Goldbach Circles and Balloons and Their Cross Correlation
This work addresses the need for random sequences in cryptography and spread spectrum systems, though it appears incremental as it builds on existing Goldbach partition concepts.
The paper extends Goldbach partitions to create concentric circles and ellipses on the number line, analyzing their counts and properties, and finds that these sequences exhibit excellent randomness and minimal dependencies, making them suitable for spread spectrum and cryptographic applications.
Goldbach partitions can be used in creation of ellipses and circles on the number line. We extend this work and determine the count and other properties of concentric Goldbach circles for different values of n. The autocorrelation function of this sequence with respect to even and odd values suggests that it has excellent randomness properties. Cross correlation properties of ellipse and circle sequences are provided that indicate that these sequences have minimal dependencies and, therefore, they can be used in spread spectrum and other cryptographic applications.