Fboemer/reference inv ntt (intel#89)

* Add reference radix-2 Inv NTT

hexl/ntt/ntt-internal.hpp

@@ -57,7 +57,8 @@ void ForwardTransformToBitReverseRadix4(
     const uint64_t* precon_root_of_unity_powers, uint64_t input_mod_factor = 1,
     uint64_t output_mod_factor = 1);
 
-/// @brief Reference NTT which is written for clarity rather than performance
+/// @brief Reference forward NTT which is written for clarity rather than
+/// performance
 /// @param[in, out] operand Input data. Overwritten with NTT output
 /// @param[in] n Size of the transform, i.e. the polynomial degree. Must be a
 /// power of two.
@@ -68,6 +69,18 @@ void ReferenceForwardTransformToBitReverse(
     uint64_t* operand, uint64_t n, uint64_t modulus,
     const uint64_t* root_of_unity_powers);
 
+/// @brief Reference inverse NTT which is written for clarity rather than
+/// performance
+/// @param[in, out] operand Input data. Overwritten with NTT output
+/// @param[in] n Size of the transform, i.e. the polynomial degree. Must be a
+/// power of two.
+/// @param[in] modulus Prime modulus. Must satisfy q == 1 mod 2n
+/// @param[in] inv_root_of_unity_powers Powers of inverse 2n'th root of unity in
+/// F_q. In bit-reversed order.
+void ReferenceInverseTransformFromBitReverse(
+    uint64_t* operand, uint64_t n, uint64_t modulus,
+    const uint64_t* inv_root_of_unity_powers);
+
 /// @brief Radix-2 native C++ NTT implementation of the inverse NTT
 /// @param[out] result Output data. Overwritten with NTT output
 /// @param[in] operand Input data.

hexl/ntt/ntt-radix-2.cpp

@@ -290,6 +290,43 @@ void ReferenceForwardTransformToBitReverse(
   }
 }
 
+void ReferenceInverseTransformFromBitReverse(
+    uint64_t* operand, uint64_t n, uint64_t modulus,
+    const uint64_t* inv_root_of_unity_powers) {
+  HEXL_CHECK(NTT::CheckArguments(n, modulus), "");
+  HEXL_CHECK(inv_root_of_unity_powers != nullptr,
+             "inv_root_of_unity_powers == nullptr");
+  HEXL_CHECK(operand != nullptr, "operand == nullptr");
+
+  size_t t = 1;
+  size_t root_index = 1;
+  for (size_t m = (n >> 1); m >= 1; m >>= 1) {
+    size_t j1 = 0;
+    for (size_t i = 0; i < m; i++, root_index++) {
+      const uint64_t W = inv_root_of_unity_powers[root_index];
+      uint64_t* X_r = operand + j1;
+      uint64_t* Y_r = X_r + t;
+      for (size_t j = 0; j < t; j++) {
+        uint64_t X_op = *X_r;
+        uint64_t Y_op = *Y_r;
+        // Butterfly X' = (X + Y) mod q, Y' = W(X-Y) mod q
+        *X_r = AddUIntMod(X_op, Y_op, modulus);
+        *Y_r = MultiplyMod(W, SubUIntMod(X_op, Y_op, modulus), modulus);
+        X_r++;
+        Y_r++;
+      }
+      j1 += (t << 1);
+    }
+    t <<= 1;
+  }
+
+  // Final multiplication by N^{-1}
+  const uint64_t inv_n = InverseMod(n, modulus);
+  for (size_t i = 0; i < n; ++i) {
+    operand[i] = MultiplyMod(operand[i], inv_n, modulus);
+  }
+}
+
 void InverseTransformFromBitReverseRadix2(
     uint64_t* result, const uint64_t* operand, uint64_t n, uint64_t modulus,
     const uint64_t* inv_root_of_unity_powers,

test/test-ntt.cpp

@@ -255,6 +255,9 @@ TEST_P(DegreeModulusInputOutput, API) {
   ReferenceForwardTransformToBitReverse(input.data(), N, modulus,
                                         ntt.GetRootOfUnityPowers().data());
   AssertEqual(input, exp_output);
+  ReferenceInverseTransformFromBitReverse(input.data(), N, modulus,
+                                          ntt.GetInvRootOfUnityPowers().data());
+  AssertEqual(input, input_copy);
 
   // Test round-trip
   input = input_copy;
@@ -448,6 +451,22 @@ TEST_P(NttNativeTest, InverseRadix4Random) {
   AssertEqual(input, input_radix4);
 }
 
+TEST_P(NttNativeTest, InverseRadix2Random) {
+  auto input = GenerateInsecureUniformRandomValues(m_N, 1, 2);
+  auto input_reference = input;
+
+  InverseTransformFromBitReverseRadix2(
+      input.data(), input.data(), m_N, m_modulus,
+      m_ntt.GetInvRootOfUnityPowers().data(),
+      m_ntt.GetPrecon64InvRootOfUnityPowers().data(), 2, 1);
+
+  ReferenceInverseTransformFromBitReverse(
+      input_reference.data(), m_N, m_modulus,
+      m_ntt.GetInvRootOfUnityPowers().data());
+
+  AssertEqual(input, input_reference);
+}
+
 INSTANTIATE_TEST_SUITE_P(
     NTT, NttNativeTest,
     ::testing::Combine(