diff --git a/library/bignum.c b/library/bignum.c
index 5b9c8cb..62cc98d 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -1583,7 +1583,17 @@
     for( ; j > 0; j-- )
         mpi_mul_hlp( i, A->p, X->p + j - 1, B->p[j - 1] );
 
-    X->s = A->s * B->s;
+    /* If the result is 0, we don't shortcut the operation, which reduces
+     * but does not eliminate side channels leaking the zero-ness. We do
+     * need to take care to set the sign bit properly since the library does
+     * not fully support an MPI object with a value of 0 and s == -1. */
+    if( ( i == 0 && ( A->n == 0 || A->p[0] == 0 ) ) ||
+        ( j == 0 && ( B->n == 0 || B->p[0] == 0 ) ) )
+    {
+        X->s = 1;
+    }
+    else
+        X->s = A->s * B->s;
 
 cleanup: