YiJing Hash v2.0: Upgrading to SL(2,F_p) for Provable Non-Abelian Security — A Cryptographic Hash Function with Physical Basis, Matrix DLP Hardness, and Quantum Resistance
Year: 2026
Type: preprint
Abstract: YiJing Hash v2.0 upgrades Layer 3 from Dihedral group D_8 (order 16) to SL(2,F_127) (order 2,048,256), a 128,016-fold increase. The 8 Posterior Heaven (Hou-Tian) Ba-Gua trigrams serve as 8 generator matrices of SL(2,F_127). All 28 generator pairs are non-commuting. Security reduces to Matrix-DLP over SL(2,F_p) -- no known quantum sub-exponential algorithm (unlike ECDLP broken by Shor). Theorem 4 establishes security separation from Tillich-Zemor attack (prime field p=127 vs F_2^n). 64-round SHA-256-compatible Feistel with SL2 fingerprints in message schedule and rounds. Empirical: avalanche 49.1%, zero collisions/50k, chi2 p=0.944. Classical 2^128, quantum 2^85 security. Supersedes v1.0 (doi:10.5281/zenodo.20257027).
Author: Kao, Yao-Kai
Institution: National Yang Ming Chiao Tung University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161486077
Cites:
Cited by:
Related to: