Geometric-Cryptographic Encoding Experiment for Cyrillic and Latin Letters

 

Objective:
To encode Cyrillic and Latin letters, as well as symbols, into a chord-based geometric figure for cryptographic and visual experimentation. The system explores both aesthetic geometry and information density in encoding.

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Geometric Structure

1. Core Shape:

   • The base figure consists of 12 petals arranged in a circular pattern, each representing a segment of the alphabet or a subset of symbols.

   • Between every pair of petals, there is a 6-lobed “tripod star” (referred to as a “вовік”), providing secondary encoding space and linking petals.

   • The geometry is chord-based: lines (chords) connect points on the circle to define both petals and stars, creating intersections that can encode additional information.

2. Visual Encoding:

   • Monochrome Version: Each letter or symbol is represented by a unique combination of filled and unfilled regions (black vs. white).

   • Colored Version: Each letter or symbol is encoded via distinct colors, with hue, saturation, or brightness providing additional distinction.

   • Unique Recognition: Each symbol has only one unique variant in the system, ensuring unambiguous identification.

3. Mapping to Geometry:

   • Each petal corresponds to a letter subset or symbol type.

   • Each tripod star encodes transitions or modifications (for example, diacritics or numeric indicators).

   • Chords define precise spatial placement of each symbol, so that the same symbol is always located in the same relative geometric position.

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Cryptographic Features

1. Single Variant Recognition:

   • Each glyph has a unique geometric signature that allows it to be recognized independently of context.

   • Variations in line thickness, filling, and minor chord placement ensure robust symbol identification.

2. Ink-Weight Distribution:

   • Symbols are categorized by the amount of “ink” used, i.e., how many lines or filled areas are required to represent them.

   • This allows a form of steganographic weighting, where frequently used letters can be represented with lighter strokes and rare letters with heavier strokes.

   • Ink-weight can also be used for redundancy, error detection, or cryptographic masking.

3. Integration with Known Encoding Tables:

   • The geometric system can be mapped to standard letter-to-number tables, such as Unicode or ASCII for Latin letters and Unicode for Cyrillic, ensuring compatibility and recoverability.

   • Each letter or symbol has a direct table reference, which aligns with its geometric representation.

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Applications and Variants

1. Visual Cryptography:

   • Can be used as a visual cipher, where letters are only legible when the geometric mapping is known.

   • Potential for layered encoding: black-and-white outlines for standard reading, colors for secondary metadata.

2. Aesthetic and Educational Uses:

   • Can serve as a teaching tool for geometry, symmetry, and coding.

   • The 12 petals and 6 tripod stars provide a visually pleasing structure, blending art with cryptography.

3. Encoding Extensions:

   • The system can be expanded to include numbers, punctuation, and control characters.

   • Additional layers (e.g., shading, chord intersections) can encode multi-symbol combinations or short words.