diff --git a/include/aidge/backend/cpu.hpp b/include/aidge/backend/cpu.hpp
index 71d8499972e419c903e24809b1bed2cb4cad70af..f3af2bf3015fb45bda9736e9925c8527e2b0cad0 100644
--- a/include/aidge/backend/cpu.hpp
+++ b/include/aidge/backend/cpu.hpp
@@ -23,6 +23,7 @@
 #include "aidge/backend/cpu/operator/FCImpl.hpp"
 #include "aidge/backend/cpu/operator/LeakyReLUImpl.hpp"
 #include "aidge/backend/cpu/operator/MatMulImpl.hpp"
+#include "aidge/backend/cpu/operator/MulImpl.hpp"
 #include "aidge/backend/cpu/operator/PadImpl.hpp"
 #include "aidge/backend/cpu/operator/PowImpl.hpp"
 #include "aidge/backend/cpu/operator/ProducerImpl.hpp"
diff --git a/include/aidge/backend/cpu/operator/MulImpl.hpp b/include/aidge/backend/cpu/operator/MulImpl.hpp
new file mode 100644
index 0000000000000000000000000000000000000000..54361e4f5f7a361032c9f4928392f18f183724ac
--- /dev/null
+++ b/include/aidge/backend/cpu/operator/MulImpl.hpp
@@ -0,0 +1,50 @@
+/********************************************************************************
+ * Copyright (c) 2023 CEA-List
+ *
+ * This program and the accompanying materials are made available under the
+ * terms of the Eclipse Public License 2.0 which is available at
+ * http://www.eclipse.org/legal/epl-2.0.
+ *
+ * SPDX-License-Identifier: EPL-2.0
+ *
+ ********************************************************************************/
+
+#ifndef AIDGE_CPU_OPERATOR_MULIMPL_H_
+#define AIDGE_CPU_OPERATOR_MULIMPL_H_
+
+#include "aidge/backend/OperatorImpl.hpp"
+#include "aidge/operator/Mul.hpp"
+#include "aidge/utils/Registrar.hpp"
+#include "aidge/utils/Types.h"
+#include <memory>
+#include <vector>
+
+namespace Aidge {
+// class Mul_Op;
+
+// compute kernel registry for forward and backward
+class MulImplForward_cpu
+    : public Registrable<MulImplForward_cpu, std::tuple<DataType, DataType, DataType>, void(const std::size_t, const std::size_t, const void*, const void*,void*)> {
+};
+class MulImplBackward_cpu
+    : public Registrable<MulImplBackward_cpu, std::tuple<DataType, DataType, DataType>, void(const std::size_t, const std::size_t, const void*, const void*, void*)> {
+};
+
+class MulImpl_cpu : public OperatorImpl {
+public:
+    MulImpl_cpu(const Mul_Op& op) : OperatorImpl(op) {}
+
+    static std::unique_ptr<MulImpl_cpu> create(const Mul_Op& op) {
+        return std::make_unique<MulImpl_cpu>(op);
+    }
+
+    NbElts_t getNbRequiredProtected(const IOIndex_t inputIdx) const override final;
+    void forward() override;
+};
+
+namespace {
+static Registrar<Mul_Op> registrarMulImpl_cpu("cpu", Aidge::MulImpl_cpu::create);
+}
+}  // namespace Aidge
+
+#endif /* AIDGE_CPU_OPERATOR_MULIMPL_H_ */
diff --git a/include/aidge/backend/cpu/operator/MulImpl_forward_kernels.hpp b/include/aidge/backend/cpu/operator/MulImpl_forward_kernels.hpp
new file mode 100644
index 0000000000000000000000000000000000000000..9caef8b88af3ca779309b60eba984a72db35f84a
--- /dev/null
+++ b/include/aidge/backend/cpu/operator/MulImpl_forward_kernels.hpp
@@ -0,0 +1,64 @@
+/********************************************************************************
+ * Copyright (c) 2023 CEA-List
+ *
+ * This program and the accompanying materials are made available under the
+ * terms of the Eclipse Public License 2.0 which is available at
+ * http://www.eclipse.org/legal/epl-2.0.
+ *
+ * SPDX-License-Identifier: EPL-2.0
+ *
+ ********************************************************************************/
+
+#ifndef AIDGE_CPU_OPERATOR_MULIMPL_FORWARD_KERNEL_H_
+#define AIDGE_CPU_OPERATOR_MULIMPL_FORWARD_KERNEL_H_
+
+#include "aidge/utils/Registrar.hpp"
+
+#include "aidge/backend/cpu/operator/MulImpl.hpp"
+
+namespace Aidge {
+template <class I1, class I2, class O>
+void MulImpl_cpu_forward_kernel(std::size_t input1Length,
+                                     std::size_t input2Length,
+                                     const void* input1_,
+                                     const void* input2_,
+                                     void* output_) {
+
+    const I1* input_1 = static_cast<const I1*>(input1_);
+    const I2* input_2 = static_cast<const I2*>(input2_);
+    O* output = static_cast<O*>(output_);
+    if (input2Length == input1Length)
+    {
+        for (std::size_t i = 0; i < input1Length; ++i) {
+            output[i] = input_1[i] * input_2[i];
+        }
+    }
+    else if (input2Length == 1)
+    {
+        for (std::size_t i = 0; i < input1Length; ++i) {
+            output[i] = input_1[i] * input_2[0];
+        }
+    }
+    else // input_2 is 1d and of size the number of channels of input_1
+    {
+        for (std::size_t i = 0; i < input1Length; ++i) {
+            std::size_t channelIdx = i % input2Length;
+            output[i] = input_1[i] * input_2[channelIdx];
+        }
+    }
+}
+
+namespace {
+static Registrar<MulImplForward_cpu> registrarMulImplForward_cpu_Float32(
+        {DataType::Float32, DataType::Float32, DataType::Float32},
+        Aidge::MulImpl_cpu_forward_kernel<float, float, float>);
+static Registrar<MulImplForward_cpu> registrarMulImplForward_cpu_Int32(
+        {DataType::Int32, DataType::Int32, DataType::Int32},
+        Aidge::MulImpl_cpu_forward_kernel<int, int, int>);
+static Registrar<MulImplForward_cpu> registrarMulImplForward_cpu_Float64(
+        {DataType::Float64, DataType::Float64, DataType::Float64},
+        Aidge::MulImpl_cpu_forward_kernel<double, double, double>);
+}  // namespace
+}  // namespace Aidge
+
+#endif /* AIDGE_CPU_OPERATOR_MULIMPL_FORWARD_KERNEL_H_ */
diff --git a/src/operator/MulImpl.cpp b/src/operator/MulImpl.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..b6eb245cf0b1afc8893dfbab13d3294b945b3e0e
--- /dev/null
+++ b/src/operator/MulImpl.cpp
@@ -0,0 +1,51 @@
+/********************************************************************************
+ * Copyright (c) 2023 CEA-List
+ *
+ * This program and the accompanying materials are made available under the
+ * terms of the Eclipse Public License 2.0 which is available at
+ * http://www.eclipse.org/legal/epl-2.0.
+ *
+ * SPDX-License-Identifier: EPL-2.0
+ *
+ ********************************************************************************/
+
+#include <cassert>
+#include <chrono>  // std::chrono::milliseconds
+#include <numeric> // std::accumulate
+#include <thread>  // std::this_thread::sleep_for
+#include <vector>
+
+#include "aidge/operator/Mul.hpp"
+#include "aidge/utils/Types.h"
+
+#include "aidge/backend/cpu/operator/MulImpl.hpp"
+#include "aidge/backend/cpu/operator/MulImpl_forward_kernels.hpp"
+
+Aidge::NbElts_t Aidge::MulImpl_cpu::getNbRequiredProtected(const Aidge::IOIndex_t /*inputIdx*/) const {
+    // this implementation can be in-place
+    return 0;
+}
+
+void Aidge::MulImpl_cpu::forward() {
+    assert(mOp.getInput(0) && "missing input #0");
+    assert(mOp.getInput(1) && "missing input #1");
+
+    assert(((mOp.getInput(1)->size() == 1) || 
+            (mOp.getInput(1)->size() == mOp.getInput(0)->size()) ||
+            (mOp.getInput(1)->nbDims() == 1 && mOp.getInput(1)->size() == mOp.getInput(0)->dims()[mOp.getInput(0)->nbDims()-1])
+           ) &&
+           "input #1 must either be a tensor of size 1, the number of channels of input # or the same size of input #0");
+
+    // Find the correct kernel type
+    auto kernelFunc = Registrar<MulImplForward_cpu>::create({
+        mOp.getInput(0)->dataType(),
+        mOp.getInput(1)->dataType(),
+        mOp.getOutput(0)->dataType()});
+
+    // Call kernel
+    kernelFunc(std::static_pointer_cast<Tensor>(mOp.getInput(0))->size(),
+        std::static_pointer_cast<Tensor>(mOp.getInput(1))->size(),
+        mOp.getInput(0)->getImpl()->rawPtr(),
+        mOp.getInput(1)->getImpl()->rawPtr(),
+        mOp.getOutput(0)->getImpl()->rawPtr());
+}
diff --git a/unit_tests/operator/Test_MulImpl.cpp b/unit_tests/operator/Test_MulImpl.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..bfb4ffc2d3aea74ada4ed3656041deb7cafb5a99
--- /dev/null
+++ b/unit_tests/operator/Test_MulImpl.cpp
@@ -0,0 +1,129 @@
+/********************************************************************************
+ * Copyright (c) 2023 CEA-List
+ *
+ * This program and the accompanying materials are made available under the
+ * terms of the Eclipse Public License 2.0 which is available at
+ * http://www.eclipse.org/legal/epl-2.0.
+ *
+ * SPDX-License-Identifier: EPL-2.0
+ *
+ ********************************************************************************/
+
+#include <catch2/catch_test_macros.hpp>
+
+#include "aidge/data/Tensor.hpp"
+#include "aidge/operator/Mul.hpp"
+
+#include "aidge/backend/cpu.hpp"
+
+#include <memory>
+
+using namespace Aidge;
+
+TEST_CASE("[cpu/operator] Mul(forward)") {
+    SECTION("2D Tensor by Singleton") {
+        std::shared_ptr<Tensor> input_1 = std::make_shared<Tensor>(Array2D<float,2,2> {
+            {
+                {0.38977361, 0.34064174},
+                {0.00427264, 0.90872520}
+            }
+        });
+        std::shared_ptr<Tensor> input_2 =  std::make_shared<Tensor>(Array2D<float,1,1>{{3.0}});
+        std::shared_ptr<Tensor> expectedOutput = std::make_shared<Tensor>(Array2D<float,2,2> {
+            {
+                {1.16932082, 1.02192521},
+                {0.01281792, 2.72617555}
+            }
+        });
+
+        std::shared_ptr<Node> myMul = Mul();
+        myMul->getOperator()->setDatatype(DataType::Float32);
+        myMul->getOperator()->setBackend("cpu");
+        myMul->getOperator()->associateInput(0, input_1);
+        myMul->getOperator()->associateInput(1, input_2);
+        myMul->getOperator()->computeOutputDims();
+        myMul->forward();
+
+        float* resPtr = static_cast<float*>(myMul->getOperator()->getOutput(0)->getImpl()->rawPtr());
+        float* expectedPtr = static_cast<float*>(expectedOutput->getImpl()->rawPtr());
+        for (std::size_t i = 0; i< 4; ++i) {
+            REQUIRE(std::abs(resPtr[i]-expectedPtr[i]) < 0.00001);
+        }
+
+    }
+
+    SECTION("2D Tensors") {
+        std::shared_ptr<Tensor> input_1 = std::make_shared<Tensor>(Array2D<float,2,2> {
+            {
+                {0.38977361, 0.34064174},
+                {0.00427264, 0.90872520}
+            }
+        });
+        std::shared_ptr<Tensor> input_2 =  std::make_shared<Tensor>(Array2D<float,2,2>{
+            {
+                {0.02362096, 0.24084556},
+                {0.94690859, 0.13512510}
+            }
+        });
+        std::shared_ptr<Tensor> expectedOutput = std::make_shared<Tensor>(Array2D<float,2,2> {
+            {
+                {0.00920683, 0.08204205},
+                {0.00404580, 0.12279158}
+            }
+        });
+
+        std::shared_ptr<Node> myMul = Mul();
+        myMul->getOperator()->setDatatype(DataType::Float32);
+        myMul->getOperator()->setBackend("cpu");
+        myMul->getOperator()->associateInput(0, input_1);
+        myMul->getOperator()->associateInput(1, input_2);
+        myMul->getOperator()->computeOutputDims();
+        myMul->forward();
+
+        float* resPtr = static_cast<float*>(myMul->getOperator()->getOutput(0)->getImpl()->rawPtr());
+        float* expectedPtr = static_cast<float*>(expectedOutput->getImpl()->rawPtr());
+        for (std::size_t i = 0; i< 4; ++i) {
+            REQUIRE(std::abs(resPtr[i]-expectedPtr[i]) < 0.00001);
+        }
+
+    }
+
+    SECTION("3D Tensor by 1D Tensor") {
+        std::shared_ptr<Tensor> input_1 = std::make_shared<Tensor>(Array3D<float,2,2,3> {
+            {
+                {{0.33647752, 0.89360154, 0.46586215},
+                 {0.71518236, 0.71481097, 0.97991812}},
+
+                {{0.17393428, 0.56849813, 0.18489265},
+                 {0.78397650, 0.00348300, 0.65758008}}
+            }
+        });
+        std::shared_ptr<Tensor> input_2 =  std::make_shared<Tensor>(Array1D<float,3>{
+            {0.15380561, 0.51063120, 0.93031412}
+        });
+        std::shared_ptr<Tensor> expectedOutput = std::make_shared<Tensor>(Array3D<float,2,2,3> {
+            {
+                {{0.05175213, 0.45630082, 0.43339813},
+                 {0.10999906, 0.36500478, 0.91163164}},
+
+                {{0.02675207, 0.29029289, 0.17200825},
+                 {0.12057999, 0.00177853, 0.61175603}}
+            }
+        });
+
+        std::shared_ptr<Node> myMul = Mul();
+        myMul->getOperator()->setDatatype(DataType::Float32);
+        myMul->getOperator()->setBackend("cpu");
+        myMul->getOperator()->associateInput(0, input_1);
+        myMul->getOperator()->associateInput(1, input_2);
+        myMul->getOperator()->computeOutputDims();
+        myMul->forward();
+
+        float* resPtr = static_cast<float*>(myMul->getOperator()->getOutput(0)->getImpl()->rawPtr());
+        float* expectedPtr = static_cast<float*>(expectedOutput->getImpl()->rawPtr());
+        for (std::size_t i = 0; i< 4; ++i) {
+            REQUIRE(std::abs(resPtr[i]-expectedPtr[i]) < 0.00001);
+        }
+
+    }
+}
\ No newline at end of file