Discover how mathematics and geometry can create secure encryption keys through polygon centroid calculations.
More sides create more complex ciphers but require more computation
Changes the shape of the polygon for different keys
Selects which centroid to use for the final key
Your cipher key will appear here
Visualization will appear here
A cipher is a method of transforming information to conceal its meaning and keep it secret. It's like a secret code that only people with the right key can understand!
Original: HELLO
Key: Shift each letter by 3 positions
Encrypted: KHOOR
We start with a polygon with 5 sides. The seed value 1083 determines the exact shape of this polygon. Each vertex is placed at a pseudo-random position based on this seed.
We form all possible triangles from the polygon's vertices. For each triangle, we calculate its centroid (the point where the three medians intersect). This gives us 10 Level 1 centroids.
Now we form triangles from the Level 1 centroids and calculate their centroids. This creates 120 Level 2 centroids. We select the 1st centroid from this set.
The coordinates of the selected centroid are combined into a large number by removing the decimal point. This creates a unique numeric key that can be used for encryption.
Ciphers protect messages sent over the internet, like emails and instant messages.
Encryption keeps your credit card information safe when shopping online.
Your phone calls and texts are encrypted to prevent eavesdropping.
Tiny changes in the input values (n, m, or k) produce completely different keys, similar to professional cryptographic algorithms.
Geometric ciphers demonstrate how mathematical concepts can be applied to create secure encryption methods.
The number of possible keys depends on the polygon sides (n). For n=5, there are 120 possible Level 2 centroids to choose from.
The number of calculations grows rapidly with more polygon sides, making brute-force attacks difficult for larger values of n.
This cipher demonstrates how mathematical concepts can be applied to cryptography, helping students understand fundamental security principles.
Geometric ciphers help develop pattern recognition skills, which are fundamental to understanding more complex encryption methods.