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Structured key family as the main configuration

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Unconstrained key training converged to disjoint sparse supports: 99
percent of each users key energy sat on three or four of the sixteen
entries, with pairwise disjoint supports and one numerically dead
codebook column. That is an orthogonal slot allocation, so the
superposition collapsed into OMA and the key space was far smaller than
the dense direction the brute-force study assumes.

The main configuration is now the structured Walsh-Hadamard family,
which is dense, exactly orthogonal, unit modulus, and already the best
family in the key-family table. base_keys generalizes to any key length
by truncating the next power-of-two Sylvester order, and the key-length
sweep keeps only lengths where the truncated rows stay exactly
orthogonal, verified numerically.

Also fixes the M-PAM energy normalization in oma_ser_keylen, which used
sqrt(6g/(M^2-1)) where unit average symbol energy gives A^2=3/(M^2-1);
the closed form was 3 dB optimistic and now reproduces a direct Monte
Carlo to 1e-5.

Results move accordingly: the proposal now stays below OMA at every SNR
and reaches 1.52x at key length 64, while the jamming margin falls to
5.5-6.3 dB and the brute-force curve to 0.59 at a million guesses.
This commit is contained in:
KiHoLee
2026-08-17 20:02:27 +09:00
parent b120364e38
commit 3d5a7fc6f3
27 changed files with 561 additions and 418 deletions
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code/replot_security.py
+49 -21
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@@ -11,9 +11,11 @@ Label dictionary is fixed here and copied verbatim into tables and prose.
fig_sec_kpa.pdf : eavesdropper SER vs known-plaintext frames (Fig. 7)
fig_sec_real.pdf : token error rate on real streams (Fig. 8)
Curves that coincide by construction are drawn deliberately layered, the
lower one wide and semi-transparent and the upper one narrow with open
markers, so every legend entry has a visible curve.
Curves that coincide by construction are drawn deliberately layered: the
lower one wide and semi-transparent, the upper one narrow with open
markers, and their markers staggered to different sample points through
markevery offsets. Marker size is uniform across every figure, so the
stagger, not the size, is what keeps each legend entry visible.
"""
from __future__ import annotations
from pathlib import Path
@@ -34,7 +36,7 @@ plt.rcParams.update({
"font.serif": ["DejaVu Serif", "Times New Roman"],
"font.size": 9,
"axes.labelsize": 9,
"legend.fontsize": 7.4,
"legend.fontsize": 6.6,
"xtick.labelsize": 8,
"ytick.labelsize": 8,
"axes.grid": True,
@@ -42,7 +44,7 @@ plt.rcParams.update({
"grid.linewidth": 0.4,
"grid.alpha": 0.6,
"lines.linewidth": 1.3,
"lines.markersize": 3.4,
"lines.markersize": 4.5,
"figure.figsize": (3.15, 2.36),
"pdf.fonttype": 42,
})
@@ -70,9 +72,9 @@ LBL = {
"outsider": "Outsider",
}
# deliberate-layering style for the LOWER of two coinciding curves
UNDER = dict(lw=2.6, ms=7, alpha=0.85)
UNDER = dict(lw=2.6, alpha=0.85) # thick filled line, layered under
# and for the curve riding on top of it
OVER = dict(lw=1.2, ms=4.5, mfc="none")
OVER = dict(lw=1.2, mfc="none") # thin open marker, rides on top
def load(name):
@@ -106,6 +108,27 @@ def save(fig, name):
f"{name}: axis label '{lbl.get_text()}' is clipped "
f"(label {b} outside figure {fbox}); shorten the "
f"label or widen the margin")
# No curve may pass under the legend box. Reading the code cannot
# reveal this, so the check is made on the rendered geometry, the
# same discipline as the clipping guard above.
leg = ax.get_legend()
if leg is not None:
lb = leg.get_window_extent()
for line in ax.get_lines():
# full-span reference lines (axhline/axvline) carry axes-
# fraction endpoints [0,1]; they are not data curves and,
# spanning the whole axis, would forbid any bottom legend
xd = list(line.get_xdata())
if xd == [0, 1] or list(line.get_ydata()) == [0, 1]:
continue
xy = line.get_xydata()
if len(xy) == 0:
continue
for px, py in ax.transData.transform(xy):
if lb.x0 <= px <= lb.x1 and lb.y0 <= py <= lb.y1:
raise RuntimeError(
f"{name}: a data curve passes under the legend "
f"box; move the legend or shrink it")
fig.savefig(FIG / f"{name}.pdf")
plt.close(fig)
print("[OK]", name)
@@ -117,11 +140,11 @@ def fig_snr():
fig, ax = plt.subplots()
# legitimate and OMA coincide by construction; layered deliberately
ax.semilogy(x, col(r, "legit"), color=C_LEGIT, marker="o", ls="-",
label=LBL["legit"], **UNDER)
markevery=(0, 3), label=LBL["legit"], **UNDER)
ax.semilogy(x, col(r, "oma"), color=C_OMA, marker="^", ls=":",
label=LBL["oma"], **OVER)
markevery=(1, 3), label=LBL["oma"], **OVER)
ax.semilogy(x, col(r, "eve_public"), color=C_PUB, marker="v",
ls="none", markersize=5.2, markerfacecolor="none",
ls="none", markevery=(2, 3), markerfacecolor="none",
label=LBL["eve_pub"])
ax.semilogy(x, col(r, "eve_wrong"), color=C_EVE, marker="s", ls="--",
label=LBL["eve_key"])
@@ -151,7 +174,9 @@ def fig_keylen():
ax.set_xlabel("Key length $L$")
ax.set_ylabel("SER")
ax.set_xscale("log", base=2)
ax.legend(loc="center right", bbox_to_anchor=(0.98, 0.72))
# the curves sweep the upper-left to lower-right diagonal, leaving the
# lower-left corner empty
ax.legend(loc="lower left")
save(fig, "fig_sec_keylen")
@@ -171,9 +196,9 @@ def fig_jam():
markevery=me, label=LBL["oma"] + ", targeted")
# the two blind curves agree to 0.002; deliberate layering
ax.plot(x, col(r, "blind"), color=C_LEGIT, marker="o", ls="-",
markevery=me, label=LBL["mask"] + ", blind", **UNDER)
markevery=(0, me), label=LBL["mask"] + ", blind", **UNDER)
ax.plot(x, col(r, "perm_blind"), color=C_EVE, marker="s", ls="-.",
markevery=me, label=LBL["perm"] + ", blind", **OVER)
markevery=(me // 2, me), label=LBL["perm"] + ", blind", **OVER)
nojam = float(load("sec_jam.csv")[0]["nojam"])
ax.axhline(nojam, color=C_OMA, ls=(0, (1, 3)), lw=0.9)
ax.text(max(x) - 0.6, nojam + 0.02, LBL["nojam"], ha="right",
@@ -194,11 +219,11 @@ def fig_sens():
x = col(r, "frac")
fig, ax = plt.subplots()
ax.plot(x, col(r, "ser_mask"), color=C_LEGIT, marker="o", ls="-",
label=LBL["mask"], **UNDER)
markevery=(0, 3), label=LBL["mask"], **UNDER)
ax.plot(x, col(r, "ser_perm"), color=C_EVE, marker="s", ls="--",
label=LBL["perm"], **OVER)
markevery=(1, 3), label=LBL["perm"], **OVER)
ax.plot(x, col(r, "ser_pad"), color=C_PUB, marker="v", ls="-.",
lw=1.2, ms=4.5, mfc="none", label=LBL["pad"])
markevery=(2, 3), lw=1.2, mfc="none", label=LBL["pad"])
chance = 1.0 - (1.0 / 16.0) ** 4
ax.axhline(chance, color=C_CH, ls=":", lw=0.9, label=LBL["chance"])
ax.set_xlabel("Fraction of the key recovered")
@@ -236,13 +261,13 @@ def fig_real():
fig, ax = plt.subplots()
# legitimate/OMA and insider/outsider coincide pairwise; layered
ax.semilogy(x, col(r, "ter_legit"), color=C_LEGIT, marker="o", ls="-",
label=LBL["legit"], **UNDER)
markevery=(0, 2), label=LBL["legit"], **UNDER)
ax.semilogy(x, col(r, "ter_oma"), color=C_OMA, marker="^", ls=":",
label=LBL["oma"], **OVER)
markevery=(1, 2), label=LBL["oma"], **OVER)
ax.semilogy(x, col(r, "ter_insider"), color=C_PUB, marker="v", ls="-.",
lw=2.6, alpha=0.85, ms=7, label=LBL["insider"])
markevery=(0, 2), lw=2.6, alpha=0.85, label=LBL["insider"])
ax.semilogy(x, col(r, "ter_eve"), color=C_EVE, marker="s", ls="--",
label=LBL["outsider"], **OVER)
markevery=(1, 2), label=LBL["outsider"], **OVER)
ax.set_xlabel("SNR (dB)")
ax.set_ylabel("TER")
ax.set_xlim(min(x), max(x))
@@ -280,7 +305,10 @@ def fig_kpa():
ax.set_xlabel("Known-plaintext frames $N$")
ax.set_ylabel("Eavesdropper SER")
ax.set_xscale("log", base=2)
ax.legend(loc="upper right")
# the 0 dB curve sweeps the upper-right, so anchor the legend at the
# top edge past the steep drops, above every curve at large N
ax.set_ylim(top=1.18)
ax.legend(loc="upper right", bbox_to_anchor=(1.0, 1.04))
save(fig, "fig_sec_kpa")