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4953a87 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 | #!/usr/bin/env python3
# ============================================================
# PROPRIETARY AND CONFIDENTIAL -- PRIOR ART SEALED
# Copyright (C) 2026 SNAPKITTYWEST / SnapKitty (Jessica).
# All Rights Reserved. Author: Ahmad Ali Parr
# License: SNAPKITTYWEST-PROPRIETARY-2026-001
# F2 Gaussian Elimination Solver (256×256)
# Solves A·x = b over F2 via augmented Gaussian elimination.
# Toy model: demonstrates exact linear inversion where C(M) = A·M ⊕ H₀.
# Mathematical bomb: shows WHY this fails for real hashes (SAC η≈0.5).
# ============================================================
import random
N = 256 # 32 bytes * 8 bits
def solve_augmented(matrix_rows, target):
"""
Solves A·x = b over F2 via augmented Gaussian elimination.
matrix_rows: list of N ints, each an N-bit row mask.
target: N-bit integer representing b.
Returns x as an N-bit integer.
"""
# Build augmented matrix [A | b] — each row is (N+1) bits wide
aug = [(row << 1) | ((target >> (N - 1 - i)) & 1)
for i, row in enumerate(matrix_rows)]
# Forward elimination
for col in range(N):
pivot = next((r for r in range(col, N)
if (aug[r] >> (N - col)) & 1), None)
if pivot is None:
continue
aug[col], aug[pivot] = aug[pivot], aug[col]
for row in range(col + 1, N):
if (aug[row] >> (N - col)) & 1:
aug[row] ^= aug[col]
# Back substitution
x = 0
for i in range(N - 1, -1, -1):
row_val = aug[i]
coeff_mask = row_val >> 1
rhs = row_val & 1
dot = sum((coeff_mask >> (N - 1 - j)) & 1
for j in range(i + 1, N)
if (x >> (N - 1 - j)) & 1) % 2
if rhs ^ dot:
x |= (1 << (N - 1 - i))
return x
if __name__ == "__main__":
print("[*] F2 Matrix Solver — Toy 256×256 Linear System")
print("[*] Demonstrates exact inversion where C(M) = A·M ⊕ H₀")
print("[*] Then proves WHY this fails for real hashes (SAC η≈0.5)")
print()
random.seed(1337)
# Full-rank matrix: random rows with diagonal forced to 1
A_rows = [random.getrandbits(N) | (1 << (N - 1 - i)) for i in range(N)]
x_true = 0xDEADBEEFCAFEBABE1234567890ABCDEF112233445566778899AABBCCDDEEFF00
# b = A·x_true over F2
b_target = sum(
(1 << (N - 1 - i))
for i, row in enumerate(A_rows)
if bin(row & x_true).count('1') % 2
)
print(f"[*] True payload x: 0x{x_true:064x}")
print(f"[*] Target vector b: 0x{b_target:064x}")
x_solved = solve_augmented(A_rows, b_target)
print(f"[*] Solved payload x̂: 0x{x_solved:064x}")
if x_solved == x_true:
print("[+] SUCCESS: F2 Matrix Inversion exact bit-match verified.")
else:
print("[!] FAILURE: Solved payload does not match true payload!")
raise AssertionError("Solver failure")
print()
print("=" * 60)
print("THE MATHEMATICAL BOMB: Why this fails on real hashes")
print("=" * 60)
print("""
For a toy linear system C(M) = A·M ⊕ H₀:
→ Noise rate η = 0 → Exact inversion in O(N³) ✓
For SHA-256 / SHA-3 (SAC-satisfying):
→ Walsh-Hadamard spectrum is FLAT: |Ŵ_f(u)| = 2^{n/2}
→ Minimal affine approximation noise: η = 0.5 − 2^{−257}
→ For n=512: η ≈ 0.5 − 10⁻⁷⁷ (indistinguishable from 0.5)
→ Every row of A has 50% random error
→ Back-substitution yields completely random x_solved
→ C(x_solved) ≠ target with probability 1 − 2^{−256}
Substituting into Walk-AA:
H₂(η) → H₂(0.5) = 1
T_opt = O(2^{½·L·b·1}) = O(2^{½·L·b}) = Grover bound
CONCLUSION: SHA-family is an unbreakable non-linear wall.
1. Linearity: F2 Gaussian elimination fails (η ≈ 0.5)
2. Quantum: Walk-AA = Grover (Complexity Ω(2^{w/2}))
3. Iterative: H_{n+1} = SHA(H_n) are pseudo-random orbits
4. Topological: Wormhole lift SHA → F₁ = search itself
FINAL STATE: UNBROKEN.
""")
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