arXiv subjects

Nikos E. Mastorakis

Publications and source records attributed to Nikos E. Mastorakis.

4 recordsLinked to original sources

arXiv2026

Methods to Find Integer Points on the Elliptic Curve of Factorizable Polynomial Equation

As a valuable theoretical and application problem, the integer points on two types of elliptic curve y^2=(x-a)(x-b)(x-c) and y^2 = (x-a)(x^2+ax+b) are studied. By using elementary number theory method, the solution of the original equations is reduced to the solution of simultaneous Pell equations or generalized Pell equation, which can improve the efficiency in searching integer solutions by computer. Effective methods are proposed to find the integer solutions of the equations, which are convenient for algorithm programming implementation. At the same time, the derivation of the methods leads to two sufficient conditions, which can determine the unsolvability of these two types of equation respectively. The methods proposed are for equations with undetermined coefficients, which are more general than the solutions of the equations with specific known coefficients, and more suitable for computer programming implementation.

math.NT↗

arXiv2026

Optimization of Quadratic Sieve Algorithm Implementation for Large Integer Factorization

The quadratic sieve method is a core tool in number theory. In this paper, we present two optimization methods for the Quadratic Sieve algorithm. In the sieving process, the original polynomial root value accumulation step is changed from the original di to the mdi (m is a small integer), which can change the complexity from O(n) to O(n/m). Another optimization method is that for all parameter lookup steps, the original traversal lookup can be changed to an efficient binary search, which can change the complexity of the loop from O(n) to O(logn). This enhancement reduces the computational complexity of RSA modulus factorization in practical settings.

math.NT↗

arXiv2026

Deepfakes and Synthetic Media: Generation, Detection, and Governance

Deepfakes, synthetic audiovisual content produced by deep generative models, have escalated into a critical threat across civilian and military domains, enabling identity fraud, disinformation campaigns, and evidence fabrication. In high-stakes environments, ranging from journalism and finance to healthcare and legal contexts, the consequences extend to severe misinformation, market manipulation, identity fraud, and the erosion of institutional trust. This entry explores how modern visual intelligence and computer vision techniques are used to detect deepfakes. It outlines key deepfake generation models, such as GANs, autoencoders, neural rendering, and diffusion systems, while also explaining how adversarial methods enhance realism and challenge existing detectors. The overview highlights visual artifacts, digital patterns, and physiological cues commonly leveraged in detection and reviews major CNN, transformer, and frequency-based approaches. It also summarizes evaluation practices and the difficulty of achieving strong generalization. Finally, it identifies emerging directions, including modern intelligence techniques for civilian and military content verification. This survey covers generation architectures (GANs, latent diffusion, neural rendering, video synthesis), the spatial, temporal, frequency-domain, and physiological artifacts they produce, and the detector families that exploit them. We examine evaluation benchmarks and protocols, highlighting cross-generator generalization as the field's central open challenge. Beyond detection, we discuss cryptographic provenance standards, watermarking, and regulatory frameworks (EU AI Act, DSA, GDPR). We conclude that effective deepfake governance requires defense-in-depth integrating forensic detection, verifiable provenance, and institutional accountability.

cs.CV↗

arXiv2021

The Dynamics of Deforming Manifold: A Mathematical Model

In order to meet the requirements of practical applications, a model of deforming manifold in the embedded space is proposed. The deforming vector and deforming field are presented to precisely describe the deforming process, which have clear physical meanings. The proposed model is a modification of the general differential dynamic model, with constraints of spatial and temporal continuity on the deforming field. The deformation integral and derivative are presented as compact expressions of manifold deforming process. Moreover, a specific autonomous deforming field with flattening effect is defined, which provides a novel geometric viewpoint on data dimension reduction. The effectiveness of this autonomous deforming field is proved by numerical computation simulations, which indicate the promising potential of the proposed model in practical dimension reduction tasks.

math.DG↗