Abstract: In illustrative implementations, shape is used to encode computer passwords or other information. The passwords may be easy for a human to remember—and yet have an extremely high number of permutations (e.g., in some cases, greater than 1030 permutations, or greater than 10261 permutations, or greater than 106264 permutations). This combination of a password being easy for a human to remember—yet having a large number of permutations—offers many practical benefits. Among other things, the huge number of permutations makes the password extremely resistant to guessing attacks. In addition, in some cases, the passwords that are created with the shapes are highly resistant to attacks by keystroke logging, mouse logging, touch-gesture logging, screen logging, shoulder surfing, phishing, and social engineering. Alternatively, the shapes may be used to encode other information, such as information that uniquely identifies a product or a machine part.

Abstract: In illustrative implementations, shape is used to encode computer passwords or other information. The passwords may be easy for a human to remember—and yet have an extremely high number of permutations (e.g., in some cases, greater than 1030 permutations, or greater than 10261 permutations, or greater than 106264 permutations). This combination of a password being easy for a human to remember—yet having a large number of permutations—offers many practical benefits. Among other things, the huge number of permutations makes the password extremely resistant to guessing attacks. In addition, in some cases, the passwords that are created with the shapes are highly resistant to attacks by keystroke logging, mouse logging, touch-gesture logging, screen logging, shoulder surfing, phishing, and social engineering. Alternatively, the shapes may be used to encode other information, such as information that uniquely identifies a product or a machine part.

Abstract: Shape-matrix geometric instruments having numerous applications including, but not limited to, anti-counterfeiting, graphical passwording, games, and geometry education. A shape-matrix geometric instrument is a manufacture and/or a method whose design is based on a shape-matrix that, in turn comprises a set of building blocks that are N-dimensional polytopes. Corner shapes are positioned in or near the interior corner spaces of at least ones of the shape-matrix building blocks. At least ones of the corner shapes differ from others in at least one property or aspect including, for example, geometric shape, orientation within the building block, and one or more surface “finishes,” such as color, shading, cross-hatching or real or apparent texture.

Abstract: A notched 2D shape may encode information. For instance, a physical tag may display, form or include a polygon that is modified by notches and by one or more holes. This notched 2D shape may encode data that identifies, or provides information regarding, a physical product to which the tag is physically attached. Alternatively, this notched 2D shape may encode any other type of information, such as information about what we sometimes call a product shape or shape matrix. The notched shape may be an octagon that is modified by notches and by one or more holes.

Abstract: A notched 2D shape may encode information. For instance, a physical tag may display, form or include a polygon that is modified by notches and by one or more holes. This notched 2D shape may encode data that identifies, or provides information regarding, a physical product to which the tag is physically attached. Alternatively, this notched 2D shape may encode any other type of information, such as information about what we sometimes call a product shape or shape matrix. The notched shape may be an octagon that is modified by notches and by one or more holes.

Abstract: Shape-matrix geometric instruments having numerous applications including, but not limited to, anti-counterfeiting, graphical passwording, games, and geometry education. A shape-matrix geometric instrument is a manufacture and/or a method whose design is based on a shape-matrix that, in turn comprises a set of building blocks that are N-dimensional polytopes. Corner shapes are positioned in or near the interior corner spaces of at least ones of the shape-matrix building blocks. At least ones of the corner shapes differ from others in at least one property or aspect including, for example, geometric shape, orientation within the building block, and one or more surface “finishes,” such as color, shading, cross-hatching or real or apparent texture.

Abstract: In illustrative implementations, shape is used to encode computer passwords or other information. The passwords may be easy for a human to remember—and yet have an extremely high number of permutations (e.g., in some cases, greater than 1030 permutations, or greater than 10261 permutations, or greater than 106264 permutations). This combination of a password being easy for a human to remember—yet having a large number of permutations—offers many practical benefits. Among other things, the huge number of permutations makes the password extremely resistant to guessing attacks. In addition, in some cases, the passwords that are created with the shapes are highly resistant to attacks by keystroke logging, mouse logging, touch-gesture logging, screen logging, shoulder surfing, phishing, and social engineering. Alternatively, the shapes may be used to encode other information, such as information that uniquely identifies a product or a machine part.

Abstract: In illustrative implementations, shape is used to encode computer passwords or other information. The passwords may be easy for a human to remember—and yet have an extremely high number of permutations (e.g., in some cases, greater than 1030 permutations, or greater than 10261 permutations, or greater than 106264 permutations). This combination of a password being easy for a human to remember—yet having a large number of permutations—offers many practical benefits. Among other things, the huge number of permutations makes the password extremely resistant to guessing attacks. In addition, in some cases, the passwords that are created with the shapes are highly resistant to attacks by keystroke logging, mouse logging, touch-gesture logging, screen logging, shoulder surfing, phishing, and social engineering. Alternatively, the shapes may be used to encode other information, such as information that uniquely identifies a product or a machine part.

Abstract: Shape-matrix geometric instruments having numerous applications including, but not limited to, anti-counterfeiting, graphical passwording, games, and geometry education. A shape-matrix geometric instrument is a manufacture and/or a method whose design is based on a shape-matrix that, in turn comprises a set of building blocks that are N-dimensional polytopes. Corner shapes are positioned in or near the interior corner spaces of at least ones of the shape-matrix building blocks. At least ones of the corner shapes differ from others in at least one property or aspect including, for example, geometric shape, orientation within the building block, and one or more surface “finishes,” such as color, shading, cross-hatching or real or apparent texture.