diff --git a/README.md b/README.md
index 19eafee..bb5c9ce 100644
--- a/README.md
+++ b/README.md
@@ -15,6 +15,15 @@ pip install pytest
 pytest
 ```
 
+## run linear and differential bias empirical tests
+
+in the venv
+
+```bash
+tea3-linear-bias
+tea3-differential-bias
+```
+
 ## run sagemath script
 
 `deactivate` the venv first, then with sagemath installed:
diff --git a/pyproject.toml b/pyproject.toml
index 60a7a8d..c5f11d6 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -10,3 +10,4 @@ testpaths = ["tests"]
 
 [project.scripts]
 tea3-linear-bias = "tea3.tea3linearbias:main"
+tea3-differential-bias = "tea3.tea3differentialbias:main"
diff --git a/src/tea3/tea3differentialbias.py b/src/tea3/tea3differentialbias.py
new file mode 100644
index 0000000..26c525c
--- /dev/null
+++ b/src/tea3/tea3differentialbias.py
@@ -0,0 +1,97 @@
+from __future__ import annotations
+
+from dataclasses import dataclass
+from random import Random
+
+from .tea3 import Tea3
+
+
+def rand_key(rng: Random) -> list[int]:
+    return [rng.getrandbits(8) for _ in range(10)]
+
+
+def xor_key_with_delta(key: list[int], delta: bytes | list[int], offset: int = 0) -> list[int]:
+    """
+    XOR a delta into a key starting at offset.
+    """
+    out = list(key)
+    for i, d in enumerate(delta):
+        j = offset + i
+        if j >= len(out):
+            break
+        out[j] ^= d & 0xFF
+    return out
+
+
+@dataclass
+class DiffBiasResult:
+    samples: int
+    matches: int
+    p_match: float
+    bias: float
+    estimated_needed_samples: float
+
+
+def estimate_black_box_differential_bias(
+    *,
+    frame_number: int,
+    key_delta: bytes | list[int],
+    key_delta_offset: int = 0,
+    output_byte_index: int = 0,
+    target_diff: int = 0x00,
+    samples: int = 10000,
+    seed: int = 1,
+) -> DiffBiasResult:
+    rng = Random(seed)
+    matches = 0
+    target_diff &= 0xFF
+
+    for _ in range(samples):
+        key1 = rand_key(rng)
+        key2 = xor_key_with_delta(key1, key_delta, key_delta_offset)
+
+        tea1 = Tea3(frame_number, key1)
+        tea2 = Tea3(frame_number, key2)
+
+        out1 = 0
+        out2 = 0
+        for _ in range(output_byte_index + 1):
+            out1 = tea1.next_byte()
+            out2 = tea2.next_byte()
+
+        diff = (out1 ^ out2) & 0xFF
+        if diff == target_diff:
+            matches += 1
+
+    p_match = matches / samples
+    random_baseline = 1.0 / 256.0
+    bias = abs(p_match - random_baseline)
+
+    needed = float("inf") if bias == 0 else 1.0 / (bias * bias)
+
+    return DiffBiasResult(
+        samples=samples,
+        matches=matches,
+        p_match=p_match,
+        bias=bias,
+        estimated_needed_samples=needed,
+    )
+
+
+def main() -> None:
+    frame = 0x12345678
+
+    key_delta = [0x01]
+
+    res = estimate_black_box_differential_bias(
+        frame_number=frame,
+        key_delta=key_delta,
+        key_delta_offset=0,
+        output_byte_index=0,
+        target_diff=0x00,
+        samples=20000,
+        seed=123,
+    )
+    print("black-box differential bias")
+    print("expected non-biased p_match: 1/256 = 0.00390625") # 256 possibilities for 1 Byte
+    print(res)
diff --git a/src/tea3/tea3linearbias.py b/src/tea3/tea3linearbias.py
index c599989..d372b18 100644
--- a/src/tea3/tea3linearbias.py
+++ b/src/tea3/tea3linearbias.py
@@ -63,4 +63,5 @@ def main():
         seed=123,
     )
     print("black-box output bias")
+    print("expected non-biased p_match: 1/2") # 2 possibilities for 1 bit
     print(res)