algebraic immunity

src/tea3/f31f32.py

@@ -1,5 +1,6 @@
 from sage.all import BooleanPolynomialRing
 from sage.crypto.sbox import SBox
+from sage.crypto.boolean_function import BooleanFunction
 
 from tea3.tea3model import F31, F32
 
@@ -45,7 +46,44 @@ def _truth_table(vecfun):
 def _sbox(vecfun):
     return SBox(_truth_table(vecfun), big_endian=False)
 
+def _coordinate_boolean_functions(vecfun):
+    tt = _truth_table(vecfun)
+
+    coords = [[] for _ in range(8)]
+
+    for value in tt:
+        for i in range(8):
+            coords[i].append((value >> i) & 1)
+
+    return [BooleanFunction(coord) for coord in coords]
+
+
+def study_algebraic_immunity(vecfun, name="F"):
+    bfs = _coordinate_boolean_functions(vecfun)
+
+    print(f"\n{name}")
+    print("-" * len(name))
+
+    ais = []
+
+    for i, bf in enumerate(bfs):
+        ai = bf.algebraic_immunity()
+        ais.append(ai)
+        print(f"coordinate {i}: AI = {ai}")
+
+    print(f"\nminimum AI : {min(ais)}")
+    print(f"maximum AI : {max(ais)}")
+    print(f"average AI : {sum(ais)/len(ais):.2f}")
+
+    return ais
+
+def run_algebraic_immunity():
+    print("Algebraic immunity:")
+    study_algebraic_immunity(F31, "F31")
+    study_algebraic_immunity(F32, "F32")
+
 def run_f31f32():
+    run_algebraic_immunity()
     f31 = _sbox(F31)
     f32 = _sbox(F32)
     print("\nF31")