I CHING Pyramid v4.0: A Memory‑Hard Key Derivation Algorithm Inspired by the Oldest Binary System in Human History.

ABSTRACT This work presents a fully original cryptographic key derivation algorithm inspired by the **I CHING (Book of Mutations)** , the oldest known binary system in human history (3000 BCE). The algorithm is built upon a 2048‑level pyramidal structure, where each level processes 2048 base elements using a circular distance transformation (modulo 10), 1024 dynamic salts, polynomial non‑linearity, and 32 rounds of XOR‑based mutations. The system is memory‑hard, requiring 128 MB of RAM per block, making it resistant to brute‑force attacks, ASICs, and parallel hardware acceleration. In an era dominated by Western cryptographic standards (AES, SHA-2, Argon2), there is a growing need for **alternative, culturally diverse cryptographic primitives**. This work presents a key derivation algorithm that: - Is **100% original**, inspired by the I CHING. - Contains **no S‑boxes, P‑boxes, or NSA‑derived constants**. - Is **memory‑hard**, resistant to ASIC and GPU attacks. - Achieves **excellent statistical properties** (entropy ~8.0, avalanche ~50%). - Is **competitive** with modern standards like Argon2id.