What question did this study set out to answer?

This research aims to prove the security of YiJing Hash v2.0 through a unified framework involving Cayley graphs and Landauer thermodynamics.

May 19, 2026Open Access

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 (v2: Dickson Subgroup Verification)

Key Points

This research aims to prove the security of YiJing Hash v2.0 through a unified framework involving Cayley graphs and Landauer thermodynamics.
Introduced Dickson subgroup verification within a new section.
Employed SL(2,F_127) to find a unipotent element at specific walk steps.
Analyzed cold-start and warm-start mixing times with statistical methods.
Proved subgroup attack is impossible by demonstrating that 8 matrices generate the entire group SL(2,F_127).
Identified a trace anomaly as a mixing-time artifact with p=0.042 in warm-start tests.
Updated B+C Conjecture with four bounds established, indicating significant security enhancements.

Abstract

v2 adds: Dickson subgroup security verification (new Section 2). Key new result: unipotent element of order p=127 found at walk step 55 in SL (2, F₁27). By Dickson's classification theorem (1901), this proves the 8 Hou-Tian Ba-Gua generator matrices generate the ENTIRE group SL (2, F₁27). Subgroup attack is impossible. Also clarifies: trace=2 anomaly (15, 695 vs expected 124) in cold-start walk is a mixing-time artifact, not a subgroup signal. Warm-start (200 steps) reduces ratio to 1. 06x (p=0. 042). Updated B+C Conjecture now has 4 bounds: C0 (subgroup, proven), C1 (BSGS Omega (1, 431), proven), C2 (Expander t>=1, 370, conditional), B (Landauer 7. 35e-19 J, P=NP independent). Supersedes v1: doi: 10. 5281/zenodo. 20257246

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