feat(poly_mul): implement synchronous PolyMul with base-case multiply

Phase 2.2: NTT-domain polynomial pointwise multiplication.
- basecase_mul.v: degree-1 base-case multiply (c0,c1) with Barrett
- poly_mul_zeta_rom.v: 128-entry zeta ROM for PolyMul
- poly_mul_sync.v: FSM (IDLE→LOAD 256 cycles→COMPUTE 256 cycles→DONE)

Verified: 5/5 vectors bit-exact vs Python PolyMul reference

test_framework/modules/poly_mul/gen_vectors.py

@@ -0,0 +1,128 @@
+"""gen_vectors.py - Test vector generator for poly_mul module.
+
+Generates random NTT-domain polynomial pairs and computes expected
+pointwise base-case multiplication results using embedded Python reference.
+"""
+
+import os
+import random
+import sys
+
+sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', '..', 'lib'))
+from vector_gen import VectorGenerator
+
+Q = 3329
+N = 256
+
+# Bit-reversed zeta values (same as NTT zeta_bitRev)
+zeta_bitRev = [1, 1729, 2580, 3289, 2642, 630, 1897, 848,
+               1062, 1919, 193, 797, 2786, 3260, 569, 1746,
+               296, 2447, 1339, 1476, 3046, 56, 2240, 1333,
+               1426, 2094, 535, 2882, 2393, 2879, 1974, 821,
+               289, 331, 3253, 1756, 1197, 2304, 2277, 2055,
+               650, 1977, 2513, 632, 2865, 33, 1320, 1915,
+               2319, 1435, 807, 452, 1438, 2868, 1534, 2402,
+               2647, 2617, 1481, 648, 2474, 3110, 1227, 910,
+               17, 2761, 583, 2649, 1637, 723, 2288, 1100,
+               1409, 2662, 3281, 233, 756, 2156, 3015, 3050,
+               1703, 1651, 2789, 1789, 1847, 952, 1461, 2687,
+               939, 2308, 2437, 2388, 733, 2337, 268, 641,
+               1584, 2298, 2037, 3220, 375, 2549, 2090, 1645,
+               1063, 319, 2773, 757, 2099, 561, 2466, 2594,
+               2804, 1092, 403, 1026, 1143, 2150, 2775, 886,
+               1722, 1212, 1874, 1029, 2110, 2935, 885, 2154]
+
+# Precomputed PolyMul zeta values: zeta_sq_mul[i] = (zeta_bitRev[i]^2 * 17) % Q
+zeta_sq_mul = [((z * z) * 17) % Q for z in zeta_bitRev]
+
+
+def basecase_multiply(a0, a1, b0, b1, zeta):
+    """Degree-1 NTT-domain base-case multiply.
+
+    Computes:
+      c0 = (a0*b0 + a1*b1*zeta) mod Q
+      c1 = (a0*b1 + a1*b0) mod Q
+
+    Uses modular arithmetic to match Barrett reduction semantics.
+    """
+    c0 = ((a0 * b0) % Q + (((a1 * b1) % Q) * zeta) % Q) % Q
+    c1 = ((a0 * b1) % Q + (a1 * b0) % Q) % Q
+    return c0, c1
+
+
+def poly_mul(f_hat, g_hat):
+    """Full NTT-domain polynomial multiplication.
+
+    Given two 256-coefficient NTT-domain polynomials f_hat and g_hat,
+    compute pointwise product using 128 degree-1 base-case multiplies.
+
+    Args:
+        f_hat: list of 256 coefficients in [0, Q-1]
+        g_hat: list of 256 coefficients in [0, Q-1]
+
+    Returns:
+        list of 256 result coefficients in [0, Q-1]
+    """
+    h_hat = []
+    for i in range(128):
+        zeta = zeta_sq_mul[i]
+        h1, h2 = basecase_multiply(
+            f_hat[2 * i], f_hat[2 * i + 1],
+            g_hat[2 * i], g_hat[2 * i + 1],
+            zeta
+        )
+        h_hat.append(h1)
+        h_hat.append(h2)
+    return h_hat
+
+
+class PolyMulVectorGenerator(VectorGenerator):
+    """Generates test vectors for the poly_mul_sync module."""
+
+    def generate_one(self, params: dict) -> dict:
+        """Generate a random polynomial pair with expected result.
+
+        Args:
+            params: Unused for basic case.
+
+        Returns:
+            dict with 'input' (A coeffs, B coeffs) and 'expected' (C coeffs).
+        """
+        # Generate random NTT-domain polynomials
+        A = [random.randint(0, Q - 1) for _ in range(N)]
+        B = [random.randint(0, Q - 1) for _ in range(N)]
+
+        # Compute expected result via Python reference
+        C = poly_mul(A, B)
+
+        return {
+            'input': {'A': A, 'B': B},
+            'expected': {'C': C}
+        }
+
+    def _format_coeffs(self, coeffs: list[int]) -> str:
+        """Format a coefficient list as space-separated 3-digit hex."""
+        return ' '.join(f'{c:03X}' for c in coeffs)
+
+    def write_hex_file(self, vectors: list[dict], filepath: str) -> None:
+        """Write input vectors: one line per vector with 512 hex values.
+
+        Format: A[0] A[1] ... A[255] B[0] B[1] ... B[255]
+        """
+        os.makedirs(os.path.dirname(filepath), exist_ok=True)
+        with open(filepath, 'w') as f:
+            for v in vectors:
+                all_coeffs = v['input']['A'] + v['input']['B']
+                hex_str = self._format_coeffs(all_coeffs)
+                f.write(f'{hex_str}\n')
+
+    def write_expected_file(self, vectors: list[dict], filepath: str) -> None:
+        """Write expected output: one line per vector with 256 hex values.
+
+        Format: C[0] C[1] ... C[255]
+        """
+        os.makedirs(os.path.dirname(filepath), exist_ok=True)
+        with open(filepath, 'w') as f:
+            for v in vectors:
+                hex_str = self._format_coeffs(v['expected']['C'])
+                f.write(f'{hex_str}\n')