diff --git a/library/bignum.c b/library/bignum.c
index 58cd2f7..d33f07c 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -867,8 +867,7 @@
 int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B )
 {
     int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
-    size_t i, j;
-    mbedtls_mpi_uint *o, *p, c, tmp;
+    size_t j;
     MPI_VALIDATE_RET( X != NULL );
     MPI_VALIDATE_RET( A != NULL );
     MPI_VALIDATE_RET( B != NULL );
@@ -882,7 +881,7 @@
         MBEDTLS_MPI_CHK( mbedtls_mpi_copy( X, A ) );
 
     /*
-     * X should always be positive as a result of unsigned additions.
+     * X must always be positive as a result of unsigned additions.
      */
     X->s = 1;
 
@@ -892,27 +891,25 @@
 
     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
 
-    o = B->p; p = X->p; c = 0;
+    /* j is the number of non-zero limbs of B. Add those to X. */
 
-    /*
-     * tmp is used because it might happen that p == o
-     */
-    for( i = 0; i < j; i++, o++, p++ )
-    {
-        tmp= *o;
-        *p +=  c; c  = ( *p <  c );
-        *p += tmp; c += ( *p < tmp );
-    }
+    mbedtls_mpi_uint *p = X->p;
+
+    mbedtls_mpi_uint c = mbedtls_mpi_core_add( p, p, B->p, j );
+
+    p += j;
+
+    /* Now propagate any carry */
 
     while( c != 0 )
     {
-        if( i >= X->n )
+        if( j >= X->n )
         {
-            MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, i + 1 ) );
-            p = X->p + i;
+            MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j + 1 ) );
+            p = X->p + j;
         }
 
-        *p += c; c = ( *p < c ); i++; p++;
+        *p += c; c = ( *p < c ); j++; p++;
     }
 
 cleanup:
diff --git a/library/bignum_core.c b/library/bignum_core.c
index 963af5b..b401fa3 100644
--- a/library/bignum_core.c
+++ b/library/bignum_core.c
@@ -316,8 +316,6 @@
     return( 0 );
 }
 
-
-
 void mbedtls_mpi_core_shift_r( mbedtls_mpi_uint *X, size_t limbs,
                                size_t count )
 {
@@ -360,7 +358,24 @@
     }
 }
 
+mbedtls_mpi_uint mbedtls_mpi_core_add( mbedtls_mpi_uint *X,
+                                       const mbedtls_mpi_uint *A,
+                                       const mbedtls_mpi_uint *B,
+                                       size_t limbs )
+{
+    mbedtls_mpi_uint c = 0;
 
+    for( size_t i = 0; i < limbs; i++ )
+    {
+        mbedtls_mpi_uint t = c + A[i];
+        c = ( t < A[i] );
+        t += B[i];
+        c += ( t < B[i] );
+        X[i] = t;
+    }
+
+    return( c );
+}
 
 mbedtls_mpi_uint mbedtls_mpi_core_add_if( mbedtls_mpi_uint *X,
                                           const mbedtls_mpi_uint *A,
diff --git a/library/bignum_core.h b/library/bignum_core.h
index 503bc1d..9a5b89f 100644
--- a/library/bignum_core.h
+++ b/library/bignum_core.h
@@ -278,6 +278,28 @@
                                size_t count );
 
 /**
+ * \brief Add two fixed-size large unsigned integers, returning the carry.
+ *
+ * Calculates `A + B` where `A` and `B` have the same size.
+ *
+ * This function operates modulo `2^(biL*limbs)` and returns the carry
+ * (1 if there was a wraparound, and 0 otherwise).
+ *
+ * \p X may be aliased to \p A or \p B.
+ *
+ * \param[out] X    The result of the addition.
+ * \param[in] A     Little-endian presentation of the left operand.
+ * \param[in] B     Little-endian presentation of the right operand.
+ * \param limbs     Number of limbs of \p X, \p A and \p B.
+ *
+ * \return          1 if `A + B >= 2^(biL*limbs)`, 0 otherwise.
+ */
+mbedtls_mpi_uint mbedtls_mpi_core_add( mbedtls_mpi_uint *X,
+                                       const mbedtls_mpi_uint *A,
+                                       const mbedtls_mpi_uint *B,
+                                       size_t limbs );
+
+/**
  * \brief Conditional addition of two fixed-size large unsigned integers,
  *        returning the carry.
  *
diff --git a/scripts/mbedtls_dev/bignum_core.py b/scripts/mbedtls_dev/bignum_core.py
index e46364b..0d238e7 100644
--- a/scripts/mbedtls_dev/bignum_core.py
+++ b/scripts/mbedtls_dev/bignum_core.py
@@ -144,12 +144,12 @@
             yield cls(a_value, b_value, 32).create_test_case()
             yield cls(a_value, b_value, 64).create_test_case()
 
-class BignumCoreAddIf(BignumCoreOperationArchSplit):
-    """Test cases for bignum core add if."""
+class BignumCoreAddAndAddIf(BignumCoreOperationArchSplit):
+    """Test cases for bignum core add and add-if."""
     count = 0
     symbol = "+"
-    test_function = "mpi_core_add_if"
-    test_name = "mbedtls_mpi_core_add_if"
+    test_function = "mpi_core_add_and_add_if"
+    test_name = "mpi_core_add_and_add_if"
 
     def result(self) -> List[str]:
         result = self.int_a + self.int_b
diff --git a/tests/suites/test_suite_bignum_core.function b/tests/suites/test_suite_bignum_core.function
index 74ee27a..57c2f37 100644
--- a/tests/suites/test_suite_bignum_core.function
+++ b/tests/suites/test_suite_bignum_core.function
@@ -5,6 +5,154 @@
 #include "constant_time_internal.h"
 #include "test/constant_flow.h"
 
+/** Verifies mbedtls_mpi_core_add().
+ *
+ * \param[in] A       Little-endian presentation of the left operand.
+ * \param[in] B       Little-endian presentation of the right operand.
+ * \param limbs       Number of limbs in each MPI (\p A, \p B, \p S and \p X).
+ * \param[in] S       Little-endian presentation of the expected sum.
+ * \param carry       Expected carry from the addition.
+ * \param[in,out] X   Temporary storage to be used for results.
+ *
+ * \return  1 if mbedtls_mpi_core_add() passes this test, otherwise 0.
+ */
+static int mpi_core_verify_add( mbedtls_mpi_uint *A,
+                                mbedtls_mpi_uint *B,
+                                size_t limbs,
+                                mbedtls_mpi_uint *S,
+                                int carry,
+                                mbedtls_mpi_uint *X )
+{
+    int ret = 0;
+
+    size_t bytes = limbs * sizeof( *A );
+
+    /* The test cases have A <= B to avoid repetition, so we test A + B then,
+     * if A != B, B + A. If A == B, we can test when A and B are aliased */
+
+    /* A + B */
+
+    /* A + B => correct result and carry */
+    TEST_EQUAL( carry, mbedtls_mpi_core_add( X, A, B, limbs ) );
+    ASSERT_COMPARE( X, bytes, S, bytes );
+
+    /* A + B; alias output and first operand => correct result and carry */
+    memcpy( X, A, bytes );
+    TEST_EQUAL( carry, mbedtls_mpi_core_add( X, X, B, limbs ) );
+    ASSERT_COMPARE( X, bytes, S, bytes );
+
+    /* A + B; alias output and second operand => correct result and carry */
+    memcpy( X, B, bytes );
+    TEST_EQUAL( carry, mbedtls_mpi_core_add( X, A, X, limbs ) );
+    ASSERT_COMPARE( X, bytes, S, bytes );
+
+    if ( memcmp( A, B, bytes ) == 0 )
+    {
+        /* A == B, so test where A and B are aliased */
+
+        /* A + A => correct result and carry */
+        TEST_EQUAL( carry, mbedtls_mpi_core_add( X, A, A, limbs ) );
+        ASSERT_COMPARE( X, bytes, S, bytes );
+
+        /* A + A, output aliased to both operands => correct result and carry */
+        memcpy( X, A, bytes );
+        TEST_EQUAL( carry, mbedtls_mpi_core_add( X, X, X, limbs ) );
+        ASSERT_COMPARE( X, bytes, S, bytes );
+    }
+    else
+    {
+        /* A != B, so test B + A */
+
+        /* B + A => correct result and carry */
+        TEST_EQUAL( carry, mbedtls_mpi_core_add( X, B, A, limbs ) );
+        ASSERT_COMPARE( X, bytes, S, bytes );
+
+        /* B + A; alias output and first operand => correct result and carry */
+        memcpy( X, B, bytes );
+        TEST_EQUAL( carry, mbedtls_mpi_core_add( X, X, A, limbs ) );
+        ASSERT_COMPARE( X, bytes, S, bytes );
+
+        /* B + A; alias output and second operand => correct result and carry */
+        memcpy( X, A, bytes );
+        TEST_EQUAL( carry, mbedtls_mpi_core_add( X, B, X, limbs ) );
+        ASSERT_COMPARE( X, bytes, S, bytes );
+    }
+
+    ret = 1;
+
+exit:
+    return ret;
+}
+
+/** Verifies mbedtls_mpi_core_add_if().
+ *
+ * \param[in] A       Little-endian presentation of the left operand.
+ * \param[in] B       Little-endian presentation of the right operand.
+ * \param limbs       Number of limbs in each MPI (\p A, \p B, \p S and \p X).
+ * \param[in] S       Little-endian presentation of the expected sum.
+ * \param carry       Expected carry from the addition.
+ * \param[in,out] X   Temporary storage to be used for results.
+ *
+ * \return  1 if mbedtls_mpi_core_add_if() passes this test, otherwise 0.
+ */
+static int mpi_core_verify_add_if( mbedtls_mpi_uint *A,
+                                   mbedtls_mpi_uint *B,
+                                   size_t limbs,
+                                   mbedtls_mpi_uint *S,
+                                   int carry,
+                                   mbedtls_mpi_uint *X )
+{
+    int ret = 0;
+
+    size_t bytes = limbs * sizeof( *A );
+
+    /* The test cases have A <= B to avoid repetition, so we test A + B then,
+     * if A != B, B + A. If A == B, we can test when A and B are aliased */
+
+    /* A + B */
+
+    /* cond = 0 => X unchanged, no carry */
+    memcpy( X, A, bytes );
+    TEST_EQUAL( 0, mbedtls_mpi_core_add_if( X, B, limbs, 0 ) );
+    ASSERT_COMPARE( X, bytes, A, bytes );
+
+    /* cond = 1 => correct result and carry */
+    TEST_EQUAL( carry, mbedtls_mpi_core_add_if( X, B, limbs, 1 ) );
+    ASSERT_COMPARE( X, bytes, S, bytes );
+
+    if ( memcmp( A, B, bytes ) == 0 )
+    {
+        /* A == B, so test where A and B are aliased */
+
+        /* cond = 0 => X unchanged, no carry */
+        memcpy( X, B, bytes );
+        TEST_EQUAL( 0, mbedtls_mpi_core_add_if( X, X, limbs, 0 ) );
+        ASSERT_COMPARE( X, bytes, B, bytes );
+
+        /* cond = 1 => correct result and carry */
+        TEST_EQUAL( carry, mbedtls_mpi_core_add_if( X, X, limbs, 1 ) );
+        ASSERT_COMPARE( X, bytes, S, bytes );
+    }
+    else
+    {
+        /* A != B, so test B + A */
+
+        /* cond = 0 => d unchanged, no carry */
+        memcpy( X, B, bytes );
+        TEST_EQUAL( 0, mbedtls_mpi_core_add_if( X, A, limbs, 0 ) );
+        ASSERT_COMPARE( X, bytes, B, bytes );
+
+        /* cond = 1 => correct result and carry */
+        TEST_EQUAL( carry, mbedtls_mpi_core_add_if( X, A, limbs, 1 ) );
+        ASSERT_COMPARE( X, bytes, S, bytes );
+    }
+
+    ret = 1;
+
+exit:
+    return ret;
+}
+
 /* END_HEADER */
 
 /* BEGIN_DEPENDENCIES
@@ -359,70 +507,28 @@
 /* END_CASE */
 
 /* BEGIN_CASE */
-void mpi_core_add_if( char * input_A, char * input_B,
-                      char * input_S, int carry )
+void mpi_core_add_and_add_if( char * input_A, char * input_B,
+                              char * input_S, int carry )
 {
     mbedtls_mpi_uint *A = NULL; /* first value to add */
-    size_t A_limbs;
     mbedtls_mpi_uint *B = NULL; /* second value to add */
-    size_t B_limbs;
     mbedtls_mpi_uint *S = NULL; /* expected result */
-    size_t S_limbs;
     mbedtls_mpi_uint *X = NULL; /* destination - the in/out first operand */
-    size_t X_limbs;
+    size_t A_limbs, B_limbs, S_limbs;
 
     TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &A, &A_limbs, input_A ) );
     TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &B, &B_limbs, input_B ) );
     TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &S, &S_limbs, input_S ) );
-    X_limbs = S_limbs;
-    ASSERT_ALLOC( X, X_limbs );
 
-    /* add_if expects all operands to be the same length */
+    /* add and add_if expect all operands to be the same length */
     TEST_EQUAL( A_limbs, B_limbs );
     TEST_EQUAL( A_limbs, S_limbs );
+
     size_t limbs = A_limbs;
-    size_t bytes = limbs * sizeof( *A );
+    ASSERT_ALLOC( X, limbs );
 
-    /* The test cases have A <= B to avoid repetition, so we test A + B then,
-     * if A != B, B + A. If A == B, we can test when A and B are aliased */
-
-    /* A + B */
-
-    /* cond = 0 => X unchanged, no carry */
-    memcpy( X, A, bytes );
-    TEST_EQUAL( 0, mbedtls_mpi_core_add_if( X, B, limbs, 0 ) );
-    ASSERT_COMPARE( X, bytes, A, bytes );
-
-    /* cond = 1 => correct result and carry */
-    TEST_EQUAL( carry, mbedtls_mpi_core_add_if( X, B, limbs, 1 ) );
-    ASSERT_COMPARE( X, bytes, S, bytes );
-
-    if ( memcmp( A, B, bytes ) == 0 )
-    {
-        /* A == B, so test where A and B are aliased */
-
-        /* cond = 0 => X unchanged, no carry */
-        memcpy( X, B, bytes );
-        TEST_EQUAL( 0, mbedtls_mpi_core_add_if( X, X, limbs, 0 ) );
-        ASSERT_COMPARE( X, bytes, B, bytes );
-
-        /* cond = 1 => correct result and carry */
-        TEST_EQUAL( carry, mbedtls_mpi_core_add_if( X, X, limbs, 1 ) );
-        ASSERT_COMPARE( X, bytes, S, bytes );
-    }
-    else
-    {
-        /* A != B, so test B + A */
-
-        /* cond = 0 => d unchanged, no carry */
-        memcpy( X, B, bytes );
-        TEST_EQUAL( 0, mbedtls_mpi_core_add_if( X, A, limbs, 0 ) );
-        ASSERT_COMPARE( X, bytes, B, bytes );
-
-        /* cond = 1 => correct result and carry */
-        TEST_EQUAL( carry, mbedtls_mpi_core_add_if( X, A, limbs, 1 ) );
-        ASSERT_COMPARE( X, bytes, S, bytes );
-    }
+    TEST_ASSERT( mpi_core_verify_add( A, B, limbs, S, carry, X ) );
+    TEST_ASSERT( mpi_core_verify_add_if( A, B, limbs, S, carry, X ) );
 
 exit:
     mbedtls_free( A );