Four-scheme jamming comparison and a fully generated refresh table

Give the orthogonal-access jammer its own Rayleigh channel in
oma_ser_jammed, matching the convention every simulated scheme already
used. Without it the closed-form curve faced a jammer at full power in
every frame while the Monte Carlo curves faced a fading one, which
inverted the ordering of the comparison.

Measure the outsider error rate for the fixed-key and naive-refresh
cases as well, and emit the two refresh tables from make_tables.py, so
no cell of the paper is hand-typed.

README.md

@@ -24,14 +24,14 @@ hold the key, at no extra bandwidth, power, or rate.
 ```
 code/
   sse_lib.py            transmit and receive core, channel, training, OMA reference
-  exp_full.py           stages A-F: SNR sweep, key length, jamming, key families,
+  exp_full.py           stages A-F and L: SNR sweep, key length, jamming across
-                        scheme comparison, attack difficulty
+                        schemes, key families, scheme comparison, attack difficulty
   exp_kpa.py            stage H: known-plaintext attack on the key
   exp_refresh.py        stage K: the key-refresh layer, invariance group
   exp_real_sec.py       stage G: real BERT WordPiece token streams
   verify_math.py        closed-form checks V1-V5 against Monte Carlo, PASS/FAIL
   replot_security.py    every result figure, from data/ to fig/
-  make_tables.py        LaTeX rows of the two result tables, from data/
+  make_tables.py        LaTeX rows of every result table, from data/
   feasibility_security.py   early CPU-sized study, kept for the record
 data/                   CSV results, one file per stage
 fig/                    figure PDFs, regenerated by replot_security.py
@@ -47,15 +47,18 @@ libraries.
 
 ```bash
 python verify_math.py        # closed-form verification, prints PASS/FAIL
-python exp_full.py           # stages A-F
+python exp_full.py           # stages A-F and L
 python exp_kpa.py            # known-plaintext attack
+python exp_refresh.py        # the key-refresh layer
 python exp_real_sec.py       # real token streams
 python replot_security.py    # all figures from the CSVs
 python make_tables.py        # LaTeX rows of the result tables
 ```
 
 Seeds are fixed: training 1, evaluation 777, attacker key guess
-20260813. Re-running reproduces the released CSV files.
+20260813, key recovery 4242, brute-force search 31, cross-scheme
+comparison 11, key refresh 5150. Re-running reproduces the released CSV
+files.
 
 ## Figure and table map
 
@@ -63,15 +66,15 @@ Seeds are fixed: training 1, evaluation 777, attacker key guess
 |---|---|---|
 | Fig. 2 SER against SNR | `exp_full.stage_A` | `sec_snr.csv` |
 | Fig. 3 key length | `exp_full.stage_B` | `sec_keylen.csv` |
-| Fig. 4 jamming | `exp_full.stage_C` | `sec_jam.csv` |
+| Fig. 4 jamming | `exp_full.stage_L` | `sec_jam_cmp.csv`, `sec_jam.csv` |
-| Fig. 5 key sensitivity | `exp_full.stage_F` | `sec_sens.csv` |
+| Fig. 5 key sensitivity | `exp_full.stage_I` | `sec_sens_cmp.csv` |
-| Fig. 6 brute-force search | `exp_full.stage_F` | `sec_brute.csv` |
+| Fig. 6 brute-force search | `exp_full.stage_J` | `sec_brute_cmp.csv`, `sec_brute.csv` |
 | Fig. 7 known-plaintext attack | `exp_kpa` | `kpa.csv` |
 | Fig. 8 real token streams | `exp_real_sec` | `real_sec_ter.csv` |
 | Scheme comparison table | `exp_full.stage_E` | `sec_compare.csv` |
 | Key family table | `exp_full.stage_D` | `sec_maskfam.csv`, `sec_regjam.csv` |
 | Headline recovery table | `exp_real_sec` | `real_sec_stats.json` |
-| Key refresh tables | `exp_refresh` | `refresh.csv`, `refresh_kpa.csv` |
+| Key refresh tables | `exp_refresh` | `refresh_summary.csv`, `refresh_kpa.csv` |
 
 ## Security scope
 

code/exp_full.py

@@ -645,6 +645,68 @@ def csv_rows(path):
         yield from _csv.DictReader(f)
 
 
+def oma_ser_jammed(snr_db, jsr_db_list, bits=16, U=4, n_grid=4096):
+    """OMA under a jammer that concentrates on the victim's slots.
+
+    An OMA user occupies d/U exclusive real dimensions that are public,
+    so a jammer needs no key to put all of its power there. With unit
+    energy per real dimension and a total jammer energy of rho times the
+    frame energy, concentrating on d/U of the d dimensions gives a
+    per-dimension jammer variance of U*rho.
+
+    The jammer reaches the victim through its own Rayleigh channel, the
+    same convention eval_scheme uses for every simulated scheme, so the
+    victim sees an effective noise variance of 1/snr + U*rho*hJ**2 with
+    E[hJ**2]=1. Averaging over the independent signal and jammer gains
+    uses a product of exponential quantile grids.
+    """
+    q = (torch.arange(n_grid, dtype=torch.float64) + 0.5) / n_grid
+    h2 = -torch.log1p(-q)                      # |h|^2 ~ Exp(1)
+    hj2 = h2.clone()                           # |hJ|^2 ~ Exp(1), independent
+    h = h2.sqrt()[:, None]                     # (n,1) signal amplitude
+    snr = 10.0 ** (snr_db / 10.0)
+    out = []
+    for jsr_db in jsr_db_list:
+        rho = 10.0 ** (jsr_db / 10.0)
+        var = (1.0 / snr + U * rho * hj2)[None, :]        # (1,n)
+        arg = (h / var.sqrt()).clamp(0, 38)
+        pe = 0.5 * torch.erfc(arg / math.sqrt(2.0))       # per-bit error
+        out.append(float((1.0 - (1.0 - pe) ** bits).mean()))
+    return out
+
+
+def stage_L():
+    """Jamming comparison across schemes at 10 dB.
+
+    proposed blind   : the strongest jammer the proposed scheme admits
+                       while the key stays secret
+    public matched   : the jammer a public-mask scheme always faces
+    permutation blind: the shuffling-style scheme, whose secret
+                       permutation also denies the jammer a target
+    OMA targeted     : the jammer an orthogonal scheme faces, since its
+                       slot assignment is public and needs no key
+    """
+    print("[L] jamming across schemes ...")
+    m = get_model(iters=4000)
+    F = 300_000
+    d = m.P * m.L
+    gp = torch.Generator().manual_seed(11)
+    perms = torch.randperm(d, generator=gp)[None].repeat(m.users, 1)
+    jsr = [-10.0, -5.0, 0.0, 5.0, 10.0, 15.0, 20.0]
+    oma = oma_ser_jammed(10.0, jsr, bits=int(math.log2(m.V)), U=m.users)
+    rows = []
+    for i, j in enumerate(jsr):
+        blind = eval_scheme(m, 10.0, F, jam_w="blind", jsr_db=j)
+        matched = eval_scheme(m, 10.0, F, jam_w="matched", jsr_db=j)
+        perm = eval_scheme(m, 10.0, F, perms=perms, jam_w="blind", jsr_db=j)
+        rows.append((j, blind, matched, perm, oma[i]))
+        print(f"   JSR={j:6.1f} blind={blind:.4f} matched={matched:.4f} "
+              f"perm={perm:.4f} oma={oma[i]:.4f}")
+    write_csv(DATA / "sec_jam_cmp.csv",
+              ["jsr_db", "blind", "matched", "perm_blind", "oma_targeted"],
+              rows)
+
+
 def main():
     print(f"device={DEVICE}")
     stage_A()
@@ -655,6 +717,7 @@ def main():
     stage_F()
     stage_I()
     stage_J()
+    stage_L()
     print("[done] full-scale security CSVs in", DATA)
 
 

code/exp_refresh.py

@@ -109,6 +109,11 @@ def main():
     B0 = m.B.detach().clone().cpu()
     ew = eve_wrong_mask(U, Lp, seed=20260813)
 
+    # the no-refresh reference: the trained keys, held for every block
+    install(m, K0, B0)
+    lg_fixed = eval_ser_sse(m, [10.0], frames=FRAMES)[0]
+    ev_fixed = eval_ser_eve(m, ew, [10.0], frames=FRAMES)[0]
+
     rows = []
     for t in range(BLOCKS):
         signs, colperm, userperm = kdf_invariant(SEED, t, U, Lp)
@@ -117,18 +122,32 @@ def main():
         ev = eval_ser_eve(m, ew, [10.0], frames=FRAMES)[0]
         install(m, kdf_naive(SEED, t, U, Lp), B0)
         lg_naive = eval_ser_sse(m, [10.0], frames=FRAMES)[0]
-        rows.append((t, lg, lg_naive, ev))
+        ev_naive = eval_ser_eve(m, ew, [10.0], frames=FRAMES)[0]
+        rows.append((t, lg, lg_naive, ev, ev_naive))
         if t < 3 or t == BLOCKS - 1:
             print(f"   block {t:3d} invariant={lg:.4f} naive={lg_naive:.4f} "
                   f"eve={ev:.4f}")
     write_csv(DATA / "refresh.csv",
-              ["block", "legit_invariant", "legit_naive", "eve_ser"], rows)
+              ["block", "legit_invariant", "legit_naive", "eve_invariant",
+               "eve_naive"], rows)
     inv = [r[1] for r in rows]; nai = [r[2] for r in rows]
-    ev = [r[3] for r in rows]
+    ev = [r[3] for r in rows]; evn = [r[4] for r in rows]
     print(f"   invariant refresh: mean={np.mean(inv):.4f} "
           f"min={min(inv):.4f} max={max(inv):.4f}")
     print(f"   naive refresh    : mean={np.mean(nai):.4f}")
-    print(f"   eavesdropper     : mean={np.mean(ev):.5f}")
+    print(f"   eavesdropper     : mean={np.mean(ev):.5f} "
+          f"min={min(ev):.5f} max={max(ev):.5f}")
+
+    # the three rows of the refresh table, so no cell is hand-typed. Both
+    # fixed and naive draw U of the L-1 non-constant Hadamard rows.
+    fam = math.lgamma(Lp) / math.log(2.0) - math.lgamma(Lp - U) / math.log(2.0)
+    write_csv(DATA / "refresh_summary.csv",
+              ["scheme", "legit", "eve", "entropy_bits"],
+              [("None (fixed key)", lg_fixed, ev_fixed, fam),
+               ("Fresh orthogonal keys", float(np.mean(nai)),
+                float(np.mean(evn)), fam),
+               ("Invariant", float(np.mean(inv)), float(np.mean(ev)),
+                entropy_bits(U, Lp))])
 
     print("[K] known plaintext across a refresh ...")
     kpa_rows = []

code/make_tables.py

@@ -23,7 +23,7 @@ NAME = {
 }
 RECEIVER = {
     "legit": "Legitimate", "oma": "OMA",
-    "insider": "Insider", "eve": "Outsider eavesdropper",
+    "insider": "Insider", "eve": "Outsider",
 }
 
 
@@ -73,7 +73,30 @@ def real_table():
         print(f"{RECEIVER[key]} & {cells}" + r" \\")
 
 
+def refresh_tables():
+    print("% Table: key refresh (from refresh_summary.csv)")
+    for r in csv.DictReader(open(DATA / "refresh_summary.csv")):
+        b = r["scheme"] == "Invariant"
+        name = r"\textbf{Invariant}" if b else r["scheme"]
+        f = (lambda t: r"\mathbf{" + t + "}") if b else (lambda t: t)
+        print(f"{name} & ${f(format(float(r['legit']), '.3f'))}$ & "
+              f"${f(format(float(r['eve']), '.4f'))}$ & "
+              f"${f(format(float(r['entropy_bits']), '.1f'))}$~bits" + r" \\")
+    print()
+    print("% Table: known plaintext across a refresh (from refresh_kpa.csv)")
+    rows = {r["n_frames"]: r for r in csv.DictReader(open(DATA / "refresh_kpa.csv"))}
+    keep = ["2", "8", "64"]
+    print("Frames used by the attacker & "
+          + " & ".join(f"${k}$" for k in keep) + r" \\")
+    for lbl, key in (("Same block", "ser_same_block"),
+                     ("Next block", "ser_next_block")):
+        print(f"{lbl} & "
+              + " & ".join(f"${float(rows[k][key]):.3f}$" for k in keep)
+              + r" \\")
+
+
 if __name__ == "__main__":
     compare_table(); print()
     maskfam_table(); print()
-    real_table()
+    real_table(); print()
+    refresh_tables()

code/replot_security.py

@@ -3,12 +3,16 @@ from ../data/*.csv and writes paper-ready PDFs to ../fig/. No experiment
 is rerun. All result plots share one canvas and axes rectangle (8:6 box).
 Label dictionary is fixed here and copied verbatim into tables and prose.
 
-  fig_sec_snr.pdf     : legitimate vs eavesdropper SER vs SNR (Fig. 2)
+  fig_sec_snr.pdf     : legitimate and outsider SER vs SNR (Fig. 2)
   fig_sec_keylen.pdf  : SER vs key length L (Fig. 3)
-  fig_sec_jam.pdf     : target-user SER vs JSR (Fig. 4)
+  fig_sec_jam.pdf     : target-user SER vs JSR, four schemes (Fig. 4)
-  fig_sec_sens.pdf    : Eve SER vs key correlation (Fig. 5)
+  fig_sec_sens.pdf    : outsider SER vs fraction of key held (Fig. 5)
-  fig_sec_brute.pdf     : Eve SER vs number of key guesses (Fig. 6)
+  fig_sec_brute.pdf   : outsider SER vs number of key guesses (Fig. 6)
-  fig_sec_brute_rho.pdf : best key correlation vs guesses (Fig. 7)
+  fig_sec_kpa.pdf     : outsider SER vs known-plaintext frames (Fig. 7)
+  fig_sec_real.pdf    : token error rate on real streams (Fig. 8)
+
+fig_sec_brute_rho.pdf is also emitted as a diagnostic and is not used in
+the paper.
 """
 from __future__ import annotations
 from pathlib import Path
@@ -138,19 +142,26 @@ def fig_keylen():
 
 
 def fig_jam():
-    # the target-user SER spans 0.3 to 1.0, less than one decade, so a
+    """Target-user SER against JSR for four schemes. A linear axis is
-    # linear axis is used: a log axis here produces wide minor tick
+    used because the range spans less than one decade, where a log axis
-    # labels (6x10^-1) that crowd out the y label under the fixed
+    would print wide minor tick labels that crowd out the y label."""
-    # axes rectangle
+    r = load("sec_jam_cmp.csv")
-    r = load("sec_jam.csv")
     x = col(r, "jsr_db")
     fig, ax = plt.subplots()
+    ax.plot(x, col(r, "oma_targeted"), color=C_PUB, marker="^", ls=":",
+            label="OMA, targeted")
     ax.plot(x, col(r, "matched"), color=C_MATCH, marker="P", ls="--",
-            label=LBL["jam_m"])
+            label="Public masks, matched")
-    ax.plot(x, col(r, "blind"), color=C_LEGIT, marker="o", ls="-",
+    # the two blind curves agree to 0.0015, so the proposed one is drawn
-            label=LBL["jam_b"])
+    # first and wide and the permutation key rides on top with open
-    nojam = col(r, "nojam")[0]
+    # markers, otherwise one legend entry would have no visible curve
-    ax.axhline(nojam, color=C_OMA, ls=":", lw=0.9, label=LBL["nojam"])
+    ax.plot(x, col(r, "blind"), color=C_LEGIT, marker="o", ls="-", lw=2.6,
+            ms=7, alpha=0.85, label="Proposed, blind")
+    ax.plot(x, col(r, "perm_blind"), color=C_EVE, marker="s", ls="-.",
+            lw=1.2, ms=4.5, mfc="none", label="Permutation key, blind")
+    nojam = float(load("sec_jam.csv")[0]["nojam"])
+    ax.axhline(nojam, color=C_OMA, ls=(0, (1, 3)), lw=0.9,
+               label=LBL["nojam"])
     ax.set_xlabel("JSR (dB)")
     ax.set_ylabel("SER")
     ax.set_xlim(min(x), max(x))

data/refresh.csv

@@ -1,25 +1,25 @@
-block,legit_invariant,legit_naive,eve_ser
+block,legit_invariant,legit_naive,eve_invariant,eve_naive
-0,0.2575,0.982775,0.9998575
+0,0.25722,0.9825916667,0.9998433333,0.999975
-1,0.256835,0.7427116667,0.9998133333
+1,0.257695,0.7424366667,0.9997983333,0.998495
-2,0.2566516667,0.8483041667,0.9999883333
+2,0.2575741667,0.8482983333,0.9999891667,0.9999966667
-3,0.2572983333,0.778605,0.9996666667
+3,0.2574108333,0.7789558333,0.9997116667,0.9998625
-4,0.2569683333,0.6199566667,0.9979908333
+4,0.2578316667,0.619975,0.9978516667,0.9999391667
-5,0.2571308333,0.6580941667,0.9997825
+5,0.2575941667,0.6579858333,0.99976,0.9997716667
-6,0.2572883333,0.7788558333,0.9997916667
+6,0.2568508333,0.7788175,0.9997783333,0.9999341667
-7,0.2577975,0.6935075,0.9999575
+7,0.2574466667,0.6938383333,0.9999633333,0.9989225
-8,0.2573458333,0.8400325,0.99839
+8,0.2568958333,0.8399391667,0.9983208333,0.99991
-9,0.25766,0.6547933333,0.9999866667
+9,0.2572158333,0.6549775,0.9999891667,0.9999816667
-10,0.2565575,0.4783583333,0.9995791667
+10,0.2575733333,0.4789683333,0.9995841667,0.9995091667
-11,0.2578183333,0.65481,0.99993
+11,0.2569025,0.6551183333,0.999925,0.9999741667
-12,0.2573583333,0.8477883333,0.9997283333
+12,0.2582966667,0.8479616667,0.9997208333,0.9999233333
-13,0.2571408333,0.6548475,0.9999741667
+13,0.2579675,0.6551841667,0.9999758333,0.9996183333
-14,0.2571491667,0.6579591667,0.9999975
+14,0.2572158333,0.6582558333,1,0.999915
-15,0.2574591667,0.4778091667,0.9994458333
+15,0.2578983333,0.4791275,0.9994441667,0.9999233333
-16,0.2568716667,0.76187,0.9999083333
+16,0.2570508333,0.7614066667,0.9998991667,0.9993675
-17,0.2572141667,0.8045925,0.9994866667
+17,0.2576233333,0.8045108333,0.9994666667,0.9999475
-18,0.2573291667,0.8065691667,0.9997483333
+18,0.2571108333,0.8073525,0.9997158333,0.999985
-19,0.2571316667,0.6892025,0.9992841667
+19,0.257955,0.6890983333,0.9992433333,0.9994441667
-20,0.2576716667,0.5278108333,0.9980375
+20,0.25777,0.5282241667,0.9981,0.9992808333
-21,0.25724,0.742345,0.9999641667
+21,0.2568141667,0.7426725,0.9999566667,0.999965
-22,0.2570333333,0.6545633333,0.9997633333
+22,0.2578066667,0.6547841667,0.9997633333,0.9990433333
-23,0.25745,0.68938,0.99989
+23,0.2575241667,0.68849,0.9998791667,0.99982

data/refresh_kpa.csv

@@ -1,7 +1,7 @@
 n_frames,ser_same_block,ser_next_block
-2,0.2777190625,0.998930625
+2,0.27116875,0.9988428125
-4,0.2615640625,0.998644375
+4,0.260861875,0.998726875
-8,0.2594196875,0.998631875
+8,0.2588515625,0.99869375
-16,0.2582471875,0.99867
+16,0.2586403125,0.998735625
-32,0.2579625,0.99871875
+32,0.2571871875,0.9986965625
-64,0.257455,0.9987190625
+64,0.25772125,0.99869375

data/refresh_summary.csv

@@ -0,0 +1,4 @@
+scheme,legit,eve,entropy_bits
+None (fixed key),0.2573025,0.9999908333,14.99964774
+Fresh orthogonal keys,0.7103737847,0.9996877083,14.99964774
+Invariant,0.2574685069,0.99957,64.83510297

data/sec_jam_cmp.csv

@@ -0,0 +1,8 @@
+jsr_db,blind,matched,perm_blind,oma_targeted
+-10,0.4691233333,0.7203966667,0.4694833333,0.6401244609
+-5,0.6347966667,0.87413,0.6333466667,0.8146859285
+0,0.80602,0.95331,0.8066566667,0.9237966241
+5,0.9194566667,0.98428,0.9189733333,0.9727474174
+10,0.9703833333,0.99481,0.97034,0.9908905586
+15,0.9903833333,0.9983633333,0.9900733333,0.9970319887
+20,0.9967733333,0.9995166667,0.9968766667,0.9990359654