equilibria. Numerical results are presented to validate analytical results.

• #mathematical and theoretical epidemiology and ecology models
• #hepatitis c virus research
• #covid-19 epidemiological studies
• #coinfection

Hash function based on arithmetic coding and public-key cryptography

René Ndoundam, Juvet Karnel Sadié, Nguembu, Patrick Nguening

arXiv (Cornell University)

We propose a hash function based on arithmetic coding and public-key cryptography. The resistance of the hash function to second preimage attack, collision and differential cryptanalysis is based on the properties of arithmetic coding as a non-linear dynamical system. The resistance of the hash function to first preimage attack is based on the public-key cryptography. The new hash function uses the strength of HMAC with the difference that it didn't need a secret key for calculating the hash (in this step, it uses one, two or three public -keys) and in the classical attack, an adversary need to break the public key algorithm or to have all the secret keys to perform his attack.

• #chaos-based image/signal encryption
• #cryptographic implementations and security
• #coding theory and cryptography
• #hash function

Parallel Chip Firing Game associated with n-cube orientations

René Ndoundam, Maurice Tchuenté, Claude Tadonki

arXiv (Cornell University)

We study the cycles generated by the chip firing game associated with n-cube orientations. We show the existence of the cycles generated by parallel evolutions of even lengths from 2 to $2^n$ on $H_n$ (n &gt;= 1), and of odd lengths different from 3 and ranging from 1 to $2^{n-1}-1$ on $H_n$ (n &gt;= 4).

• #mathematical dynamics and fractals
• #computability, logic, ai algorithms
• #theoretical and computational physics
• #cube (algebra)

Opinion dynamics using majority functions

Paulin Melatagia Yonta, René Ndoundam

Mathematical Social Sciences

• #opinion dynamics and social influence
• #complex network analysis techniques
• #mathematical and theoretical epidemiology and ecology models
• #convergence (economics)

Non realization of a Boolean function by polynomial-size unbounded fan-in circuits of AND and MOD{sub 6} gates

René Ndoundam, Departement d'Informatique

We show the existence of a linear threshold function on n Boolean variables that cannot be computed by a polynomial size unbounded fan-in circuits of AND and MOD6 gates.

• #quantum computing algorithms and architecture
• #machine learning and algorithms
• #low-power high-performance vlsi design
• #boolean function

Réseaux d'Automates de Caianiello Revisité

René Ndoundam, Maurice Tchuenté

arXiv (Cornell University)

We exhibit a family of neural networks of McCulloch and Pitts of size $2nk+2$ which can be simulated by a neural networks of Caianiello of size $2n+2$ and memory length $k$. This simulation allows us to find again one of the result of the following article: [Cycles exponentiels des réseaux de Caianiello et compteurs en arithmétique redondante, Technique et Science Informatiques Vol. 19, pages 985-1008] on the existence of neural networks of Caianiello of size $2n+2$ and memory length $k$ which describes a cycle of length $k \times 2^{nk}$.

• #semigroups and automata theory
• #algorithms and data compression
• #advanced combinatorial mathematics
• #humanities

Exponential Period of Neuronal Recurrence Automata with Excitatory Memory

Electronic mail address: ndoundam@uycdc.uninet.cm., René Ndoundam, Maurice Tchuenté

Complex Systems

The sequences generated by a neuronal recurrence equation with memory of the form x ⁡ ( n ) = 1 [ ∑ i = 1 h a i ⁢ x ⁡ ( n - i ) - θ ] , where h is the size of the memory, are studied. It is shown that in the case where all the parameters ( a i ) 1 ≤ i ≤ h are positive reals, there exists a neuronal recurrence equation of memory length h that generates a sequence of period Ω ⁡ ( e h ⁡ ( ln ⁡ ( h ) ) 2 3 ) . This result shows that in the case where all the weighting coefficients are positive reals, the neuronal recurrence equation exhibits a complex behavior.

• #advanced memory and neural computing
• #cellular automata and applications
• #dna and biological computing
• #period (music)

Parallel Chip Firing Game Associated with n-cube Edges Orientations

René Ndoundam, Claude Tadonki, Maurice Tchuenté

Lecture notes in computer science

• #mathematical dynamics and fractals
• #computability, logic, ai algorithms
• #cellular automata and applications
• #cube (algebra)

Exponential transient length generated by a neuronal recurrence equation

René Ndoundam, Maurice Tchuenté

Theoretical Computer Science

• #neural dynamics and brain function
• #receptor mechanisms and signaling
• #neural networks and applications
• #transient (computer programming)

Cyclic Evolution of Neuronal Automata with Memory When All the Weighting Coefficients are Strictly Positive.

René Ndoundam, Martı́n Matamala

Complex Systems

In this paper we study the sequences generated by a neuronal equation of the form xn 1[!ki1 aixn#i # Θ], where k is the size of the memory. We show that in the case where all the parameters (ai)1%i%k are strictly positive reals and k is a multiple of 6 (i.e., k 6m), there exists a subset B w first, for all integer m greater than or equal to 3, we exhibit a neuronal recurrence equation of memory length 2k with weighting coefficients that are all strictly positive and which generates a sequence of period 2(3m # 1)(3m # 2); and second, for all odd integer m greater than or equal to 5, we exhibit a neuronal equation of memory length 3k with strictly positive weighting coefficients that generates a sequence of period 3(3m # 1)(3m # 2)(3m # 4).

• #receptor mechanisms and signaling
• #neural networks and applications
• #ferroelectric and negative capacitance devices
• #weighting

No Polynomial Bound for the Period of Neuronal Automata with Inhibitory Memory.

René Ndoundam, Martı́n Matamala

We study the sequences generated by a neuronal equation with memory of the form xn = 1 [ Pk i=1 aixn−i−θ], where k is the size of the memory. We show that in the case where all the parameters (ai)1≤i≤k are negative real numbers, there exists a neuronal equation of memory length k that generates a sequence of period e Ω( √ klogk). This result shows that in the case where all weighting coefficients are negative, the neuronal recurrence equation exhibits a complex behavior. 1

• #semigroups and automata theory
• #cellular automata and applications
• #computability, logic, ai algorithms
• #period (music)

No polynomial bound for the period of the parallel chip firing game on graphs

Marcos Kiwi, René Ndoundam, Maurice Tchuenté, E. Goles

Theoretical Computer Science

• #stochastic processes and statistical mechanics
• #theoretical and computational physics
• #mathematical dynamics and fractals
• #node (physics)