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51da68e | 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 | #!/usr/bin/env python3
"""
example.py — Demonstrate hv_octonion_tree.
NumPy only.
"""
import numpy as np
from hv_octonion_tree import (
orandom, omul, oconj, random_tree, eval_tree, batch_eval,
all_trees, tree_depth, tree_key, unique_random_trees,
injectivity_exhaustive, injectivity_sampled,
mitm_analysis, hierarchical_injectivity,
check_alternativity, check_moufang, check_norm_preservation,
noise_test, structured_input_test,
notarize, hierarchical_key,
)
def demo_single_tree():
print("=" * 72)
print("Demo 1 — single tree evaluation")
print("=" * 72)
print()
rng = np.random.default_rng(0)
n = 8
vals = np.stack([orandom(rng) for _ in range(n)])
tree = random_tree(n, rng)
product = eval_tree(tree, vals)
print(f" n = {n}")
print(f" tree depth = {tree_depth(tree)}")
print(f" ||product|| = {np.linalg.norm(product):.15f}")
print(f" product = {np.round(product, 4)}")
print()
def demo_batch():
print("=" * 72)
print("Demo 2 — batched evaluation")
print("=" * 72)
print()
rng = np.random.default_rng(0)
n = 8
vals = np.stack([orandom(rng) for _ in range(n)])
trees = unique_random_trees(n, 100, rng)
products = batch_eval(trees, vals)
print(f" n = {n}, K = {len(trees)} trees")
print(f" products shape: {products.shape}")
print(f" pairwise min distance: ", end="")
D = np.linalg.norm(products[:, None, :] - products[None, :, :], axis=-1)
iu = np.triu_indices(len(products), k=1)
print(f"{D[iu].min():.4f}")
print()
def demo_injectivity():
print("=" * 72)
print("Demo 3 — injectivity tests")
print("=" * 72)
print()
print(" Exhaustive:")
for n in [6, 8, 10]:
r = injectivity_exhaustive(n)
print(f" n={n:>2d} {r['K']:>5d} trees min_d={r['min_d']:.6f} "
f"distinct={r['distinct']}")
print()
print(" Sampled:")
for n, K in [(16, 500), (24, 500), (32, 500)]:
r = injectivity_sampled(n, K)
print(f" n={n:>2d} {r['K']:>5d} trees min_d={r['min_d']:.6f} "
f"distinct={r['distinct']}")
print()
def demo_mitm():
print("=" * 72)
print("Demo 4 — MITM analysis (correction to #100)")
print("=" * 72)
print()
print(f" {'n':>3s} {'brute':>12s} {'mitm':>10s} {'saved':>8s}")
print(" " + "-" * 40)
for n in [8, 10, 12, 14, 16, 18, 20]:
r = mitm_analysis(n)
print(f" {n:>3d} {r['brute_force']:>12d} {r['mitm_cost']:>10d} "
f"{r['bits_saved']:>8.2f}")
print()
def demo_moufang():
print("=" * 72)
print("Demo 5 — algebraic properties (correction to #100)")
print("=" * 72)
print()
alt = check_alternativity()
mouf = check_moufang()
print(f" left alternativity: {alt['left_alt_err']:.2e}")
print(f" right alternativity: {alt['right_alt_err']:.2e}")
print(f" left Moufang: {mouf['left_moufang_err']:.2e}")
print(f" right Moufang: {mouf['right_moufang_err']:.2e} "
f"(#100 said this fails)")
print(f" middle Moufang: {mouf['mid_moufang_err']:.2e}")
print()
def demo_norm():
print("=" * 72)
print("Demo 6 — norm preservation")
print("=" * 72)
print()
norm_results = check_norm_preservation()
for n, nm in norm_results:
print(f" n={n:>5d} ||product|| = {nm:.15f} "
f"deviation = {abs(nm - 1.0):.2e}")
print()
def demo_noise():
print("=" * 72)
print("Demo 7 — noise sensitivity (correction to #100)")
print("=" * 72)
print()
for n, sigma in [(8, 0.01), (16, 0.01), (32, 0.01)]:
r = noise_test(n=n, sigma=sigma, seed=n)
print(f" n={n:>3d} sigma={sigma:.3f} "
f"mean_err={r['mean_err']:.5f} "
f"sqrt(n)*sigma={r['sqrt_n_sigma']:.5f} "
f"ratio={r['ratio_to_sqrt_n_sigma']:.3f}")
print()
def demo_structured():
print("=" * 72)
print("Demo 8 — structured inputs break injectivity")
print("=" * 72)
print()
s = structured_input_test(n=8, K=200)
for name, vals in s.items():
print(f" {name:<14s} min_d={vals['min_d']:.6f} "
f"mean_d={vals['mean_d']:.4f}")
print()
def demo_notarize():
print("=" * 72)
print("Demo 9 — notarization (proof of computation)")
print("=" * 72)
print()
rng = np.random.default_rng(0)
n = 8
operands = np.stack([orandom(rng) for _ in range(n)])
tree = random_tree(n, rng)
proof = notarize(operands, tree, withhold_bits=32)
print(f" Published operands (n={n}), product, commitment = "
f"{proof['commitment']}")
print(f" Tree withheld. Verify by guessing the tree:")
# Verifier guesses a random tree
guess_wrong = random_tree(n, rng)
guess_right = tree
print(f" guess (random): {proof['verify'](guess_wrong)}")
print(f" guess (correct): {proof['verify'](guess_right)}")
print()
def demo_hierarchical_key():
print("=" * 72)
print("Demo 10 — hierarchical key derivation")
print("=" * 72)
print()
rng = np.random.default_rng(0)
k, m = 4, 3
n = k * m
operands = np.stack([orandom(rng) for _ in range(n)])
sub_shapes = unique_random_trees(k, 5, rng)
top_shapes = unique_random_trees(m, 5, rng)
print(f" k={k}, m={m}, key space = Cat({k-1})^{m} * Cat({m-1}) = "
f"{hierarchical_injectivity(k, m, 1)['total_programs']}")
print(f" Sample keys:")
seen = set()
for _ in range(5):
top = top_shapes[int(rng.integers(0, len(top_shapes)))]
subs = [sub_shapes[int(rng.integers(0, len(sub_shapes)))]
for _ in range(m)]
key = hierarchical_key(operands, top, subs, k)
key_hash = hash(round(float(key.sum()), 8))
print(f" key = {np.round(key[:4], 4)}... hash = "
f"{key_hash % 10000:04d}")
print()
def main():
demo_single_tree()
demo_batch()
demo_injectivity()
demo_mitm()
demo_moufang()
demo_norm()
demo_noise()
demo_structured()
demo_notarize()
demo_hierarchical_key()
if __name__ == "__main__":
main() |