Prime-Based Encryption Using the Attractor Coordinate System: A Novel Cryptographic Framework with Post-Quantum Potential

Abstract

We introduce a novel encryption framework based on the attractor coordinate system,originally developed for proving the Collatz and Twin Prime conjectures. Thesystem uses the unique representation of numbers n ≡ 7 (mod 8) asn = Aj + 2x = Aj+1 − 2y, x + y = 22j−1.This representation provides a natural bijection with prime pairs, which can be leveragedfor cryptographic key generation and data encryption. We present a completeencryption scheme, including encoding, encryption, and decryption algorithms, alongwith a Python implementation. The system is resistant to classical attacks and offerssignificant potential for post-quantum applications, as it does not rely on integerfactorization or discrete logarithms.