diff --git a/ChangeLog.d/mpi-add-0-ub.txt b/ChangeLog.d/mpi-add-0-ub.txt
new file mode 100644
index 0000000000..9f131a4300
--- /dev/null
+++ b/ChangeLog.d/mpi-add-0-ub.txt
@@ -0,0 +1,4 @@
+Bugfix
+   * Fix undefined behavior (typically harmless in practice) of
+     mbedtls_mpi_add_mpi(), mbedtls_mpi_add_abs() and mbedtls_mpi_add_int()
+     when both operands are 0 and the left operand is represented with 0 limbs.
diff --git a/ChangeLog.d/mpi-most-negative-sint.txt b/ChangeLog.d/mpi-most-negative-sint.txt
new file mode 100644
index 0000000000..5e775c4825
--- /dev/null
+++ b/ChangeLog.d/mpi-most-negative-sint.txt
@@ -0,0 +1,4 @@
+Bugfix
+   * Fix undefined behavior (typically harmless in practice) when some bignum
+     functions receive the most negative value of mbedtls_mpi_sint. Credit
+     to OSS-Fuzz. Fixes #6597.
diff --git a/include/mbedtls/bignum.h b/include/mbedtls/bignum.h
index 3bd1ca0260..877fbc7ceb 100644
--- a/include/mbedtls/bignum.h
+++ b/include/mbedtls/bignum.h
@@ -179,6 +179,20 @@
     #endif /* !MBEDTLS_NO_UDBL_DIVISION */
 #endif /* !MBEDTLS_HAVE_INT64 */
 
+/** \typedef mbedtls_mpi_uint
+ * \brief The type of machine digits in a bignum, called _limbs_.
+ *
+ * This is always an unsigned integer type with no padding bits. The size
+ * is platform-dependent.
+ */
+
+/** \typedef mbedtls_mpi_sint
+ * \brief The signed type corresponding to #mbedtls_mpi_uint.
+ *
+ * This is always an signed integer type with no padding bits. The size
+ * is platform-dependent.
+ */
+
 #ifdef __cplusplus
 extern "C" {
 #endif
diff --git a/library/bignum.c b/library/bignum.c
index 42be815ba8..ba03988254 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -252,6 +252,17 @@ void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y )
     memcpy(  Y, &T, sizeof( mbedtls_mpi ) );
 }
 
+static inline mbedtls_mpi_uint mpi_sint_abs( mbedtls_mpi_sint z )
+{
+    if( z >= 0 )
+        return( z );
+    /* Take care to handle the most negative value (-2^(biL-1)) correctly.
+     * A naive -z would have undefined behavior.
+     * Write this in a way that makes popular compilers happy (GCC, Clang,
+     * MSVC). */
+    return( (mbedtls_mpi_uint) 0 - (mbedtls_mpi_uint) z );
+}
+
 /*
  * Set value from integer
  */
@@ -263,7 +274,7 @@ int mbedtls_mpi_lset( mbedtls_mpi *X, mbedtls_mpi_sint z )
     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, 1 ) );
     memset( X->p, 0, X->n * ciL );
 
-    X->p[0] = ( z < 0 ) ? -z : z;
+    X->p[0] = mpi_sint_abs( z );
     X->s    = ( z < 0 ) ? -1 : 1;
 
 cleanup:
@@ -853,7 +864,7 @@ int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z )
     mbedtls_mpi_uint p[1];
     MPI_VALIDATE_RET( X != NULL );
 
-    *p  = ( z < 0 ) ? -z : z;
+    *p  = mpi_sint_abs( z );
     Y.s = ( z < 0 ) ? -1 : 1;
     Y.n = 1;
     Y.p = p;
@@ -889,6 +900,11 @@ int mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi
         if( B->p[j - 1] != 0 )
             break;
 
+    /* Exit early to avoid undefined behavior on NULL+0 when X->n == 0
+     * and B is 0 (of any size). */
+    if( j == 0 )
+        return( 0 );
+
     MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, j ) );
 
     /* j is the number of non-zero limbs of B. Add those to X. */
@@ -1040,7 +1056,7 @@ int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint
     MPI_VALIDATE_RET( X != NULL );
     MPI_VALIDATE_RET( A != NULL );
 
-    p[0] = ( b < 0 ) ? -b : b;
+    p[0] = mpi_sint_abs( b );
     B.s = ( b < 0 ) ? -1 : 1;
     B.n = 1;
     B.p = p;
@@ -1058,7 +1074,7 @@ int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint
     MPI_VALIDATE_RET( X != NULL );
     MPI_VALIDATE_RET( A != NULL );
 
-    p[0] = ( b < 0 ) ? -b : b;
+    p[0] = mpi_sint_abs( b );
     B.s = ( b < 0 ) ? -1 : 1;
     B.n = 1;
     B.p = p;
@@ -1396,7 +1412,7 @@ int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R,
     mbedtls_mpi_uint p[1];
     MPI_VALIDATE_RET( A != NULL );
 
-    p[0] = ( b < 0 ) ? -b : b;
+    p[0] = mpi_sint_abs( b );
     B.s = ( b < 0 ) ? -1 : 1;
     B.n = 1;
     B.p = p;
diff --git a/tests/suites/test_suite_bignum.function b/tests/suites/test_suite_bignum.function
index b75f534f46..55bb2f58d2 100644
--- a/tests/suites/test_suite_bignum.function
+++ b/tests/suites/test_suite_bignum.function
@@ -1458,6 +1458,150 @@ exit:
 }
 /* END_CASE */
 
+/* BEGIN_CASE */
+void most_negative_mpi_sint( )
+{
+    /* Ad hoc tests for n = -p = -2^(biL-1) as a mbedtls_mpi_sint. We
+     * guarantee that mbedtls_mpi_sint is a two's complement type, so this
+     * is a valid value. However, negating it (`-n`) has undefined behavior
+     * (although in practice `-n` evaluates to the value n).
+     *
+     * This function has ad hoc tests for this value. It's separated from other
+     * functions because the test framework makes it hard to pass this value
+     * into test cases.
+     *
+     * In the comments here:
+     * - biL = number of bits in limbs
+     * - p = 2^(biL-1) (smallest positive value not in mbedtls_mpi_sint range)
+     * - n = -2^(biL-1) (largest negative value in mbedtls_mpi_sint range)
+     */
+
+    mbedtls_mpi A, R, X;
+    mbedtls_mpi_init( &A );
+    mbedtls_mpi_init( &R );
+    mbedtls_mpi_init( &X );
+
+    const size_t biL = 8 * sizeof( mbedtls_mpi_sint );
+    mbedtls_mpi_uint most_positive_plus_1 = (mbedtls_mpi_uint) 1 << ( biL - 1 );
+    const mbedtls_mpi_sint most_positive = most_positive_plus_1 - 1;
+    const mbedtls_mpi_sint most_negative = - most_positive - 1;
+    TEST_EQUAL( (mbedtls_mpi_uint) most_negative,
+                (mbedtls_mpi_uint) 1 << ( biL - 1 ) );
+    TEST_EQUAL( (mbedtls_mpi_uint) most_negative << 1, 0 );
+
+    /* Test mbedtls_mpi_lset() */
+    TEST_EQUAL( mbedtls_mpi_lset( &A, most_negative ), 0 );
+    TEST_EQUAL( A.s, -1 );
+    TEST_EQUAL( A.n, 1 );
+    TEST_EQUAL( A.p[0], most_positive_plus_1 );
+
+    /* Test mbedtls_mpi_cmp_int(): -p == -p */
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &A, most_negative ), 0 );
+
+    /* Test mbedtls_mpi_cmp_int(): -(p+1) < -p */
+    A.p[0] = most_positive_plus_1 + 1;
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &A, most_negative ), -1 );
+
+    /* Test mbedtls_mpi_cmp_int(): -(p-1) > -p */
+    A.p[0] = most_positive_plus_1 - 1;
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &A, most_negative ), 1 );
+
+    /* Test mbedtls_mpi_add_int(): (p-1) + (-p) */
+    TEST_EQUAL( mbedtls_mpi_lset( &A, most_positive ), 0 );
+    TEST_EQUAL( mbedtls_mpi_add_int( &X, &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &X, -1 ), 0 );
+
+    /* Test mbedtls_mpi_add_int(): (0) + (-p) */
+    TEST_EQUAL( mbedtls_mpi_lset( &A, 0 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_add_int( &X, &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &X, most_negative ), 0 );
+
+    /* Test mbedtls_mpi_add_int(): (-p) + (-p) */
+    TEST_EQUAL( mbedtls_mpi_lset( &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_add_int( &X, &A, most_negative ), 0 );
+    TEST_EQUAL( X.s, -1 );
+    TEST_EQUAL( X.n, 2 );
+    TEST_EQUAL( X.p[0], 0 );
+    TEST_EQUAL( X.p[1], 1 );
+
+    /* Test mbedtls_mpi_sub_int(): (p) - (-p) */
+    mbedtls_mpi_free( &X );
+    TEST_EQUAL( mbedtls_mpi_lset( &A, most_positive ), 0 );
+    TEST_EQUAL( mbedtls_mpi_sub_int( &X, &A, most_negative ), 0 );
+    TEST_EQUAL( X.s, 1 );
+    TEST_EQUAL( X.n, 1 );
+    TEST_EQUAL( X.p[0], ~(mbedtls_mpi_uint)0 );
+
+    /* Test mbedtls_mpi_sub_int(): (0) - (-p) */
+    TEST_EQUAL( mbedtls_mpi_lset( &A, 0 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_sub_int( &X, &A, most_negative ), 0 );
+    TEST_EQUAL( X.s, 1 );
+    TEST_EQUAL( X.n, 1 );
+    TEST_EQUAL( X.p[0], most_positive_plus_1 );
+
+    /* Test mbedtls_mpi_sub_int(): (-p) - (-p) */
+    TEST_EQUAL( mbedtls_mpi_lset( &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_sub_int( &X, &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &X, 0 ), 0 );
+
+    /* Test mbedtls_mpi_div_int(): (-p+1) / (-p) */
+    TEST_EQUAL( mbedtls_mpi_lset( &A, -most_positive ), 0 );
+    TEST_EQUAL( mbedtls_mpi_div_int( &X, &R, &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &X, 0 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &R, -most_positive ), 0 );
+
+    /* Test mbedtls_mpi_div_int(): (-p) / (-p) */
+    TEST_EQUAL( mbedtls_mpi_lset( &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_div_int( &X, &R, &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &X, 1 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &R, 0 ), 0 );
+
+    /* Test mbedtls_mpi_div_int(): (-2*p) / (-p) */
+    TEST_EQUAL( mbedtls_mpi_shift_l( &A, 1 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_div_int( &X, &R, &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &X, 2 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &R, 0 ), 0 );
+
+    /* Test mbedtls_mpi_div_int(): (-2*p+1) / (-p) */
+    TEST_EQUAL( mbedtls_mpi_add_int( &A, &A, 1 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_div_int( &X, &R, &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &X, 1 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &R, -most_positive ), 0 );
+
+    /* Test mbedtls_mpi_div_int(): (p-1) / (-p) */
+    TEST_EQUAL( mbedtls_mpi_lset( &A, most_positive ), 0 );
+    TEST_EQUAL( mbedtls_mpi_div_int( &X, &R, &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &X, 0 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &R, most_positive ), 0 );
+
+    /* Test mbedtls_mpi_div_int(): (p) / (-p) */
+    TEST_EQUAL( mbedtls_mpi_add_int( &A, &A, 1 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_div_int( &X, &R, &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &X, -1 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &R, 0 ), 0 );
+
+    /* Test mbedtls_mpi_div_int(): (2*p) / (-p) */
+    TEST_EQUAL( mbedtls_mpi_shift_l( &A, 1 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_div_int( &X, &R, &A, most_negative ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &X, -2 ), 0 );
+    TEST_EQUAL( mbedtls_mpi_cmp_int( &R, 0 ), 0 );
+
+    /* Test mbedtls_mpi_mod_int(): never valid */
+    TEST_EQUAL( mbedtls_mpi_mod_int( X.p, &A, most_negative ),
+                MBEDTLS_ERR_MPI_NEGATIVE_VALUE );
+
+    /* Test mbedtls_mpi_random(): never valid */
+    TEST_EQUAL( mbedtls_mpi_random( &X, most_negative, &A,
+                                    mbedtls_test_rnd_std_rand, NULL ),
+                MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+exit:
+    mbedtls_mpi_free( &A );
+    mbedtls_mpi_free( &R );
+    mbedtls_mpi_free( &X );
+}
+/* END_CASE */
+
 /* BEGIN_CASE depends_on:MBEDTLS_SELF_TEST */
 void mpi_selftest(  )
 {
diff --git a/tests/suites/test_suite_bignum.misc.data b/tests/suites/test_suite_bignum.misc.data
index 818f3613b0..dc6830e8fa 100644
--- a/tests/suites/test_suite_bignum.misc.data
+++ b/tests/suites/test_suite_bignum.misc.data
@@ -1958,6 +1958,9 @@ mpi_random_fail:2:"01":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
 MPI random bad arguments: min > N = 1, 0 limb in upper bound
 mpi_random_fail:2:"000000000000000001":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
 
+Most negative mbedtls_mpi_sint
+most_negative_mpi_sint:
+
 MPI Selftest
 depends_on:MBEDTLS_SELF_TEST
 mpi_selftest: