explore more variable changes

src/tea3/variable_search.py

@@ -11,22 +11,32 @@ def count_monomials(poly):
 
 
 def apply_variable_change(model, coeffs):
-    orig_x = [list(model.v[i * 8 : (i + 1) * 8]) for i in range(5)]
+    """
+    Variable change inside each 8-bit register:
+        x_{r,0} = y_{r,0} + a1*y_{r,1} + ... + a7*y_{r,7}
+        x_{r,j} = y_{r,j} for j = 1..7
+    for every register r in {0,...,4}.
+    """
+    orig_x = [list(model.v[r * 8 : (r + 1) * 8]) for r in range(5)]
     orig_y = model.y_bits
+
     subs = {}
-    for i in range(1, 5):
+
-        for j in range(8):
+    for r in range(5):
-            subs[orig_x[i][j]] = orig_y[i][j]
+        for j in range(1, 8):
-    for j in range(8):
+            subs[orig_x[r][j]] = orig_y[r][j]
-        new_expr = orig_y[0][j]
+
-        for i, ai in enumerate(coeffs, start=1):
+        new_expr = orig_y[r][0]
+        for j, ai in enumerate(coeffs, start=1):
             if ai:
-                new_expr = new_expr + orig_y[i][j]
+                new_expr += orig_y[r][j]
-        subs[orig_x[0][j]] = new_expr
+        subs[orig_x[r][0]] = new_expr
+
     new_R = []
     for i in range(8):
         row = [poly.subs(subs) for poly in model.R_bits[i]]
         new_R.append(row)
+
     return new_R
 
 
@@ -44,14 +54,13 @@ def run_exhaustive(steps: int, target_reg: int = 0, target_bit: int = -1):
         bits = [target_bit]
 
     best_coeffs: tuple | None = None
-    best_label: str = ""
     best_total: int = -1
     best_R: list | None = None
 
-    for idx, coeffs in enumerate(iproduct([0, 1], repeat=4)):
+    for idx, coeffs in enumerate(iproduct([0, 1], repeat=7)):
         new_R = apply_variable_change(snapshot, coeffs)
         label = "".join(map(str, coeffs))
-        print(f"\n[{idx:02d}] (a1,a2,a3,a4) = {label}")
+        print(f"\n[{idx:03d}] (a1,a2,a3,a4,a5,a6,a7) = {label}")
 
         total = 0
         for j in bits:
@@ -63,12 +72,10 @@ def run_exhaustive(steps: int, target_reg: int = 0, target_bit: int = -1):
         if best_total == -1 or total < best_total:
             best_total = total
             best_coeffs = coeffs
-            best_label = label
             best_R = new_R
 
-
     print("\nBest variable change (fewest total monomials)")
-    print(f"  (a1,a2,a3,a4) = ({', '.join(map(str, best_coeffs))})")
+    print(f"  (a1,a2,a3,a4,a5,a6,a7) = ({', '.join(map(str, best_coeffs))})")
     print(f"  Total monomials: {best_total}")
     print("  Polynomial:\n")
     for j in bits: