Physical Hardness of Cryptographic Hash Functions: A Unified Framework via Cayley Graph Expanders and Landauer Thermodynamics -- The B+C Conjecture Applied to YiJing Hash v2.0
Year: 2026
Type: preprint
Abstract: We propose the B+C Conjecture: a unified framework grounding cryptographic hash hardness in algebraic graph theory (C: Cayley Graph Expanders) and thermodynamic physics (B: Landauer Principle). Applied to YiJing Hash v2.0 (SL(2,F_127), 8 Hou-Tian Ba-Gua generators): (C1) BSGS algebraic lower bound: Omega(1,431) matrix multiplications. (C2) Expander Mixing Lemma: t >= 1,370 steps for epsilon=2^{-128} statistical indistinguishability. Empirically confirmed: SL(2,F_5) Cayley graph is Ramanujan (lambda_2/d=0.809, exact computation). (B) Landauer weak bound (proven): any physical inverter dissipates >= 7.35e-19 J. Independent of P vs NP. Landauer strong bound (open conjecture): thermal inaccessibility of erased information. Companion: YiJing Hash v1.0 (doi:10.5281/zenodo.20257027), v2.0 (doi:10.5281/zenodo.20257132).
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: W7161487875
Cites:
Cited by:
Related to: