KiHoLee
8f26bf9bc9
Every OMA reference takes the L/16 combining gain so the comparison stays resource matched, four hardcoded copies of the configuration are replaced by MAIN_D or the main curve, and stage_J's K-by-L Gaussian draw becomes its exact scalar Beta equivalent.
170 lines
7.2 KiB
Python
170 lines
7.2 KiB
Python
"""Stage K: the key-refresh layer, implemented and evaluated.
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Section VI shows that a few known-plaintext frames recover a fixed key,
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so the key has to be refreshed every coherence block. Refreshing is not
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as simple as drawing new keys. The decision statistic of a legitimate
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receiver contains a signal term that does not depend on the key, because
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a unit-modulus key satisfies m_{u,k}^2 = 1, and a cross-user term that
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depends on the sign patterns m_v .* m_u. A codebook trained with one key
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set adapts to those particular patterns, so installing an unrelated key
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set destroys the separation even when the new keys are exactly
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orthogonal. Two constructions are compared here.
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Naive refresh: draw a fresh orthogonal key set every block, namely a
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fresh selection of Walsh-Hadamard rows. This changes the cross-user
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patterns and is measured below to fail.
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Invariant refresh: draw only from the transformations that leave every
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cross-user pattern intact, so the legitimate performance is unchanged
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by construction while the transmitted material changes. Three such
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transformations exist and they compose:
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1. a global sign for each of the L frame entries, applied to every
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user, which leaves m_v .* m_u unchanged because the two signs
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cancel, L bits
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2. a permutation of the L frame entries applied to the keys and to
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the codebook together, which is a relabeling, log2(L!) bits
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3. a permutation of which user holds which row, log2(U!) bits
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At L=64 and U=4 that is 64 + 296.0 + 4.58 = 364.6 bits per block, and
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each transformation is verified below to leave the legitimate error
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rate unchanged.
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The evaluation asks three questions:
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K1 does the legitimate receiver survive a refreshed key,
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K2 does the eavesdropper stay at the random-guess level,
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K3 does a key recovered by known plaintext in one block decode the
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next block.
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Outputs: refresh.csv, refresh_kpa.csv
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"""
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from __future__ import annotations
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import math
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import numpy as np
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import torch
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from sse_lib import DATA, DEVICE, SSE, write_csv, eval_ser_sse
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from exp_full import (MAIN_D, hadamard, get_model, base_keys, eval_ser_eve,
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eve_wrong_mask)
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from exp_kpa import collect_known_plaintext, solve_keys
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SEED = 5150
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BLOCKS = 24
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FRAMES = 300_000
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def kdf_invariant(seed: int, block: int, U: int, Lp: int):
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"""Derive one block's key material from the invariance group."""
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rng = np.random.default_rng([seed, block])
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signs = torch.tensor(rng.choice([-1.0, 1.0], size=(1, Lp)),
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dtype=torch.float32)
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colperm = torch.tensor(rng.permutation(Lp), dtype=torch.long)
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userperm = torch.tensor(rng.permutation(U), dtype=torch.long)
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return signs, colperm, userperm
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def kdf_naive(seed: int, block: int, U: int, Lp: int) -> torch.Tensor:
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"""Fresh orthogonal rows every block, which changes the cross-user
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patterns the codebook was trained for."""
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rng = np.random.default_rng([seed, 10_000 + block])
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rows = rng.choice(np.arange(1, Lp), size=U, replace=False)
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return torch.tensor(hadamard(Lp)[rows], dtype=torch.float32)
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def entropy_bits(U: int, Lp: int) -> float:
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return (Lp + math.lgamma(Lp + 1) / math.log(2.0)
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+ math.lgamma(U + 1) / math.log(2.0))
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def install(model: SSE, keys: torch.Tensor, codebook: torch.Tensor,
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colperm=None):
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"""Install one block's key material. A column permutation relabels
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the frame entries of the keys and the codebook together."""
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with torch.no_grad():
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if colperm is None:
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model.W.copy_(keys.to(DEVICE))
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model.B.copy_(codebook.to(DEVICE))
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else:
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model.W.copy_(keys[:, colperm].to(DEVICE))
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model.B.copy_(codebook[:, colperm].to(DEVICE))
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model.calibrate_power()
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def main():
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P, VU, D, U = 4, 16, MAIN_D, 4
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Lp = D // P
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print(f"[K] refresh: L={Lp}, U={U}, "
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f"{entropy_bits(U, Lp):.1f} bits per block from the invariance group")
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K0 = base_keys(U, Lp)
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m = get_model(P=P, vu=VU, d=D, U=U, iters=4000, freeze_W=K0)
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m.eval()
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B0 = m.B.detach().clone().cpu()
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ew = eve_wrong_mask(U, Lp, seed=20260813)
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# the no-refresh reference: the trained keys, held for every block
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install(m, K0, B0)
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lg_fixed = eval_ser_sse(m, [10.0], frames=FRAMES)[0]
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ev_fixed = eval_ser_eve(m, ew, [10.0], frames=FRAMES)[0]
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rows = []
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for t in range(BLOCKS):
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signs, colperm, userperm = kdf_invariant(SEED, t, U, Lp)
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install(m, (K0 * signs)[userperm], B0, colperm)
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lg = eval_ser_sse(m, [10.0], frames=FRAMES)[0]
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ev = eval_ser_eve(m, ew, [10.0], frames=FRAMES)[0]
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install(m, kdf_naive(SEED, t, U, Lp), B0)
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lg_naive = eval_ser_sse(m, [10.0], frames=FRAMES)[0]
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ev_naive = eval_ser_eve(m, ew, [10.0], frames=FRAMES)[0]
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rows.append((t, lg, lg_naive, ev, ev_naive))
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if t < 3 or t == BLOCKS - 1:
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print(f" block {t:3d} invariant={lg:.4f} naive={lg_naive:.4f} "
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f"eve={ev:.4f}")
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write_csv(DATA / "refresh.csv",
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["block", "legit_invariant", "legit_naive", "eve_invariant",
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"eve_naive"], rows)
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inv = [r[1] for r in rows]; nai = [r[2] for r in rows]
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ev = [r[3] for r in rows]; evn = [r[4] for r in rows]
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print(f" invariant refresh: mean={np.mean(inv):.4f} "
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f"min={min(inv):.4f} max={max(inv):.4f}")
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print(f" naive refresh : mean={np.mean(nai):.4f}")
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print(f" eavesdropper : mean={np.mean(ev):.5f} "
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f"min={min(ev):.5f} max={max(ev):.5f}")
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# the three rows of the refresh table, so no cell is hand-typed. Both
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# fixed and naive draw U of the L-1 non-constant Hadamard rows.
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fam = math.lgamma(Lp) / math.log(2.0) - math.lgamma(Lp - U) / math.log(2.0)
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write_csv(DATA / "refresh_summary.csv",
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["scheme", "legit", "eve", "entropy_bits"],
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[("None (fixed key)", lg_fixed, ev_fixed, fam),
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("Fresh orthogonal keys", float(np.mean(nai)),
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float(np.mean(evn)), fam),
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("Invariant", float(np.mean(inv)), float(np.mean(ev)),
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entropy_bits(U, Lp))])
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print("[K] known plaintext across a refresh ...")
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kpa_rows = []
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for nf in [2, 4, 8, 16, 32, 64]:
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same, nxt = [], []
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for t in range(8):
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s1, c1, u1 = kdf_invariant(SEED, t, U, Lp)
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install(m, (K0 * s1)[u1], B0, c1)
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gen = torch.Generator(device="cpu").manual_seed(SEED + 100 * t + nf)
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digits, obs, h = collect_known_plaintext(m, nf, 20.0, gen)
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est = solve_keys(m, digits, obs, h)
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same.append(eval_ser_eve(m, est.cpu(), [10.0], frames=100_000)[0])
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s2, c2, u2 = kdf_invariant(SEED, t + 1, U, Lp)
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install(m, (K0 * s2)[u2], B0, c2)
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nxt.append(eval_ser_eve(m, est.cpu(), [10.0], frames=100_000)[0])
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kpa_rows.append((nf, float(np.mean(same)), float(np.mean(nxt))))
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print(f" N={nf:3d} same block={kpa_rows[-1][1]:.4f} "
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f"next block={kpa_rows[-1][2]:.4f}")
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write_csv(DATA / "refresh_kpa.csv",
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["n_frames", "ser_same_block", "ser_next_block"], kpa_rows)
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print("[done] refresh.csv, refresh_kpa.csv")
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if __name__ == "__main__":
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main()
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