diff --git a/library/bignum.c b/library/bignum.c
index bbadd01..9544dc9 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -34,6 +34,7 @@
 #include "polarssl/bignum.h"
 #include "polarssl/bn_mul.h"
 
+#include <limits.h>
 #include <stdlib.h>
 
 /* Implementation that should never be optimized out by the compiler */
@@ -47,9 +48,10 @@
 
 /*
  * Convert between bits/chars and number of limbs
+ * Divide first in order to avoid potential overflows
  */
-#define BITS_TO_LIMBS(i)  (((i) + biL - 1) / biL)
-#define CHARS_TO_LIMBS(i) (((i) + ciL - 1) / ciL)
+#define BITS_TO_LIMBS(i)  ( (i) / biL + ( (i) % biL != 0 ) )
+#define CHARS_TO_LIMBS(i) ( (i) / ciL + ( (i) % ciL != 0 ) )
 
 /*
  * Initialize one MPI
@@ -287,6 +289,9 @@
 
     if( radix == 16 )
     {
+        if( slen > SIZE_T_MAX >> 2 )
+            return( POLARSSL_ERR_MPI_BAD_INPUT_DATA );
+
         n = BITS_TO_LIMBS( slen << 2 );
 
         MPI_CHK( mpi_grow( X, n ) );