Analysis of the Number of Sides of Voronoi Polygons in PassPoint

Suárez-Plasencia, Lisset; Herrera-Macías, Joaquín A.; Legón-Pérez, Carlos Miguel; Llanes, Raisa Socorro; Rojas, Omar; Sosa-Gómez, Guillermo

doi:10.1007/978-3-030-69839-3_13

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…A Voronoi tessellation of an infinite plane is a partitioning of the plane into regions based on the distance to a specified discrete set of points (called seeds or nuclei and shown with black squares in Figure 4). For each seed, there is a corresponding region, consisting of all points closer to that seed than to any other [70][71][72][73][74][75][76][77]. The Voronoi (Shannon) entropy of a given set of points located in a plane is given by:…”

Section: Mathematical Measures Of Symmetry and Ordering In Biological...mentioning

confidence: 99%

Fibonacci Sequences, Symmetry and Ordering in Biological Patterns, Their Sources, Information Origin and the Landauer Principle

Bormashenko¹

2022

Preprint

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Physical roots, exemplifications and consequences of periodic and aperiodic ordering (represented by Fibonacci series) in biological systems are discussed. The role and physical and biological roots of symmetry and asymmetry appearing in biological patterns is addressed. Generalization of the Curie-Neumann Principle as applied to biological objects is presented, briefly summarized as: “asymmetry is what creates a biological phenomenon”. The “up-bottom approach” and “bottom up” approaches to the explanation of symmetry in organisms are presented in detail. The “up-bottom approach”, implies that the symmetry of the biological structure follows the symmetry of media in which this structure is functioning; the “bottom-up” approach, in turn, adopt that the symmetry of biological structures emerges from the symmetry of molecules constituting the structure. A diversity of mathematical measures applicable for quantification of ordering in biological patterns is introduced. The continuous, Shannon and Voronoi measures of symmetry/ordering and their application to biology objects are addressed. The fine structure of the notion of “ordering” is discussed. Informational/algorithmic roots of ordering inherent for the biological systems are considered. Ordered/symmetrical patterns provide economy of biological information, necessary for algorithmic description of a biological entity. Application of the Landauer principle bridging physics and theory of information to the biological systems is discussed.

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Section: Mathematical Measures Of Symmetry and Ordering In Biological...mentioning

confidence: 99%

Fibonacci Sequences, Symmetry and Ordering in Biological Patterns, Their Sources, Information Origin and the Landauer Principle

Bormashenko¹

2022

Preprint

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“…is condition is known as Delaunay's condition. e Voronoi diagrams and the Delaunay triangulation in the two-dimensional case present a series of characteristics determined by the behavior of the point pattern observed in the initial set of points [9,29,30].…”

Section: Applications Of Voronoi Diagrams and Delaunaymentioning

confidence: 99%

“…Recently, in [30], the application of the characteristic "number of sides of the Voronoi polygons" was evaluated for the detection of graphical passwords formed by patterns clustered in PassPoint, but it also proved to be ineffective using the proposed criteria.…”

Section: Detection Of Weak Graphicalmentioning

confidence: 99%

Weak PassPoint Passwords Detected by the Perimeter of Delaunay Triangles

Suárez-Plasencia

Legón-Pérez

Herrera-Macías

et al. 2022

Security and Communication Networks

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PassPoint is a graphical authentication technique that is based on the selection of five points in an image. A detected vulnerability lies in the possible existence of a pattern in the points that make up the password. The objective of this work is to detect nonrandom graphical passwords in the PassPoint scenario. A spatial randomness test based on the average of Delaunay triangles’ perimeter is proposed, given the ineffectiveness of the classic tests in this scenario, which only consists of five points. A state-of-the-art of various applications of Voronoi polygons and Delaunay triangulations are presented to detect clustered and regular patterns. The distributions of the averages of the triangles’ perimeters in the PassPoint scenario for various sizes of images are disclosed, which were unknown. The test’s decision criterion was constructed from one of the best distributions to which the data were adjusted. Type I and type II errors were estimated, and it was concluded that the proposed test could detect clustered and regular graphical passwords in PassPoint, therefore being more effective in detecting clustering than regularity.

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Detection of DIAG and LINE Patterns in PassPoints Graphical Passwords Based on the Maximum Angles of Their Delaunay Triangles

Suárez-Plasencia

Herrera-Macías

Legón-Pérez

et al. 2022

Sensors

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An alternative authentication method to traditional alphanumeric passwords is graphical password authentication, also known as graphical authentication, for which one of the most valuable cued-recall techniques is PassPoints. This technique stands out for its security and usability. However, it can be violated if the user follows a predefined pattern when selecting the five points in an image as their passwords, such as the DIAG and LINE patterns. Dictionary attacks can be built using these two patterns to compromise graphical passwords. So far, no reports have been found in the state of the art about any test capable of detecting graphical passwords with DIAG or LINE patterns in PassPoints. Studies carried out in other scenarios have shown the effectiveness of the characteristics of Delaunay triangulations in extracting information about the dependence between the points. In this work, graphical passwords formed by five randomly selected points on an image are compared with passwords whose points contain patterns of the DIAG or LINE type. The comparison is based on building for each password its Delaunay triangulation and calculating the mean value of the maximum angles of the triangles obtained; such a mean value is denoted by amadt. It is experimentally shown that in passwords containing DIAG and LINE patterns, the value of amadt is higher than the one obtained in passwords formed by random dots. From this result, it is proposed to use this amadt value as a statistic to build a test of means. This result constitutes the work’s main contribution: The proposal of a spatial randomness test to detect weak graphic passwords that contain DIAG and LINE type patterns. The importance and novelty of this result become evident when two aspects are taken into account: First, these weak passwords can be exploited by attackers to improve the effectiveness of their attacks; second, there are no prior criteria to detect this type of weak password. The practical application of said test contributes to increasing PassPoints security without substantially affecting its efficiency.

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Analysis of the Number of Sides of Voronoi Polygons in PassPoint

Cited by 3 publications

References 19 publications

Fibonacci Sequences, Symmetry and Ordering in Biological Patterns, Their Sources, Information Origin and the Landauer Principle

Fibonacci Sequences, Symmetry and Ordering in Biological Patterns, Their Sources, Information Origin and the Landauer Principle

Weak PassPoint Passwords Detected by the Perimeter of Delaunay Triangles

Detection of DIAG and LINE Patterns in PassPoints Graphical Passwords Based on the Maximum Angles of Their Delaunay Triangles

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