diff --git a/src/gf2m.h b/src/gf2m.h
index a3af554..5406aa6 100644
--- a/src/gf2m.h
+++ b/src/gf2m.h
@@ -61,6 +61,18 @@ public:
 		return antilog[ (n - 1 - log[a]) % (n - 1)];
 	}
 
+	inline uint inv_square (uint a) {
+		if (!a) return 0;
+		return antilog[ (2 * (n - 1 - log[a]) )
+		                % (n - 1)];
+	}
+
+	inline uint div (uint a, uint b) {
+		if (! (a && b) ) return 0;
+		return antilog[ (n - 1 - log[b] + log[a])
+		                % (n - 1)];
+	}
+
 	inline uint sq_root (uint a) {
 		if (!a) return 0;
 		uint t = log[a];
diff --git a/src/mce_qd.cpp b/src/mce_qd.cpp
index 029669d..0fa56d1 100644
--- a/src/mce_qd.cpp
+++ b/src/mce_qd.cpp
@@ -411,8 +411,8 @@ int privkey::decrypt (const bvector & in, bvector & out, bvector & errors)
 	synd.clear();
 	synd.resize (h_size, 0);
 	for (i = 0; i < cipher_size(); ++i) if (in[i]) {
-			tmp = fld.inv (g.eval (permuted_support[i], fld) );
-			tmp = fld.mult (tmp, tmp); //g(Li)^{-2}
+			tmp = fld.inv_square //g(Li)^{-2}
+			      (g.eval (permuted_support[i], fld) );
 			synd[0] = fld.add (synd[0], tmp);
 			for (j = 1; j < h_size; ++j) {
 				tmp = fld.mult (tmp, permuted_support[i]);
diff --git a/src/polynomial.cpp b/src/polynomial.cpp
index 12df833..dedf38c 100644
--- a/src/polynomial.cpp
+++ b/src/polynomial.cpp
@@ -378,7 +378,7 @@ void polynomial::ext_euclid (polynomial&a_out, polynomial&b_out,
 		A.swap (a);
 		B.swap (b);
 		while ( (j = A.degree() - a.degree() ) >= 0) {
-			h = fld.mult (A.head(), fld.inv (a.head() ) );
+			h = fld.div (A.head(), a.head() );
 			tmp = a;
 			tmp.shift (j);
 			A.add_mult (tmp, h, fld);