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)

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,F_127). By Dickson's classification theorem (1901), this proves the 8 Hou-Tian Ba-Gua generator matrices generate the ENTIRE group SL(2,F_127). 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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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-17
DOI
https://doi.org/10.5281/zenodo.20257245
Primary Topic
Cryptographic Implementations and Security
Type
preprint
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preprint

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)

Yao-Kai Kao
Zenodo (CERN European Organization for Nuclear Research)
Cryptographic Implementations and Security
preprint

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)

Yao-Kai Kao
preprint en

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,F_127). By Dickson's classification theorem (1901), this proves the 8 Hou-Tian Ba-Gua generator matrices generate the ENTIRE group SL(2,F_127). 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

Zenodo (CERN European Organization for Nuclear Research)
Allen Institute for Brain Science (US), Taipei Institute of Pathology (TW)
Cryptographic Implementations and Security
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