diff --git a/ChangeLog b/ChangeLog
index 43e9f0ea8..33af03073 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -7,6 +7,8 @@ Bugfix
      when MBEDTLS_ECP_ALT is defined. Reported by jwhui. Fixes #2242.
    * Run the AD too long test only if MBEDTLS_CCM_ALT is not defined.
      Raised as a comment in #1996.
+   * Reduce the stack consumption of mbedtls_mpi_fill_random() which could
+     previously lead to a stack overflow on constrained targets.
 
 = mbed TLS 2.16.0 branch released 2018-12-21
 
diff --git a/library/bignum.c b/library/bignum.c
index f968a0ad7..d3d02b1a0 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -715,14 +715,101 @@ cleanup:
 }
 #endif /* MBEDTLS_FS_IO */
 
+
+/* Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint
+ * into the storage form used by mbedtls_mpi. */
+
+static mbedtls_mpi_uint mpi_uint_bigendian_to_host_c( mbedtls_mpi_uint x )
+{
+    uint8_t i;
+    mbedtls_mpi_uint tmp = 0;
+    /* This works regardless of the endianness. */
+    for( i = 0; i < ciL; i++, x >>= 8 )
+        tmp |= ( x & 0xFF ) << ( ( ciL - 1 - i ) << 3 );
+    return( tmp );
+}
+
+static mbedtls_mpi_uint mpi_uint_bigendian_to_host( mbedtls_mpi_uint x )
+{
+#if defined(__BYTE_ORDER__)
+
+/* Nothing to do on bigendian systems. */
+#if ( __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ )
+    return( x );
+#endif /* __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ */
+
+#if ( __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ )
+
+/* For GCC and Clang, have builtins for byte swapping. */
+#if defined(__GNUC__) && defined(__GNUC_PREREQ)
+#if __GNUC_PREREQ(4,3)
+#define have_bswap
+#endif
+#endif
+
+#if defined(__clang__) && defined(__has_builtin)
+#if __has_builtin(__builtin_bswap32)  &&                 \
+    __has_builtin(__builtin_bswap64)
+#define have_bswap
+#endif
+#endif
+
+#if defined(have_bswap)
+    /* The compiler is hopefully able to statically evaluate this! */
+    switch( sizeof(mbedtls_mpi_uint) )
+    {
+        case 4:
+            return( __builtin_bswap32(x) );
+        case 8:
+            return( __builtin_bswap64(x) );
+    }
+#endif
+#endif /* __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__ */
+#endif /* __BYTE_ORDER__ */
+
+    /* Fall back to C-based reordering if we don't know the byte order
+     * or we couldn't use a compiler-specific builtin. */
+    return( mpi_uint_bigendian_to_host_c( x ) );
+}
+
+static void mpi_bigendian_to_host( mbedtls_mpi_uint * const p, size_t limbs )
+{
+    mbedtls_mpi_uint *cur_limb_left;
+    mbedtls_mpi_uint *cur_limb_right;
+    if( limbs == 0 )
+        return;
+
+    /*
+     * Traverse limbs and
+     * - adapt byte-order in each limb
+     * - swap the limbs themselves.
+     * For that, simultaneously traverse the limbs from left to right
+     * and from right to left, as long as the left index is not bigger
+     * than the right index (it's not a problem if limbs is odd and the
+     * indices coincide in the last iteration).
+     */
+    for( cur_limb_left = p, cur_limb_right = p + ( limbs - 1 );
+         cur_limb_left <= cur_limb_right;
+         cur_limb_left++, cur_limb_right-- )
+    {
+        mbedtls_mpi_uint tmp;
+        /* Note that if cur_limb_left == cur_limb_right,
+         * this code effectively swaps the bytes only once. */
+        tmp             = mpi_uint_bigendian_to_host( *cur_limb_left  );
+        *cur_limb_left  = mpi_uint_bigendian_to_host( *cur_limb_right );
+        *cur_limb_right = tmp;
+    }
+}
+
 /*
  * Import X from unsigned binary data, big endian
  */
 int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t buflen )
 {
     int ret;
-    size_t i, j;
-    size_t const limbs = CHARS_TO_LIMBS( buflen );
+    size_t const limbs    = CHARS_TO_LIMBS( buflen );
+    size_t const overhead = ( limbs * ciL ) - buflen;
+    unsigned char *Xp;
 
     MPI_VALIDATE_RET( X != NULL );
     MPI_VALIDATE_RET( buflen == 0 || buf != NULL );
@@ -734,11 +821,17 @@ int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf, size_t bu
         mbedtls_mpi_init( X );
         MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
     }
-
     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
 
-    for( i = buflen, j = 0; i > 0; i--, j++ )
-        X->p[j / ciL] |= ((mbedtls_mpi_uint) buf[i - 1]) << ((j % ciL) << 3);
+    /* Avoid calling `memcpy` with NULL source argument,
+     * even if buflen is 0. */
+    if( buf != NULL )
+    {
+        Xp = (unsigned char*) X->p;
+        memcpy( Xp + overhead, buf, buflen );
+
+        mpi_bigendian_to_host( X->p, limbs );
+    }
 
 cleanup:
 
@@ -2008,18 +2101,28 @@ int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
                      void *p_rng )
 {
     int ret;
-    unsigned char buf[MBEDTLS_MPI_MAX_SIZE];
+    size_t const limbs = CHARS_TO_LIMBS( size );
+    size_t const overhead = ( limbs * ciL ) - size;
+    unsigned char *Xp;
+
     MPI_VALIDATE_RET( X     != NULL );
     MPI_VALIDATE_RET( f_rng != NULL );
 
-    if( size > MBEDTLS_MPI_MAX_SIZE )
-        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+    /* Ensure that target MPI has exactly the necessary number of limbs */
+    if( X->n != limbs )
+    {
+        mbedtls_mpi_free( X );
+        mbedtls_mpi_init( X );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_grow( X, limbs ) );
+    }
+    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( X, 0 ) );
 
-    MBEDTLS_MPI_CHK( f_rng( p_rng, buf, size ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( X, buf, size ) );
+    Xp = (unsigned char*) X->p;
+    f_rng( p_rng, Xp + overhead, size );
+
+    mpi_bigendian_to_host( X->p, limbs );
 
 cleanup:
-    mbedtls_platform_zeroize( buf, sizeof( buf ) );
     return( ret );
 }