Fix evaluation of linear functions with EvalPoly

The `internalEvalPolyLinearWithPrecomp` contained an off-by-one error
that caused it to throw an exception when the polynomial to evaluate was
a linear function. This patch fixes that mistake, and adds a test that
evaluates a linear polynomial on a CKKS ciphertext.

Author: hsanzg

src/pke/lib/scheme/ckksrns/ckksrns-advancedshe.cpp

@@ -331,9 +331,10 @@ std::shared_ptr<seriesPowers<DCRTPoly>> AdvancedSHECKKSRNS::EvalPowers(
 template <typename VectorDataType>
 static inline Ciphertext<DCRTPoly> internalEvalPolyLinearWithPrecomp(std::vector<Ciphertext<DCRTPoly>>& powers,
                                                                      const std::vector<VectorDataType>& coefficients) {
+    if (coefficients.size() < 2)
+        OPENFHE_THROW("EvalPolyLinear: The coefficients vector should contain at least 2 elements");
+
     uint32_t k = coefficients.size() - 1;
-    if (k <= 1)
-        OPENFHE_THROW("The coefficients vector should contain at least 2 elements");
 
     if (!IsNotEqualZero(coefficients[k]))
         OPENFHE_THROW("EvalPolyLinear: The highest-order coefficient cannot be set to 0.");

src/pke/unittest/utckksrns/UnitTestCKKSrns.cpp

@@ -1801,6 +1801,9 @@ class UTCKKSRNS : public ::testing::TestWithParam<TEST_CASE_UTCKKSRNS> {
             // x + x^2 - x^3
             // low-degree function to check linear implementation
             std::vector<double> coefficients5{0, 1, 1, -1};
+            // 1 + 2x
+            // linear function to check linear implementation
+            std::vector<double> coefficients6{1.0, 2.0};
 
             Plaintext plaintext1 = cc->MakeCKKSPackedPlaintext(input);
 
@@ -1819,6 +1822,9 @@ class UTCKKSRNS : public ::testing::TestWithParam<TEST_CASE_UTCKKSRNS> {
             std::vector<std::complex<double>> output5{0.625, 0.847, 0.9809999999, 0.995125, 0.990543};
             Plaintext plaintextResult5 = cc->MakeCKKSPackedPlaintext(output5);
 
+            std::vector<std::complex<double>> output6{2.0, 2.4, 2.8, 2.9, 2.86};
+            Plaintext plaintextResult6 = cc->MakeCKKSPackedPlaintext(output6);
+
             // Generate encryption keys
             KeyPair<Element> kp = cc->KeyGen();
             // Generate multiplication keys
@@ -1878,6 +1884,16 @@ class UTCKKSRNS : public ::testing::TestWithParam<TEST_CASE_UTCKKSRNS> {
                     << " - we get: " << results5->GetCKKSPackedValue();
             checkEquality(plaintextResult5->GetCKKSPackedValue(), results5->GetCKKSPackedValue(), epsHigh,
                           failmsg + " EvalPoly for low-degree polynomial failed: " + buffer5.str());
+
+            Ciphertext<Element> cResult6 = cc->EvalPolyLinear(ciphertext1, coefficients6);
+            Plaintext results6;
+            cc->Decrypt(kp.secretKey, cResult6, &results6);
+            results6->SetLength(encodedLength);
+            std::stringstream buffer6;
+            buffer6 << "should be: " << plaintextResult6->GetCKKSPackedValue()
+                    << " - we get: " << results6->GetCKKSPackedValue();
+            checkEquality(plaintextResult6->GetCKKSPackedValue(), results6->GetCKKSPackedValue(), epsHigh,
+                          failmsg + " EvalPoly for linear polynomial failed: " + buffer6.str());
         }
         catch (std::exception& e) {
             std::cerr << "Exception thrown from " << __func__ << "(): " << e.what() << std::endl;