feat(tb): add Vivado XSIM Verilog testbenches for all 10 sync modules

Add file-based vector testbenches ( + ) for:
- mod_add_sync, rng_sync, poly_arith_sync, comp_decomp_sync
- s_bram/sd_bram, sha3_chain_top
- ntt_core, poly_mul_sync
- sample_cbd_sync, sample_ntt_sync

Each module includes:
- tb_<module>_xsim.v: Vivado XSIM testbench
- gen_vectors.py: Python vector generator (stdlib only)
- vectors/<module>_input.hex: test input vectors
- xsim_run.tcl: compile + elaborate + simulate script

sync_rtl/sha3_chain/TB/gen_vectors.py

@@ -0,0 +1,85 @@
+#!/usr/bin/env python3
+"""gen_vectors.py — Generate SHA3-512 test vectors for tb_sha3_chain_xsim.v
+
+Computes expected rho and sigma values for sha3_chain_top (ML-KEM G function).
+
+The RTL computes: SHA3-512(d_in || 0x02)
+  - d_in: 256-bit input (32 bytes, big-endian)
+  - 0x02: single byte appended (k=2 parameter for ML-KEM)
+  - G(d || 0x02) uses SHA3-512 mode (rate=576, suffix=01)
+  - rho  = hash[255:0]   (first 256 bits of hash)
+  - sigma = hash[511:256] (next 256 bits of hash)
+
+Output:
+  vectors/sha3_chain_input.hex — 256-bit d_in values (64 hex chars per line)
+
+Usage:
+  python3 gen_vectors.py
+"""
+
+import hashlib
+import os
+
+VECTORS_DIR = os.path.join(os.path.dirname(__file__), "vectors")
+OUTPUT_FILE = os.path.join(VECTORS_DIR, "sha3_chain_input.hex")
+
+# Test vectors: (label, d_in value)
+TEST_VECTORS = [
+    ("all-zeros",    0x0000000000000000000000000000000000000000000000000000000000000000),
+    ("all-ones",     0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF),
+    ("lsb-one",      0x0000000000000000000000000000000000000000000000000000000000000001),
+    ("msb-one",      0x8000000000000000000000000000000000000000000000000000000000000000),
+    ("pattern-aa",   0xAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA),
+    ("pattern-55",   0x5555555555555555555555555555555555555555555555555555555555555555),
+    ("random-1",     0x1A2B3C4D5E6F708192A3B4C5D6E7F8091A2B3C4D5E6F708192A3B4C5D6E7F80),
+    ("random-2",     0xF0E1D2C3B4A5968778695A4B3C2D1E0FF0E1D2C3B4A5968778695A4B3C2D1E0F),
+]
+
+
+def sha3_512_g(d_in: int) -> tuple:
+    """Compute rho, sigma = G(d_in || 0x02) using SHA3-512.
+
+    Returns (rho, sigma) as 256-bit integers.
+    """
+    # d_in as 32 bytes, big-endian (MSB first)
+    d_bytes = d_in.to_bytes(32, "big")
+    # Append k=2 as single byte 0x02
+    message = d_bytes + b"\x02"
+    # SHA3-512 hash → 64 bytes
+    h = hashlib.sha3_512(message).digest()
+    # rho = first 256 bits, sigma = next 256 bits
+    rho = int.from_bytes(h[0:32], "big")
+    sigma = int.from_bytes(h[32:64], "big")
+    return rho, sigma
+
+
+def main():
+    os.makedirs(VECTORS_DIR, exist_ok=True)
+
+    d_in_values = []
+    print("// Expected values computed by gen_vectors.py")
+    print("// SHA3-512(d_in || 0x02)")
+    print("//" + "=" * 72)
+
+    with open(OUTPUT_FILE, "w") as f:
+        for label, d_in in TEST_VECTORS:
+            # Write d_in to hex file (256 bits = 64 hex chars)
+            f.write(f"{d_in:064X}\n")
+            d_in_values.append(d_in)
+
+            # Compute expected values
+            rho, sigma = sha3_512_g(d_in)
+            print(f"// {label}")
+            print(f"//   d_in  = 0x{d_in:064x}")
+            print(f"//   rho   = 0x{rho:064x}")
+            print(f"//   sigma = 0x{sigma:064x}")
+            print()
+
+    print(f"Generated {len(TEST_VECTORS)} vectors → {OUTPUT_FILE}")
+    print()
+    print("// Copy the expected values above into tb_sha3_chain_xsim.v")
+    print("// as hardcoded parameters/initial blocks.")
+
+
+if __name__ == "__main__":
+    main()