non linearity

src/walsh/cli.py

@@ -2,7 +2,7 @@ from __future__ import annotations
 
 import sys
 
-from .walsh import walsh_transform
+from .walsh import walsh_transform, nonlinearity
 
 
 def main() -> None:
@@ -12,6 +12,7 @@ def main() -> None:
         expr = input("Enter formula: ").strip()
 
     print(walsh_transform(expr))
+    print("non-linearity:", nonlinearity(expr))
 
 
 if __name__ == "__main__":

src/walsh/walsh.py

@@ -66,3 +66,19 @@ def walsh_transform(
         coeffs.append(total)
 
     return coeffs
+
+def nonlinearity(
+    expr: str | Poly,
+    variables: Sequence[str] | None = None,
+) -> int:
+    """
+    NL(f) = 2^(n-1) - max_u |W_f(u)| / 2
+    """
+    poly = parse_boolean_expression(expr) if isinstance(expr, str) else expr
+
+    vars_ = list(variables) if variables is not None else infer_variables(poly)
+    n = len(vars_)
+
+    spectrum = walsh_transform(poly, vars_)
+
+    return (1 << (n - 1)) - max(abs(w) for w in spectrum) // 2

tests/test_nonlinearity.py

@@ -0,0 +1,13 @@
+from walsh.walsh import nonlinearity
+
+
+def test_nonlinearity_linear_function():
+    assert nonlinearity("x1 XOR x2") == 0
+
+
+def test_nonlinearity_or():
+    assert nonlinearity("x1 OR x2") == 1
+
+
+def test_nonlinearity_majority():
+    assert nonlinearity("x1*x2 XOR x1*x3 XOR x2*x3") == 2